Managing Supply Chain Risk and Vulnerability: Tools

Managing Supply Chain Risk and Vulnerability
Teresa Wu Jennifer Blackhurst
Editors
Managing Supply Chain Risk
and Vulnerability
Tools and Methods
for Supply Chain Decision Makers
123
Editors
Assoc. Prof. Teresa Wu
Department of Industrial Engineering
Ira A. Fulton School of Engineering
Arizona State University
P.O. Box 875906
Tempe, AZ 85287-5906
USA
teresa.wu@asu.edu
Assoc. Prof. Jennifer Blackhurst
Department of Logistics, Operations
and Management Information Studies
College of Business
Iowa State University
Ames, IA 50011
USA
jvblackh@iastate.edu
ISBN 978-1-84882-633-5
e-ISBN 978-1-84882-634-2
DOI 10.1007/978-1-84882-634-2
Springer Dordrecht Heidelberg London New York
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Contents
1
Book Introduction : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : :
Jennifer Blackhurst, Teresa Wu
References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
1
5
Section I Understanding and Assessing Risk in the Supply Chain
2
3
Effective Management of Supply Chains: Risks and Performance : : :
Bob Ritchie, Clare Brindley
2.1
Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
2.2
Supply Chain Risk . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
2.2.1
Risk and Uncertainty . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
2.2.2
Risk and Outcomes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
2.3
Supply Chain Risk Management . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
2.4
Performance . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
2.4.1
Performance Criteria . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
2.4.2
Risk and Performance – Timeframe . . . . . . . . . . . . . . . . . .
2.5
Performance and Risk Metrics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
2.6
Risk-Performance: Sources, Profiles and Drivers . . . . . . . . . . . . . . .
2.7
Risk Management Responses . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
2.8
Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Managing Supply Chain Disruptions
via Time-Based Risk Management : : : : : : : : : : : : : : : : : : : : : : : : : : : : : :
ManMohan S. Sodhi, Christopher S. Tang
3.1
Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
3.2
Background . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
3.3
Time-Based Risk Management . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
3.3.1
Response Time and Impact . . . . . . . . . . . . . . . . . . . . . . . . .
3.3.2
Modeling Disruption Impact over Time . . . . . . . . . . . . . . .
3.3.3
Time-Based Risk Management in Practice . . . . . . . . . . . . .
9
9
10
10
12
16
17
18
19
20
22
24
26
26
29
29
30
31
32
33
35
v
vi
Contents
3.4
Risk and Reward Considerations . . . . . . . . . . . . . . . . . . . . . . . . . . . . 37
3.5
Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 38
References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 39
4
5
Prioritization of Risks in Supply Chains : : : : : : : : : : : : : : : : : : : : : : : : :
Mohd. Nishat Faisal
4.1
Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
4.2
Literature Review . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
4.2.1
Risk . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
4.2.2
Supply Chain Risk Management . . . . . . . . . . . . . . . . . . . . .
4.2.3
Supply Chain Risk Mitigation Strategies . . . . . . . . . . . . . .
4.3
Supply Chain Risks Taxonomy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
4.3.1
Risks in Physical Sub-Chain . . . . . . . . . . . . . . . . . . . . . . . .
4.3.2
Risks in Financial Sub-Chain . . . . . . . . . . . . . . . . . . . . . . . .
4.3.3
Risks in Relational Sub-Chain . . . . . . . . . . . . . . . . . . . . . . .
4.3.4
Risks in Informational Sub-Chain . . . . . . . . . . . . . . . . . . . .
4.4
Methodology . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
4.4.1
A Numerical Application . . . . . . . . . . . . . . . . . . . . . . . . . .
4.5
Concluding Remarks . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
A Generalized Simulation Framework
for Responsive Supply Network Management : : : : : : : : : : : : : : : : : : : :
Jin Dong, Wei Wang, Teresa Wu
5.1
Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
5.2
Review of Supply Chain Simulation . . . . . . . . . . . . . . . . . . . . . . . . . .
5.3
GBSE: A Supply Chain Simulation Environment . . . . . . . . . . . . . .
5.3.1
GBSE Architecture . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
5.3.2
GBSE for Supply Chain Simulation . . . . . . . . . . . . . . . . . .
5.4
Experiments . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
5.4.1
Notation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
5.4.2
Scenario I: Impact of Demand Forecast Accuracy . . . . . . .
5.4.3
Scenario II: Impact of Supplier Selection . . . . . . . . . . . . . .
5.4.4
Scenario III: Impact of Different Transportation Mode . . .
5.4.5
Scenario IV: Impact of Quality Uncertainty . . . . . . . . . . . .
5.5
Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
41
41
43
43
44
45
46
47
49
49
51
52
56
61
63
67
67
68
70
71
73
78
80
81
83
83
85
87
87
Section II Decision Making and Risk Mitigation in the Supply Chain
6
Modeling of Supply Chain Risk Under Disruptions
with Performance Measurement and Robustness Analysis : : : : : : : : : : 91
Qiang Qiang, Anna Nagurney, June Dong
6.1
Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 91
6.2
The Supply Chain Model with Disruption Risks
and Random Demands . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 94
Contents
vii
6.2.1
The Behavior of the Manufacturers . . . . . . . . . . . . . . . . . . . 97
6.2.2
The Behavior of the Retailers . . . . . . . . . . . . . . . . . . . . . . . 98
6.2.3
The Market Equilibrium Conditions . . . . . . . . . . . . . . . . . . 100
6.2.4
The Equilibrium Conditions of the Supply Chain . . . . . . . 101
6.3
A Weighted Supply Chain Performance Measure . . . . . . . . . . . . . . . 103
6.3.1
A Supply Chain Network Performance Measure . . . . . . . . 103
6.3.2
Supply Chain Robustness Measurement . . . . . . . . . . . . . . . 104
6.4
Examples . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 105
6.5
Summary and Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 109
References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 109
7
The Effects of Network Relationships
on Global Supply Chain Vulnerability : : : : : : : : : : : : : : : : : : : : : : : : : : : 113
Jose M. Cruz
7.1
Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 113
7.2
The Global Supply Chain Networks Model . . . . . . . . . . . . . . . . . . . . 115
7.2.1
The Behavior of the Manufacturers . . . . . . . . . . . . . . . . . . . 120
7.2.2
The Multicriteria Decision-Making Problem
Faced by a Manufacturer . . . . . . . . . . . . . . . . . . . . . . . . . . . 121
7.2.3
The Optimality Conditions of Manufacturers . . . . . . . . . . . 122
7.2.4
The Behavior of the Retailers . . . . . . . . . . . . . . . . . . . . . . . 122
7.2.5
A Retailer’s Multicriteria Decision-Making Problem . . . . 123
7.2.6
The Optimality Conditions of Retailers . . . . . . . . . . . . . . . 124
7.2.7
The Consumers at the Demand Markets . . . . . . . . . . . . . . . 125
7.2.8
The Equilibrium Conditions of the Network . . . . . . . . . . . 126
7.2.9
Remark . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 129
7.3
The Supply Chain Network Efficiency
and Vulnerability Measures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 129
7.4
Numerical Examples . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 131
7.5
Managerial Implications . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 137
7.6
Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 138
References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 138
8
A Stochastic Model for Supply Chain Risk Management
Using Conditional Value at Risk : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : 141
Mark Goh, Fanwen Meng
8.1
Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 141
8.2
A Stochastic Model with Conditional Value at Risk . . . . . . . . . . . . . 143
8.3
Sample Average Approximation Program . . . . . . . . . . . . . . . . . . . . . 146
8.4
An Illustration of the Stochastic Model . . . . . . . . . . . . . . . . . . . . . . . 149
8.5
A Wine Supply Chain Problem . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 151
8.6
Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 155
References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 156
viii
9
Contents
Risk Intermediation in Supply Chains : : : : : : : : : : : : : : : : : : : : : : : : : : : 159
Ying-Ju Chen, Sridhar Seshadri
9.1
Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 159
9.1.1
Relevant Literature . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 164
9.2
Model, Assumptions, and Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . 165
9.2.1
A Single Retailer . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 166
9.3
Multiple Contracts . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 172
9.4
Risk Aversion and Channel Structure . . . . . . . . . . . . . . . . . . . . . . . . . 174
9.5
Continuous Formulation and the Optimality of the Menu . . . . . . . . 177
9.5.1
Continuous Type Space . . . . . . . . . . . . . . . . . . . . . . . . . . . . 178
9.5.2
Optimal Contract Menu in the Continuous Case . . . . . . . . 178
9.6
Future Research and Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 182
References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 184
10 Forecasting and Risk Analysis in Supply Chain Management:
GARCH Proof of Concept : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : 187
Shoumen Datta, Don P. Graham, Nikhil Sagar, Pat Doody,
Reuben Slone, Olli-Pekka Hilmola
10.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 187
10.2 Supply Chain Management and Demand Amplification . . . . . . . . . 188
10.3 Beer Game and Role of Advanced Forecasting Methods . . . . . . . . . 191
10.4 Advanced Statistical Models . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 194
10.5 Temporary Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 200
References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 201
11 Supply Chain Risk Management: Annotation of Knowledge
Using a Semi-Structured Knowledge Model : : : : : : : : : : : : : : : : : : : : : : 205
Chun-Che Huang, Tzu-Liang (Bill) Tseng
11.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 205
11.2 The Generation and Representation
of Semi-Structured Knowledge . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 208
11.2.1 The Generation of Semi-Structured Knowledge . . . . . . . . 208
11.2.2 Semi-Structured Knowledge Representation . . . . . . . . . . . 211
11.3 Annotation Framework for Supply Chain Risk Management
Knowledge . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 216
11.4 Interaction of Annotated SCRM Knowledge Documents
with the Benchmark Ontology . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 223
11.4.1 Extracting and Mapping . . . . . . . . . . . . . . . . . . . . . . . . . . . . 223
11.4.2 Interaction Between SSK and the Benchmark Ontology . 226
11.5 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 230
References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 231
List of Contributors
Jennifer Blackhurst
Department of Logistics, Operations and MIS College of Business, Iowa State
University, Ames, IA 50011, USA
Clare Brindley
Nottingham Business School, Nottingham Trent University, UK,
e-mail: clare.brindley@ntu.ac.uk
Ying-Ju Chen
University of California, Berkeley and University of Texas, Austin
Jose M. Cruz
Department of Operations and Information Management, School of Business,
University of Connecticut, Storrs, CT 06269, e-mail: jcruz@business.uconn.edu
Shoumen Datta
Engineering Systems Division, Department of Civil and Environmental Engineering, MIT Forum for Supply Chain Innovation, School of Engineering,
Massachusetts Institute of Technology, 77 Massachusetts Avenue,
Cambridge MA 02139
Jin Dong
IBM China Research Lab, Zhongguancun Software Park, Beijing 100193,
P.R. China
June Dong
Department of Marketing and Management, School of Business, State University
of New York at Oswego, Oswego, New York, 13126
ix
x
List of Contributors
Pat Doody
Department of Mathematics and Computing, Centre for Innovation in Distributed
Systems, Institute of Technology Tralee, County Kerry, Ireland
Mohd. Nishat Faisal
Institute of Management Technology Dubai, P.O. Box 345006, Dubai International
Academic City, Dubai, United Arab Emirates, e-mail: nishat786@yahoo.com
Mark Goh
NUS Business School, The Logistics Institute – Asia Pacific, National University of Singapore, 7 Engineering Drive 1, Singapore 117543, Singapore,
e-mail: mark_goh@nus.edu.sg
Don P. Graham
INNOVEX LLC
Olli-Pekka Hilmola
Lappeenranta University of Technology, Kouvola Research Unit, Prikaatintie 9,
FIN-45100 Kouvola, Finland
Chun-Che Huang
Department of Information Management, National Chi Nan University, No. 1,
University Road, Pu-Li, Na-Tau, 545, Taiwan, R. O. C.
Fanwen Meng
NUS Business School, The Logistics Institute – Asia Pacific, National University of Singapore, 7 Engineering Drive 1, Singapore 117543, Singapore,
e-mail: tlimf@nus.edu.sg
Anna Nagurney
Department of Finance and Operations Management, Isenberg School of Management, University of Massachusetts, Amherst, Massachusetts 01003
Qiang Qiang
Department of Finance and Operations Management, Isenberg School of Management, University of Massachusetts, Amherst, Massachusetts 01003
Bob Ritchie
Lancashire Business School, University of Central Lancashire,
e-mail: rritchie@uclan.ac.uk
List of Contributors
xi
Nikhil Sagar
Retail Inventory Management, OfficeMax Inc, 263 Shuman Boulevard, Naperville,
IL 60563
Sridhar Seshadri
University of California, Berkeley and University of Texas, Austin
Reuben Slone
OfficeMax Inc, 263 Shuman Boulevard, Naperville, IL 60563
ManMohan S. Sodhi
Cass Business School, City University of London, e-mail: m.sodhi@city.ac.uk
Christopher S. Tang
UCLA Anderson School, e-mail: ctang@anderson.ucla.edu
Tzu-Liang (Bill) Tseng
Department of Industrial Engineering, University of Texas at El Paso, 500 W.
University Ave., El Paso, TX 79968, USA
Wei Wang
IBM China Research Lab, Zhongguancun Software Park, Beijing 100193,
P.R. China
Teresa Wu
Department of Industrial Engineering, College of Engineering, Arizona State
University, Tempe, AZ 85287, USA
Chapter 1
Book Introduction
Jennifer Blackhurst and Teresa Wu
A supply chain is a network of entities such as manufacturer, suppliers and distributors working together to transform goods from raw material to final product while
moving them to the end customer. Effective supply chain management is a critical
component of a firm’s ability to fill consumer demand, regardless of the industry.
Supply chain performance may be decreased by disruptive events occurring in the
supply chain system. Supply chain disruptions are “unplanned events that may occur in the supply chain which might affect the normal or expected flow of materials
and components” (Svensson, 2000).
Managing the risk of these events occurring in the supply chain has become
known as supply chain risk management (SCRM) and may be defined as “the management of supply chain risks through coordination or collaboration among the supply chain partners so as to ensure profitability and continuity” (Tang, 2006). SCRM
has recently raised the attention of both academics and practitioners and is the focus
of this book.
One needs only to check the daily news to hear about disruptive events affecting
supply chain performance. Some of the better known examples include the 2002
longshoreman union strike at a U.S. West Coast port and affected supply chain performance for up to 6 months for some firms (Cavinato, 2004) or the 2000 lightning
bolt at a Philips semiconductor plant in New Mexico which resulted in a small fire,
destroying millions of chips and ultimately their customers Nokia and Ericsson (Latour, 2001).
Because a supply chain disruption can potentially be so harmful and costly, there
has been a recent surge in interest and publications in the area of SCRM – from
academics and practitioners alike – regarding supply chain disruptions and related
issues. The purpose of this book will be to present tools and techniques for decision
making related to supply chain risk.
In general, a supply risk management process consists of four components:
(1) Risk identification; (2) Risk assessment; (3) Risk management decisions and
implementation; and (4) Risk monitoring (Hallikas et al., 2004). In the risk identification step, risks facing the firm’s supply chain are identified. Exemplary reT. Wu, J. Blackhurst (eds.), Managing Supply Chain Risk and Vulnerability
© Springer 2009
1
2
J. Blackhurst, T. Wu
search in this step may be found in Chopra and Sodhi (2004) where general risks
in the supply chain are categorized and discussed. The risk assessment step involves understanding the impact of risks facing the supply chain. Examples of
previous risk assessment work includes that by Zsidisin et al. (2004) and Hallikas et al. (2004). Assessing risk is a complicated step and can help a firm to
prioritize which risks will affect the vulnerability of a supply chain. Risk management decision making requires supply chain managers to decide which mitigation strategies should be employed and where scarce resources may be allocated.
Certainly, these are by no means easy decisions with many aspects and factors
affecting these decisions. Finally, risk monitoring includes monitoring risks over
time.
In this book, the chapters presents tools and methods to assist supply chain managers and researchers alike in the tasks of risk impact and assessment and decision
making in the supply chain considering risk. We feel these areas are the most difficult steps of the supply chain risk management process. Therefore, the book is
divided into two main sections:
1. Understanding and Assessing Risk in the Supply Chain
2. Decision Making and Risk Mitigation in the Supply Chain
These sections consist of 10 chapters from world class researchers from around the
world and employ a variety of methods to address timely issues in SCRM. The
methods include industry-based cases and illustrative example, fuzzy logic and analytical hierarchy process (AHP), simulation, stochastic models and knowledge management protocols. The use of this broad array of methods strengthens the contribution of this book as a whole and provides a wide range of tools and techniques for
both researchers and academics alike. The method employed is chosen because it
best fits the problem or issue being addressed.
The two sections are described as follows:
Section I: Understanding and Assessing Risk in the Supply Chain.
This section presents four insightful chapters relating to developing an overall
understanding of risk and its relationship to supply chain performance, investigating the relationship between response time and disruption impact, assessing and
prioritizing risks, and assessing supply chain resilience.
In Chap. 2, “Effective Management of Supply Chains: Risk and Performance” by
Bob Ritchie and Clare Brindley the authors present an overview of SCRM and its
importance to managing overall business performance. The chapter seeks to better
understand the relationship between risk and performance by exploring sources,
drivers, consequences, and management responses. The chapter culminates with
guidelines for selecting appropriate strategies for particular drivers to maximize supply chain performance. This chapter gives the reader a high level understanding of
SCRM.
The next chapter provides a more detailed level of granularity in understanding
risk in supply chains. In Chap. 3, “Managing Supply Chain Disruptions via Time-
1 Book Introduction
3
Based Risk Management” by ManMohan S. Sodhi and Christopher S. Tang a time
based risk mitigation concept is developed. The promise of such a concept is to
reduce the impact of rare but disruptive supply chain risk events. The authors discuss
the concept that if a firm can shorten response time, the impact if the disruption is
also reduced.
In Chap. 4, “Prioritization of Risks in Supply Chains of Small and Medium Enterprise (SMEs) Clusters Using Fuzzy-AHP Approach” by Mohd Nishat Faisal. The
chapter focuses on supply chain failures for small to medium enterprises who may
have limited resources and lack of adequate risk planning tools. The chapter introduces a Fuzzy-AHP based framework to prioritize supply chain risk. Such an
approach shows promise to help firms develop strategies for managing risks in accordance with their importance.
Finally, a simulation framework is presented to better understand supply chain
resiliency. In Chap. 5, “A Generalized Simulation Framework for Responsive Supply Network Management” by Jin Dong, Wei Wang and Teresa Wu a simulation
tool is developed to assess the resilience of a supply network to a disruption. The
chapter was created with the assistance of the IBM China Research Lab.
Section II: Decision Making and Risk Mitigation in the Supply Chain.
The first section has helped the reader to better understand and assess risk in the
supply chain. From a managerial persepctive, now that supply chain risks are better
understood, tools and methods are needed to assist in decision making. This section
presents six chapters with tools and methods for assisting with decision making and
risk mitigation in the supply chain. The chapters reflect the dizzying array of factors
that need to be considered in supply chain risk decision making including supplyside and demand-side risk as well as risk attitude; contracts in the supply chain;
the impact of forecasting, supply chain structure and operational policies; logistics
factors and uncertainty; the impact and effect of relationships in the supply chain;
and supply chain knowledge considerations. Each chapter presents a novel approach
to decision making and considers certain factors.
In this section the first three chapters (6–8) investigate uncertainty and risk in
a supply chain from a network perspective. Stochastic programming is a popular
and powerful tool for evaluating supply chain design. Chaps. 6, 7 and 8 use this
approach.
First, a network model is developed with various risks on the supply and demand
side. In Chap. 6, “Modeling of Supply Chain Risk Under Disruptions with Performance Measurement and Robustness Analysis” by Qiang Qiang, Anna Nagurney
and June Dong develops a multi-tier supply chain network game-theoretic model
which considers, both supply-side and demand-side risks as well as uncertainty
in costs such as transportation. Additionally, attitude toward risk is incorporated
and a weighted supply chain performance and robustness measure is developed.
This chapter is quite unique in that both supply and demand side risks are considered.
4
J. Blackhurst, T. Wu
Relationships between the nodes in a supply chain are studied in the next chapter.
In Chap. 7, “The Effects of Network Relationships on Global Supply Chain Vulnerability” by Jose M. Cruz different levels of a relationship are assumed to influence
costs and risks for supply chain decision makers. A game theoretic model is developed to study different relationships among the supply chain players and how that
is associated with supply chain vulnerability.
Next, the stochastic programming method is extended by adding conditional
value at risk to achieve optimality. In Chap. 8, “A Stochastic Model for Supply
Chain Risk Management Using Conditional Value at Risk” by Mark Goh and Fanwen Meng a stochastic programming formulation is developed using a measure
termed the conditional value at risk. The focus of the chapter is on logistics-focused
problem decision making where uncertainty exists.
The next two chapters in the book recognize that risks and mitigation efforts in
supply chains may be much more specific in nature.
In Chap. 9, “Risk Intermediation in Supply Chains” by Sridhar Seshadri and
Ying Ju Chen also explore supply chain decision making under uncertainty from the
perspective of the seller distributor in the context of contract design. The chapter
presents two models which can be used to create contracts where the individual
retailer has different degrees of risk aversion.
In Chap. 10, “Forecasting and Risk Analysis in Supply Chain Management:
Garch Proof of Concept” by Shoumen Datta, Don P. Graham, Nikhil Sagar, Pat
Doody, Reuben Sloan and Olli-Pekka Hilmola advanced forecasting tools are explored to decision making in supply chain scenarios. In particular, the impact on
demand amplification is investigated. Results of the chapter indicate that these advanced forecasting methods may be useful but supply chain structure and operations
policies as well as data availability must be considered.
We conclude the book with a general framework which presents a method for
knowledge representation in a supply chain risk context. In Chap. 11, “Supply Chain
Risk Management: Annotation of Knowledge Using Semi-Structured Knowledge
Model” by Chun-Che Huang and Bill Tseng develops a semi-structured knowledge
model which is used to represent knowledge in the supply chain. Such a model may
be used to assist in decision making related to supply chain risk.
Our goal in developing the book was to solicit contributions from top SCRM
researchers around the world to develop a text that both practitioners and students
can use to better understand and manage supply chain risk. We are delighted with
the insightful contributions that now form this book. We look forward to the book
helping to spur and contribute to interesting and insightful research as well as developing tools and methods to help supply chain managers effectively manage and
mitigate risk in today’s complex global supply chains.
We wish to thank each of our contributors as well as the editorial team at Springer
for the opportunity to edit this interesting and insightful book.
1 Book Introduction
5
References
Cavinato, J.L. (2004), “Supply chain logistics risk”, International Journal of Physical Distribution & Logistics Management, Vol. 34 No. 5, pp. 383–387
Chopra, S. and Sodhi, M. (2004), “Managing risk to avoid supply-chain breakdown”, MIT Sloan
Management Review, Vol. 46 No. 1, pp. 53–61
Hallikas, J., Karvonen, I., Pulkkinen, U., Virolainen, V.-M. and Tuominen, M. (2004), “Risk
management processes in supplier networks”, International Journal of Production Economics,
Vol. 90, pp. 47–58
Latour, A. (2001), “Trial by fire: A blaze in Albuquerque sets off major crisis for cell-phone giants –
Nokia handles supply shock with aplomb as Ericsson of Sweden gets burned – Was SISU the
difference?”, Wall Street Journal, January 29, A1
Svensson, G. (2000), “A conceptual framework for the analysis of vulnerability in supply chains”,
International Journal of Physical Distribution & Logistics Management, Vol. 30 No. 9,
pp. 731–749
Tang, C. (2006), “Perspectives in supply chain risk management”, International Journal of Production Economics, Vol. 103, pp. 451–488
Zsidisin, G., Ellram, L., Carter, J., and Cavinato, J. (2004), “An analysis of supply chain assessment
techniques”, International Journal of Physical Distribution & Logistics Management, Vol. 34
No. 5, pp. 397–413
Section I
Understanding and Assessing Risk
in the Supply Chain
Chapter 2
Effective Management of Supply Chains:
Risks and Performance
Bob Ritchie and Clare Brindley
2.1 Introduction
A significant feature of the rapidly evolving business climate spurred on by significant technology shifts, innovation, communication technologies and globalization,
is the increasing prevalence of risk in almost every aspect of our lives. Whether
real or imagined, we perceive greater exposure, increased likelihood and more severe consequences of already known risks whilst becoming aware of other risks
previously unknown. FM Global (2007) concluded from their study of the views of
500 financial executives in Europe and America that most anticipated an increase
in overall business risks in the foreseeable future. The top three risk areas featured
global competition, supply chains and property-related risks. Individual organizations are continuously receiving information inputs identifying new risk sources,
enhanced exposure to existing risks and escalating costs associated with compensation should such risks materialize. The emergence of risk management is an important response to such developments providing a contribution to most fields of
management decision and control (e. g. Smallman, 1996; Giannakis et al., 2004).
Supply Chain Risk Management (SCRM) represents the risk management response
primarily to supply chain risks, although as will be seen later in the chapter, it has
a much wider influence at the strategic enterprise risk level.
As the range, intensity and pace of developments in the ‘risk management’ field
accelerates and organizations seek to mitigate their risk exposure, questions are being raised concerning the cost-effectiveness of risk management. Engagement in the
processes and practices of risk management involves the commitment of resources
and expenditure. The question posed is what is the impact of risk management on
the performance of the organization? Against the explicit and implicit costs incurred
by the organization is the need to match the impact on different performance criteria
(e. g. profitability; security of supply; enhanced risk preparedness). In essence, what
evidence is available to justify the SCRM investment in terms of benefits to corporate performance? The emerging field of Supply Chain Management is an appropri-
T. Wu, J. Blackhurst (eds.), Managing Supply Chain Risk and Vulnerability
© Springer 2009
9
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B. Ritchie, C. Brindley
ate field to evaluate such issues, since it has the capacity to demonstrate a diversity
of risks together with risk management responses as well as producing an impact
across most dimensions of an enterprise’s performance. Brindley (2004) identifies
global competition, technological change and the continuous search for competitive
advantage as the primary motives behind organizations turning towards risk management approaches, emphasizing that the supply chains simultaneously represent
the most important solution to such challenges whilst generating the most significant sources of risk. This view is re-affirmed by Christopher and Lee (2004) who
recognize the increasing risk in organizational supply chains and identify the need
for new responses to manage these.
The chapter is designed to explore the nature of the interaction between risk
and performance, and on the basis of this improved knowledge and understanding
to assess more effectively how the engagement in supply chain risk management
strategies and activities might impact on corporate performance. The primary constructs of performance and risk are examined and the key linkages are identified,
adopting an approach that addresses the perspectives of both researchers and practitioners and aiming to generate new and wider perspectives. The earlier sections
review the significant developments in conceptual and empirical work, primarily in
the fields of supply chain management, SCRM and corporate performance. These
are not claimed to be exhaustive in relation to their particular field but rather sufficient to facilitate the linkages across all three fields. The nature and incidence of
risk in the supply chain is explored in terms of risk and performance – the sources,
drivers, consequences and management responses. The mutual interdependence of
risk management and performance management are examined employing the context of the supply chain. The product of this development is the production of guidelines for practitioners and researchers which will support the generation of appropriate strategies to address particular risk drivers and the effective management of
the risk management – performance interaction to maximize the benefits of SCRM.
2.2 Supply Chain Risk
2.2.1 Risk and Uncertainty
Agreeing a definition for the term risk has proved challenging for academics and
practitioners alike for over a century, leading to the conclusion that there are probably as many definitions as writers on the theme (Ritchie and Marshall, 1992). The
reason for this variety of definitions reflects different academic and professional disciplines and variations in the specific settings, decision contexts and problems being
addressed. Sitkin and Pablo (1992, p. 9) reflect this in their generalized definition
of risk as being ‘the extent to which there is uncertainty about whether potentially
significant and/or disappointing outcomes of decisions will be realized.’ Zsidisin
(2003, p. 15) addressing the supply chain context more specifically defines risk as
2 Effective Management of Supply Chains: Risks and Performance
11
‘the potential occurrence of an incident or failure to seize opportunities with inbound supply in which its outcomes result in a financial loss for the [purchasing]
firm.’ Most definitions (e. g. MacCrimmon and Wehrung, 1986) of risk comprise
three common elements:
Likelihood of occurrence of a particular event or outcome,
Consequences of the particular event or outcome occurring,
Exposure or Causal pathway leading to the event.
Conceptually, these three elements appear to be readily identifiable and measurable,
lending themselves to formulaic and precise resolution (e. g. rolling the dice at the
casino). However, transferring these concepts to the practical business environment
within risk management yields a totally different set of challenges. The likelihood of
occurrence, more usually termed the probability, can be expressed in objective terms
or in subjective terms, each being capable of measurement. Objective measurement
relies on previous records of the occurrence of such events. Subjective assessment
of the likelihood of occurrence relies more on the translation of previous experience
and intuition. In practice there is likely to be the application of subjective judgments
on any objective data.
Consequences are typically expressed as a multiple of simultaneous outcomes,
many of which interact with one another (e. g. failure of a new product launch may
generate consequences for the organization’s reputation, financial performance and
the standing of the individual product champion). Consequences should not simply
be regarded as only or primarily negative, since the essence of risk taking is the potential opportunity to produce positive outcomes (Blume, 1971). The third element
of the risk construct, the causal pathway, has particularly important implications
for risk management. Understanding the nature, sources and causes of factors that
generate the events or circumstances which might influence the type and scale of
consequences (i. e. both positive and negative), and the likelihood of their occurrence are fundamental requirements for effective risk management.
Line A in Fig. 2.1 demonstrates a classic linear and consistent relationship
through all levels of risk and outcomes considered (i. e. risk and performance out
comes change directly in proportion with each other). Line B on the other hand
Fig. 2.1 Risk and performance relationships
B
High
A
Risk
Perceived
Low
C
Low
High
Expected Performance Outcome
12
B. Ritchie, C. Brindley
suggests some deterioration – as the risk perceived increases beyond a particular
level then expected improvements in performance decline rapidly until the point is
reached where improvements cease altogether and potentially become negative. For
example, if the business continues to invest more resources into managing higher
risks (e. g. buying information to refine risk sources and triggers, managerial time
on data analysis, insurance cover for potential consequences) the cost of these actions may directly influence performance. Line C for completeness illustrates another commonly experienced risk-management-performance profile. As risk management activities are applied then the rate of perceived increase in risk slows reflecting the success of risk management, performance continues to increase and risk
flattens off.
For our present purposes we consider that the essence of risk and risk taking
involves the preparedness of the individual or organization to expose themselves to
adverse outcomes on the basis that they may also achieve positive outcomes. The
important point is recognizing that risk taking has ‘upside’ benefits as well as the
‘downside’ costs, although the emphasis is usually placed on the latter. Risk itself
is not solely assessed in terms of the outcomes, positive or negative, but in terms of
the scale of such outcomes and the likelihood of the outcomes happening. Thus risk
may be portrayed as the acceptance of less desirable consequences or outcomes in
return for the opportunity to achieve more desirable outcomes.
The terms risk and uncertainty are frequently used interchangeably in practice,
although technically they describe distinctive situations. Uncertainty is viewed by
many authors as a special case of the risk construct (Paulsson, 2004), in which there
is insufficient information (Rowe, 1977), knowledge or understanding to enable the
decision taker to identify all of the potential outcomes (Ritchie and Marshall, 1993),
their consequences or likelihood of occurrence (MacCrimmon and Wehrung, 1986).
Uncertainty typically relates to the situations where there is an absence of certain
parameters such as potential outcomes, likelihood of each occurring and the consequences if they do. Pure risk sits at the other end of the continuum, typically
representing the fully defined scenario of potential outcomes, objective probabilities of occurrence and fully determined consequences from each outcome. The
further into the future the decision context, variables and outcomes under consideration (e. g. long-term strategic planning) the greater the difficulty in identifying,
estimating and measuring these parameters, or in other words the greater the uncertainty involved. The terms risk and uncertainty are frequently used interchangeably,
as typically risk contexts involving decisions are often somewhere in the middle of
the risk-uncertainty spectrum (i. e. neither pure ‘objective’ risk taking nor complete
uncertainty).
2.2.2 Risk and Outcomes
The clarification of four points relating to risk and outcomes may prove helpful at
this stage, although we return to performance measures in more detail subsequently.
2 Effective Management of Supply Chains: Risks and Performance
13
Firstly, the term outcome relates to an infinite range of performance measures and
not just those associated with financial performance. Although much of the early
research in the risk field related to financial decision contexts (e. g. Knight, 1921),
more contemporary studies have argued for the inclusion of wider dimensions of
performance criteria (e. g. Ritchie and Brindley, 2008) as risk management is increasingly applied in more diverse fields (e. g. Supply Chain Management). Secondly, the adverse consequences need not necessarily be negative or indeed significantly lower than the positive outcomes sought, providing that the degree of
desirability of the positive outcomes is sufficiently attractive to accept the possible
consequences of failure. In other words, if we are indifferent to the range of outcomes that may materialize then there is no reason to contemplate actions which
seek to influence the nature or likelihood of these outcomes. Thirdly, risk is somewhat meaningless if divorced from those involved in taking the decision. Consideration of the nature of the impact on the individuals or the group involved represents
an important dimension of risk appraisal. Personal perceptions of the likelihood and
the potential impact will vary between individual group members and hence groups.
In theory, the individual ought to be prepared to expend resources to reduce either
the likelihood until the investment (marginal cost) is equivalent to the anticipated
benefits (marginal revenues). Finally, the normal expectation in most decision situations is that risk is directly and inversely related to performance. Hence, an increase
in risk as the determining variable is more likely to lead to higher outcomes in
performance terms with the obverse being lower levels of risk resulting in lower
performance outcomes. It is not strictly true to categorize risk as the independent
variable and performance outcomes as the dependent variable. We cannot for example stipulate that higher risk taking causes better performance. More correctly
we have an association between the two variables such that higher risk and higher
performance are often equated with each other. In cases where the initial perception
is one of low risk this does not imply poor performance since such profiles may represent the vast number of routine activities carried out in most businesses, providing
the ‘cash cow’ for the business performance.
In a given situation, the initial risk perceived will be an assessment by the stakeholders or decision makers concerning the anticipated performance and the potential
effects that risk may have on the performance outcomes. If there is a sufficient level
of concern about the risks involved then the decision making unit may institute certain actions designed to obviate or mitigate such risks. Three broad categories of
actions may be observed, including, searching for further information to clarify or
resolve the risks; assessing the possible options to manage the risk sources, risk
drivers and likely occurrence; and undertaking insurance cover and other management actions to mitigate against the consequences for performance should the risks
materialise. There is in a sense an iterative loop with the feedback of information
from the review of actions taken being followed by the revision of the risk perception and then perhaps a further iteration of the process (Fig. 2.2). Further iterations
of this process will continue until either the decision makers feel that they have
sufficiently resolved the risks or alternatively exhausted the available resources and
timescales.
14
B. Ritchie, C. Brindley
Fig. 2.2 Perfomance and risk assessment in profiling process
Risk then has a number of components which drive the perception:
Decision making unit and stakeholders,
Complexity and dynamism,
Level of aggregation,
Portfolio,
Time frame,
Decomposition of risk parameters,
Distribution and sharing.
The stakeholders and the members of the decision making unit need not be the same,
indeed the shareholders in a business organization may represent the primary stakeholders yet not be directly engaged in the business risk management process. Correspondingly, managers involved in the decision making unit ought to address the
interests of all of the stakeholder groups, recognizing that these may at times be inconsistent and at odds with each other. The shareholder may desire performance outcomes related to share price gains in the longer term whilst the commercial lender
may seek more immediate assurances about short term profits, cash flows and solvency. Mixed in with such external interests are those of the individual members of
the decision making unit who may gain from performance-related bonuses, employment security and status as a successful manager. Disentangling fully such interests
and aspirations is seldom possible, although there has to be some clarity on the prioritization of these complementary and conflicting demands by the decision making
unit to guide decisions within risk management. Added to this complexity is the dynamism or flux inherent in many decision situations, especially those experiencing
above average risk levels. Indeed, the belief or perception that the situation under
consideration may be subject to continuous change will in itself engender a greater
perception of risk, especially if the scale of the changes and consequences are high.
2 Effective Management of Supply Chains: Risks and Performance
15
The level of aggregation of the decision will often influence the perceived level
of risk involved. If decisions are treated independently and in isolation from each
other the business may remain quite comfortable with the individual risks involved.
However, if these individual decisions are then aggregated or considered as a whole
then the overall perception of risk is likely to change, most probably in an upward
direction (i. e. more risky). It is important for the organization to determine the appropriate level in the hierarchy for the aggregation of the risk profile. Associated
with the level of aggregation is the concept of a Portfolio of risk and performance
outcomes. The consideration of a business as comprising a number of investments
or projects at any one time represents an important feature associated with risky
decisions and their impact on performance. This portfolio of investments approach
enables a group of activities, investments or projects to be viewed together rather
than in isolation which means that individual projects or investments may provide
offsetting contributions to performance and risk parameters. Early work in the financial economics field dealing with investment risk and returns resulted in a number
of theoretical developments (e. g. Capital Asset Pricing Method – Ball and Brown
1968) which have resulted in some interesting and useful guidance for practical
decisions in securities markets but have failed to provide similar benefits in the
‘messier, partial and fragmented’ situation found in most organizations.
The timeframe is an important consideration as there is an evident relationship
between the perspective of time and the perception of risk. Focus on the immediate or short term risks may result in decisions that effectively resolve the present
position but expose the business to higher risk exposure in the longer term. The
converse may equally apply when focusing on the longer term and ignoring the
short term consequences of the decisions taken. Another notable feature relating to
the timeframe concerns the anticipated length of time from the decision being taken
to the realization of the outcomes or consequences. It is likely that the shorter the
anticipated elapsed period from the decision to outcome realization, then the higher
the predictability or greater confidence there will be and hence lower perceptions of
risk (i. e. short term decisions may on balance be perceived as less risky than long
term decisions).
Faced with a risky decision there is a natural tendency to explore the nature and
scale of the risks perceived. In essence this results in the decomposition of risk parameters. The decision maker may seek to divide the situation encountered into
a number of component parts and to seek more information about each in the anticipation that this process of investigation will aid in gaining a better understanding of
the relationships involved thereby resolving even if not reducing the risks perceived.
A further important feature associated with risk and its management relates to
the distribution and sharing of risks. There has been a long-standing tradition in
the financial services sector (e. g. banks and insurance businesses) of distributing
large risks amongst a number of businesses such that the exposure for any single
institution is kept low, on the basis that the realization of the risk will have less
than disastrous consequences for any single business. The supply chain context provides a similar opportunity to share or distribute certain risks across the members
of the chain. This may be far more achievable for the operational level decisions
16
B. Ritchie, C. Brindley
(e.g quality assurance, avoidance of stock-outs) than the more strategic level though
the development of alliances with supply chain partners may provide risk sharing
opportunities for strategic developments into new markets.
2.3 Supply Chain Risk Management
There may not yet be agreement on the definition of Supply Chain Risk Management (SCRM) but there is agreement on the main components of SCRM, although
these may be differently termed. Most definitions would incorporate the following
clusters of activities:
• Risk identification and modeling – including the sources and characteristics of
risks, what may trigger them and the relationship to the supply chain performance
in terms of effectiveness and efficiency.
• Risk Analysis, Assessment and Impact Measurement assessing the likelihood of
occurrence and potential consequences.
• Risk Management – generating and considering alternative scenarios and solutions, judging their respective merits, selecting solutions and undertaking the implementation.
• Risk Monitoring and Evaluation – monitoring, controlling and managing solutions and assessing their impact on business performance outcomes.
• Organizational and Personal Learning including Knowledge Transfer – seeking to capture, extract, distill and disseminate lessons and experiences to others
within the organization and its associated supply chain members.
These components of the SCRM approach represent an integrated decision making approach and one which interacts extensively with other members of the supply chain. In essence, SCRM represents a more pro-active approach to managing
risks and performance in the supply chain in advance to avoid or minimize potential
undesirable consequences. Such a pro-active approach does not necessarily ensure
that all such potential risks can be identified in advance or if identified, sufficiently
well resolved to prevent some or all of the undesirable consequences. SCRM like
other management approaches is dependent on good quality management in terms
of knowledge, abilities, experiences and skills. The concepts, tools and technologies
provide support but are unable to replace the judgments required in most risky decision situations. SCRM of necessity covers a number of levels of activities, from
operational through tactical to strategic since in many supply chains these are inseparable. For example, procedures for monitoring in-bound component quality provide
an early warning signal of potential disruption or complaints.
SCRM in common with other organizational functions, shares a number of more
generic characteristics and influences associated with the corporate level of organizational decision making involving risk (Ritchie and Marshall, 1993). These include
the nature of the relationship between risk and performance at the corporate level;
2 Effective Management of Supply Chains: Risks and Performance
17
the distribution of risk across the existing and prospective portfolio of corporate investments; the capacity to redistribute or share risks internally and externally; the
time-span over which risks and outcomes are normally measured and assessed; and
the attitude or the preparedness of the organization to engage with risk and its consequences. These factors will be present in most business organizations although
may vary depending on sector, history, prior experiences, decision makers and other
contextual factors. It is true that much of the early work in these elements has related to the financial and securities markets although increasingly attention has been
directed to application in other business sectors. The remainder of the discussion in
the present chapter will focus on supply chain risks and their management. Several authors (e. g. Child and Faulkner, 1998) have argued that decisions relating to
changes in the supply chain structure and relationships ought to involve the analysis
and evaluation of the associated potential outcomes in terms of benefits, costs and
risks. Lonsdale and Cox (1998) likewise contend that performance and risk are inextricably interconnected and thus require the development and application of supplier management tools and controls to maximize performance whilst controlling
the consequential risks.
2.4 Performance
The second of our key terms, performance, has also generated an almost infinite variety of definitions. Even within the general confines of business performance there
will be variations relating to specific sectors, contexts or functional perspectives.
Anthony (1965) provided a generic and now well-established definition of performance, dividing this construct into two primary components, efficiency and effectiveness. Efficiency addresses performance from a resource utilization perspective indicating that greater efficiency is derived from producing a greater quantity of outputs
(i. e. products and/or services) for a given volume of resource inputs. Effectiveness
addresses performance related to the degree to which the planned outcomes are
achieved (e. g. achieving the objective of avoiding supply disruptions during a given
period may be viewed as an effective outcome). Colloquially, effectiveness is often
described as ‘doing the right things’ whilst efficiency may be expressed as ‘doing
things well.’ However, these two primary components need not necessarily be consistent and almost certainly do not demonstrate the practice of operating in unison.
For example, the avoidance of supply disruptions during the period may have required maintaining high buffer stocks or special incentive payments to the supplier.
Such actions may well prove highly effective against a requirement to enhance customer service and satisfaction levels, but prove highly inefficient in terms of profitability. Earlier definitions of aggregate business performance tended to focus on
the efficiency dimension, featuring financial performance and other quantifiable parameters as the primary outcome measure. Subsequently, more encompassing definitions of performance have evolved, most notably the Balanced Scorecard (Kaplan and Norton, 1992, 1996) which incorporates not only the Financial Perspective
18
B. Ritchie, C. Brindley
but also the Internal Perspective, the Customer Perspective and the Innovative and
Learning Perspective. The search continues to determine appropriate performance
measures and metrics which can be adopted or adapted to all fields of business activity, providing easily captured and communicated; readily understood; reliable and
robust measures to support the business unit in terms of effectiveness and efficiency.
Melnyk et al. (2004, p. 210), reflecting on metrics and performance measurement
concluded that ‘performance measurement continues to present a challenge to operations managers as well as researchers of operations management’.
2.4.1 Performance Criteria
There are several performance criteria associated with most supply chains, although
their relative importance may change depending on the specific supply chain context, timeframe, relationships etc. These may vary in terms of significance depending on the position in the chain itself and the position from which it is viewed.
These criteria may also be more or less tangible and hence more or less difficult to
measure. The more tangible measures include:
Timeliness – the availability of the components or services at the agreed time, recognizing the problems resulting from delayed delivery and often the storage, deterioration and stock management costs associated with earlier than agreed delivery.
Security of Supply – ensuring that complete interruptions or disruptions to the supply
of goods or services are avoided.
Quality – is itself a multi-faceted dimension although principally the requirement
is that the component or service is ‘fit for purpose’ as agreed in the specification
between the supplier and customer at the contractual stage. The consequences of
poor quality include downtime, reworking and subsequent failure to satisfy the customer’s requirements in terms of quality and timeliness. Poor quality products or
service, either upstream or downstream, may impact on the level of satisfaction of
the customer with consequences for future revenues and possibly more immediate
claims for financial compensation.
Price – although price may be fixed in many supply arrangements at the time of
contracting there are many supply chain arrangements where price may be subject
to variation (e. g. changes in local taxation, exchange rate movements). Volatility in
terms of price may result in difficulties in passing on price changes to the customer
and potentially have consequences in lost profit.
Associated Costs – the procurement, logistics and stock management costs may be
largely predictable for those transactions which flow through the chain without any
problems. However, difficulties arising from problems associated with timeliness,
quality and price may absorb significant time and costs to remedy.
2 Effective Management of Supply Chains: Risks and Performance
19
Support – the level and quality of the support provided by suppliers in the chain may
have a considerable impact in resolving adverse performance outcomes in terms of
timeliness, quality and price and may indeed help to anticipate these.
Less tangible measures of performance, although no less important are the effectiveness of the communication channels; the willingness to share information with
other supply chain members; the development of professional relationships; and ultimately the establishment of trust between the organizations and their members.
Other factors such as the reputation of the firm, often generated by issues not directly related to the supply chain itself, may pose risks. Inadvertent comments by
senior executives or the failure to endorse certain protocols may damage the reputation of the organization, with subsequent impact on the overall performance.
2.4.2 Risk and Performance – Timeframe
Time represents an important dimension when considering risk and performance.
Risk perception is influenced by the passage of time. Perceptions at an early stage
are likely to be influenced by high levels of uncertainty, largely reflecting a lack of
or imprecise information and knowledge (e. g. what are the possible risks and key
drivers?). The Risk Management process involving the investment of time, information gathering and data analysis may help to resolve the risks perceived, although
not necessarily removing them. There is a corollary to this anticipated outcome in
that gaining more information and knowledge about possible risks and outcomes
may equally diminish confidence and heighten risk perceptions as new unforeseen
risks are revealed. In ‘one-off’ decision we can envisage that the progression of time
combined with the investment in risk management may ideally lead to a reduction in
risk perception and increased confidence. In the continuous flow context associated
with many supply chain activities and processes, the passage of time either without any incidents or incidents that have been well handled and foreseen may again
build the confidence level of the risk management team. The difference in this latter
context is that responses have to be made to risk outcomes as they occur including making changes immediately to avoid their recurrence in the continuous flow in
the next cycle. Time may be an implicit parameter in the risk management process
but is nevertheless important. The timeframe may also be used to categorize decisions, for example, operational, tactical and strategic. Paulsson (2004) utilizes this
approach to differentiating supply chain risks into Operational Disturbance, Tactical
Disruption and Strategic Uncertainty. Kleindorfer and Wassenhove (2003), however,
subdivided supply chain risks into only two categories Supply Co-ordination Risks
and Supply Disruption Risks, dividing Paulsson’s (2004) tactical level decisions between the two categories. Whilst such categorization may prove helpful conceptually, Mintzberg and Waters (1985) highlighted the difficulty in differentiating these
in practice, suggesting that strategic decisions are in essence the aggregation of a sequence of operational and tactical decisions, leading to some common planned or
20
B. Ritchie, C. Brindley
emergent pattern. Similarly, the differentiation between tactical and operational decisions may prove somewhat arbitrary in practice.
2.5 Performance and Risk Metrics
The inter-relationship between the investment in SCRM and the outcomes in terms
of changes in performance and risk (i. e. the resulting risk and performance profiles
for the organization as a whole) are increasingly important aspects of SCRM. The
measurement of corporate performance and risk may be addressed at different levels of aggregation and from a number of different although not mutually exclusive
perspectives. Different stakeholders, both external and internal, may seek a different
balance in terms of the timeframe (i. e. short-term versus long-term performance),
emphasise different criteria (e. g. profitability, cash flow or customer service) and
display different attitudes to risk exposure (e. g. avoidance of excessive risk). Stainer
and Stainer (1998) identified eight different categories of stakeholder (i. e. shareholders, suppliers, creditors, employees, customers, competitors, Government and
society) together with their differing performance expectations from the business.
A common feature of most, if not all, stakeholders is the underlying requirement for
generating performance in terms of profit consistent with the risks associated with
achieving this performance. Mathur and Kenyon (1997) support the importance of
financial performance metrics as providing the basis for confidence in the business
providing reassurance to all stakeholders including those associated with the wider
societal concerns (e. g. Stainer and Stainer, 1998), There is no question that financial
performance outcomes remain the primary metrics for commercial situations such
as SCRM. Within this there may be different emphases, focusing on more long-term
perspectives rather than short term timeframes often implied by many financial performance measures (Marsden, 1997).
A generic model of corporate performance incorporating the risk measure links
performance to the three independent variables Industry Characteristics (IC), Strategic Decisions (S) and Risk (R):
Performance D f .IC; S; R/ :
Risk in turn is viewed as being determined by the two variables Industry Characteristics and the Strategy developed. As Ritchie and Marshall (1993, p. 165) concluded
‘a well devised strategy could simultaneously reduce risks and increase returns’. The
generic performance metrics typically employ a financial definition of performance
(e. g. return on assets (ROA); return on investment (ROI)) and generally seek to
maximize this performance over the longer term period as opposed to the short term
such as the current year.
The SCRM Framework (Fig. 2.3) comprises two major groups of components.
The more strategic and enduring group of components are located at the core–risk
profile, performance profile, strategic timeframe and the stakeholders participating
2 Effective Management of Supply Chains: Risks and Performance
21
in the supply chain. The outer ring comprises the key components or activities involved in the risk and performance management process.
Considering initially the core components:
1. The Performance Profile represents a multi-dimensional view of the organization (i. e. equivalent say to the Balanced Scorecard (Kaplan and Norton, 1992,
1996) incorporating Financial, Internal, Customer, Innovative and Learning perspectives. This profile engenders the strategic aims of the organization and its
stakeholders, recognizing the need for flexibility and balancing between the various, often incompatible, performance criteria and stakeholder demands.
2. Similarly, the Risk Profile represents the scale and nature of the risk exposure that the organization is prepared to accept. In many respects this profile
comprises a portfolio of different types of risk and the organization may well
be prepared to accept high risk exposure in one element of the business if
this is counter-balanced by lower risk exposure elsewhere in the portfolio of
projects/activities/investments.
3. The Timeframe, as discussed earlier, indicates the importance of locating the
point in time at which risk and performance are viewed, assessed and managed.
4. The inclusion of the Supply Chain Stakeholders as a component in the risk/performance core is designed to emphasize the inter-dependence of the members
of the supply chain. The performance and risk profiles for the organization are
dependent to differing degrees on the other partners and stakeholders in the
supply chain.
The outer ring (Fig. 2.3) represents the ongoing processes of risk and performance
management. The Risk Management components comprise a sequence of
• identifying risk sources and drivers,
• assessing their potential impact,
• instituting appropriate risk management responses,
Performance
Sources and
Drivers
Risk
Sources
and Drivers
Risk
Assessment
Risk
Management
Risk
Profile
Performance
Profile
Supply Chain
Stakeholders
Timeframe
Risk
Outcomes
Performance
Assessment
Performance
Management
Performance
Outcomes
Fig. 2.3 Supply Chain Risk Management Framework – Process overview
22
B. Ritchie, C. Brindley
• evaluating the impact on risk outcomes.
The performance management sequence parallels that for risk management.
•
•
•
•
identifying performance sources and drivers,
assessing their potential impact,
instituting appropriate performance management responses,
evaluating the impact on performance outcomes.
Three important points relate to the interpretation of the risk and performance management process elements in the Framework:
1. The sequence of actions within each of the processes is not linear nor necessarily
progressive from one to the other, it often requires the re-iteration of previous
stages to achieve greater understanding or verification.
2. The risk and performance processes are inextricably joined in practice with decision makers continuously involved in balancing risk and performance information.
3. The outer ring of more tactical or operational activities involved are informed
by and also inform the core components, namely the performance profile, risk
profile and stakeholder profile, albeit often from a different timeframe.
2.6 Risk-Performance: Sources, Profiles and Drivers
Risk and performance in the supply chain context are influenced by a variety of
different factors. Structuring these factors may prove helpful in appreciating the
range and complexity of the situation faced in SCRM. A generic categorization
based on the model initially developed by Ritchie and Marshall (1993) divides the
sources and risk drivers in to seven groups of elements:
Risk (R) D f .Er Ir SCr SSr Or Pr DMr / ;
where:
Er
D
D
Ir
SCr
D
SSr
D
D
Or
pr
D
DMr D
environmental variables;
industry variables;
supply chain configuration;
supply chain stakeholders;
organizational strategy variables;
problem specific variables;
decision-maker related variables:
Note: The Industry Characteristic (IC) variable referred to earlier in the Performance–Risk
relationship model has been decomposed into the first three groups of element in the current
model. The subscript ‘r’ seeks to emphasize the focus on the risk dimensions of each group
of elements, especially those associated with risk sources and risk drivers.
2 Effective Management of Supply Chains: Risks and Performance
23
These elements are translated into the upper boxes in Fig. 2.4. The elements have
been further divided on the basis of those that are largely unavoidable or not capable
of being influenced by the organization (i. e. systematic risks) on the left arm in the
figure and those that are avoidable by the organization and result directly from its
decisions and actions (i. e. unsystematic risks) on the right arm in the figure. The
merging of the two arms indicates that all seven elements interact with each other as
part of the SCRM process and that the management process requires the handling
of both the unavoidable and avoidable risks generated. All of these elements relate
to both risk and performance and either singly or in combination, determine the
risk and performance profile for the organization at that point in time and for that
particular decision or set of decisions. This is a dynamic situation and any of these
seven sources may generate new risks at any time on a continuous basis, affecting
both the risk and performance profiles of the organization.
The sources identified in Fig. 2.4 are only representative of an almost infinite
number of factors exposing the business to undesirable consequences in terms of
performance and risk. The organization needs to establish which are critical and
which are less so, with the former likely to be a very small proportion of the total.
The term driver has been introduced to differentiate those factors most likely to have
Organization
Strategy
Environment
Characteristics
Industry
Characteristics
Decision Making Unit
Supply Chain
Configuration
Supply Chain
Members
Systematic (Unavoidable)
Risk Exposure
Problem Specific
Variables
Unsystematic (Avoidable)
Risk Exposure
Portfolio of Risk and Performance Outcomes
Performance Profile
Fig. 2.4 Risk and performance: Sources and drivers
Risk Profile
24
B. Ritchie, C. Brindley
a significant impact on the exposure (i. e. sources, causal pathways, likelihood and
consequences) to undesirable performance and risk outcomes. Performance drivers
may well offer opportunities to enhance performance outcomes, albeit by incurring
increased risk. For example the decision to develop a new direct channel to the consumer, bypassing existing distribution channel members would expose the business
to new risks both from the reaction of the consumer and the retaliatory actions of
the other channel members, although possibly improving potential performance outcomes. Key risk and performance drivers will usually be associated with each of the
seven sources listed in Fig. 2.4. The dynamism referred to earlier suggests that the
composition of key drivers may well vary over time and change as the supply chain
situation changes in terms of structure and membership.
The elements in Fig. 2.4 relate to risks that pose a major threat to the survival and
future development as well as those influencing the more ‘normal’ performance of
the business in terms of effectiveness and efficiency. Management attention should
focus on those drivers which are likely to have a significant impact on the performance or risk profile. Since SCRM concerns the interrelationships within the typical
supply chain network, all members within a network will be potentially exposed to
the risks, although the direct impact may be ameliorated or modified by the actions
taken by others in the chain. Collectively, members throughout the supply chain may
benefit if everyone engages in systematic SCRM activities.
The underlying presumption of SCRM is that the risk and performance sources
and drivers can be foreseen, identified, evaluated, prioritized and managed. The
practical reality suggests considerably more ‘fuzziness’ relating to these drivers,
their impact on performance and the effectiveness of possible management solutions. This begs the question as to why organizations bother to prepare themselves
for risk encounters and invoke SCRM. Quite simply, organizations believe that the
best approach is to accept that they will be exposed to risks and the best strategy is
to become more aware and pro-active towards the risks and better prepared to respond more quickly should such risks materialize (Kovoor-Misra et al., 2000). The
simultaneous presence of different drivers may have a compounding effect both on
the exposure and potential consequences. For example, the dislocation of supplies
due to transport failures may be compounded by inadequate communications between supply chain members and further exacerbated by poor management controls
in the principal organization. Alternatively, the risk drivers may be counterbalanced
by high levels of performance, enabling the management to effectively control the
worst consequences of supply disruption.
2.7 Risk Management Responses
The range of risk management responses is typically extensive, although some exemplars of risk management responses (Fig. 2.5) include risk insurance, information
sharing, relationship development, agreed performance standards, regular joint reviews, joint training and development programmes, joint pro-active assessment and
2 Effective Management of Supply Chains: Risks and Performance
RISK &
PERFORMANCE
TARGETS
Performance
Effectiveness
Efficiency
25
RISK &
PERFORMANCE
SOURCES
&
DRIVERS
RISK
MANAGEMENT
RESPONSES
RISK &
PERFORMANCE
OUTCOMES
Insurance
Performance Drivers
Risk Sharing
Stakeholders
Financial
Non-financial
Risk Sources
Systematic
Unsystematic
Information
exchange
Risk Profile
Relationship
Development
Timeframe
Strategic
Operational
Risk Profile
Fig. 2.5 SCRM framework
planning exercises, developing risk management awareness and skills, joint strategies, partnership structures and relationship marketing initiatives. A number of supply chain groups have displayed some degree of progression in the risk management
responses, leading from the more individualistic and independent responses (e. g.
insurance, establishing supplier service levels) to the more co-operative responses
(e. g. sharing strategic information, relationship development and partnering). Similar developmental trends were discovered by Kleindorfer and Saad (2005) when
examining disruption risks in supply chains in the US chemical Industry. Progressing to more integrated and comprehensive approaches may be the result of the nature
and severity of the potential risk consequences, the number of members involved in
the supply chain and enhancements in terms of confidence and trust between the
parties engaged in the supply chain. The initiation of such developments is often
undertaken by the larger organizations in the supply chain, since they may have the
resource base and expertise, as well as the comparative power to encourage participation by smaller enterprises.
Risk management needs to target both the systematic and unsystematic risk
sources. Whilst the organization may not be able to control sources of systematic
risk (e. g. changes in interest rates or political instability), the adoption of particular management approaches may enable the organization to better understand the
risks and to respond more quickly and effectively to modify or ameliorate the impact on performance (e. g. reducing financial risk exposure in advance by limiting
borrowing). Similarly, improving the awareness and understanding of unsystematic
risks can enable the development of strategies which either avoid or minimize exposure to identified risks. Equally, developing relationships and partnerships with key
members of the supply chain may provide a more generic shield against exposure to
other unsystematic risks emanating from elsewhere in the supply chain.
26
B. Ritchie, C. Brindley
2.8 Conclusions
The chapter aimed to develop an understanding of the main constructs underpinning risk and performance within the supply chain, especially the inherent linkage
between these two. The dimension of time was introduced as another key dimension
influencing risk perceptions (i. e. uncertainty reduction and risk resolution as time
progresses. Risk Management has been implicit in the management of supply chains
over a long period of time. More recently (see Mentzer, 2001; Brindley, 2004) a concerted effort has been made to study these in a more logical and coherent manner.
This was in response to the significant pressures experienced both contextually and
from within the supply chain to modify and in some situations radically change the
structures, modes of operations and relationships. These developments themselves
may further engender an increased sense of uncertainty and risk throughout the various stages of the supply chain.
The evidence suggests that organizations are increasingly recognizing the interaction between performance and risk. There is also a trend towards risk and performance metrics which are much more widely based (i. e. not dependent primarily
on quantitative, financially oriented and short-term metrics). The new metrics are
evolving and are designed to tackle some of the broader risk-performance issues
at the enterprise level (i. e. Enterprise Risk Management systems) and are more
strategically oriented. The development of improved relationships leading to more
formalized associations is an evident trend in many supply chain situations with the
emergence of issues such as confidence and trust emerging in the discussions and
developments between supply chain partners. The recognition that SCRM can create both positive and negative consequences for the businesses in the supply chain
highlights the importance of developing reliable, robust and practical measurement
systems. Such multi-dimensional risk-performance measures need to be well understood and applied appropriately. The chapter has sought to make a contribution to
this requirement.
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Chapter 3
Managing Supply Chain Disruptions
via Time-Based Risk Management
ManMohan S. Sodhi and Christopher S. Tang
Abstract We wish to motivate research on the practice of preplanned response to
rare events that can disrupt the supply chain. We present a time-based risk mitigation
concept and illustrate how this concept could enable companies to reduce the impact
of such events while potentially increasing their competitiveness. The underlying
idea is that if a firm can shorten the response time by deploying a recovery plan soon
after a disruption, then this firm can reduce the impact of the disruption by way of
fast recovery. We present examples from a wide variety of contexts to highlight the
value of time-based risk management.
Key words: Time-based competition; supply chain disruption; supply chain risk
management; business continuity; contingency planning; supply chain responsiveness
3.1 Introduction
Our aim is to motivate research on the practice of systematic and preplanned response to rare events that can cause huge disruption to the supply chain. Such events
are costly to prevent and companies may be reluctant to invest in prevention as the
returns are unclear. However, they may be able to respond effectively to such risk
incidents after they occur by containing their impact through quick response. We
provide a simple framework to think about response and motivate further research
and improved practice through a variety of examples both within and outside supply
chain management.
Our proposal extends business continuity efforts in practice from a local context to a supply-chain wide one. We break up response to supply chain disruptions
into three time elements – detect the event across the supply chain (D1), design
a response (D2), and deploy the response (D3). We refer to these elements as the
3-D framework. By focusing its efforts on ensuring that systems and processes are
T. Wu, J. Blackhurst (eds.), Managing Supply Chain Risk and Vulnerability
© Springer 2009
29
30
M.S. Sodhi, C.S. Tang
in place to reduce to these three time elements, a company reduces the overall response time (R1) and thus recovery time (R2) and total impact. We illustrate this
concept through examples from a variety of contexts.
Our contribution is to highlight a potentially rich area of empirical and modeling research that can complement the existing literature that focuses on prevention
rather than post-incident recovery. Time-based risk management dovetails into the
company’s business continuity efforts and provides a basis for risk reporting for its
lenders and investors. With time-based risk management, investment in risk management is low while increasing competitiveness due to improved responsiveness
through more awareness of supply chain processes and of disruptions as well as
more communication across the supply chain within the company and with its partners.
This chapter presents the concept of time-based risk management, its importance
through a variety of examples, and its implementation. We provide avenues for research and the basis for improved practice.
3.2 Background
Many companies are expanding their supply chains to more external partners in different countries as a way to reduce cost and product development cycle and to explore new markets. For example, Boeing increased the outsourced content from 50%
to 70% when developing its new 787 model and spread its suppliers over 20 countries. Also, according to an industry study conducted by AMR in 2006, over 42%
of the companies manage more than 5 different global supply chains for different
products in different markets. As supply chains become more complex, companies
find their supply chains more vulnerable to unforeseen disruptions – rare but severe
events that disrupt the flow of goods and information in a supply chain. Without
a disruption management system in place, these disruptions can have huge impact
in terms of cost and recovery time to the company and its customers.
Examples of impact include Ericsson losing 400 million euros in the quarter following a minor fire at their supplier’s semiconductor plant in 2000. In addition, due
to a design flaw of the Pentium microprocessors, the recall of 5.3 million chips has
cost Intel $ 500 million in 1994. Furthermore, New Orleans has not fully recovered
as of 2008 – three years after the landfall of Hurricane Katrina in August 2005. Over
100 patients have died in 2008 as a result of blood thinning drug Heparin contaminated with unsafe substance (Pyke and Tang, 2008).
Based on an analysis of 827 disruption announcements made over a 10-year period, Hendricks and Singhal (2005) found that companies suffering from supply
chain disruptions experienced 33–40% lower stock returns relative to their industry
benchmarks over a 3-year time period that starts one year before and ends two years
after the disruption announcement date.
Other examples of significant supply chain disruption include Mattel’s recall of
over 18 millions of toys in 2007 (Casey and Pasztor, 2007). Dell recalled 4 million
3 Managing Supply Chain Disruptions via Time-Based Risk Management
31
laptop computer batteries made by Sony in 2006. Land Rover laid 1400 workers
off after their supplier became insolvent in 2001 as production could not continue
without parts. Dole suffered a large revenue decline after their banana plantations
were destroyed after Hurricane Mitch hit South America in 1998. Among the many
instances of disruptions after 9/11 attacks in 2001, Ford had to close five plants for
several days owing to the suspension of all air traffic. For more details, see Martha
and Subbakrishna (2002), and Chopra and Sodhi (2004).
Supply-chain disruptions are getting CEOs’ attention these days because of both
short-term effects (negative publicity, low consumer confidence, market share loss,
etc.) and long-term effects (stock prices and equity risk). Despite these effects, not
many firms are willing to invest in initiatives to decrease disruption risk. According
to a study conducted by Computer Sciences Corporation in 2004, 60% of the firms
reported that their supply chains are vulnerable to disruption (Poirier and Quinn,
2003). The lack of credible cost/benefit or return on investment (ROI) analyses may
be one key reason why companies are not investing in disruption management (Rice
and Caniato, 2004; Zsidisin et al., 2001, 2004).
Another survey conducted by CFO Research Services concluded that 38% of 247
companies acknowledged that they had too much unmanaged supply chain risk (cf.
Eskew, 2004). While the exact reasons are not known, Rice and Caniato (2003) and
Zsidisin et al. (2000) conjecture two key reasons: (1) firms are not familiar with
ways to manage supply chain risk; and that (2) firms find it difficult to return on
investment analysis to justify certain risk reduction programs or contingency plans.
To garner support for implementing certain risk reduction programs without exact cost/benefit analyses of certain risk reduction programs, effective risk reduction
programs must provide strategic value and reduce supply chain risks at the same
time (Tang, 2006). Therefore, as articulated by Chopra and Sodhi (2004), the biggest
challenge is to determine ways to mitigate supply chain risks and increase profits simultaneously so that companies can achieve a higher level of efficiency by reducing
risk while increasing reward – this is also our aim with time-based risk management.
One stream of the risk-mitigation literature focuses on preventing rare risk events.
For instance, Lee and Wolfe (2003) describe how different initiatives developed by
Homeland Security (e. g., smart containers, Customs-Trade Partnership against Terrorism) would prevent terrorist attacks at various ports in the United States. However, such initiatives may not always be economical for preventing disruptions that
are rare and could occur anywhere in a complex supply chain. Our proposed approach aims at preparedness in the supply chain to reduce impact once such an
incident occurs.
3.3 Time-Based Risk Management
Akin to various time-based initiatives such as time-based competition (cf. Blackburn, 1990; Stalk and Hout, 1991), our “time-based risk management” concept focuses on time and response processes instead of cost, probabilities or impact.
32
M.S. Sodhi, C.S. Tang
Our time-based management concept is based on three elements of time: time to
detect a disruption (D1), time to design (or prescribe) a solution in response to the
disruption (D2), and time to deploy the solution (D3). After deployment, the time it
takes to restore the supply chain operations is the recovery time R2. Companies can
reduce the impact of supply chain risk incidents by shortening these three elements
of time and hence the response time. Increasing responsiveness can help in general
and may help increase market competitiveness for the company.
Although there have been efforts to prescribe effective recovery plans for reducing the impact of supply chain disruptions (cf. Chopra and Sodhi, 2004; Lee, 2004;
Sheffi, 2005; Tang, 2006), the focus is on recovery after the event has occurred.
In contrast, our time based risk management concept focuses on planning and setting up procedures and protocols before a risk event occurs: detection systems and
procedures to reduce D1, pre-packaged designs to reduce D2, and identified communication channels for deployment to reduce D3. Just as 80% of the total cost
of a product is determined during the product design phase, the activities that take
place for designing response can have significant effect on the overall impact of
a disruption.
The 3 “D” components of time can be illustrated by using the failed relief efforts
associated with Hurricane Katrina. Despite live TV coverage of Katrina’s aftermath
in late August of 2005, it took three days for FEMA director Michael Brown to
learn of those 3000 stranded evacuees at New Orleans’ Convention Center. In our
terminology, the detect lead time D1 D 3 days. According to the Reynolds (2005),
communication and coordination between FEMA and local authorities were poor: it
took days to sort out who was to do what, when and how. For example, it took two
days for Louisiana Governor Blanco to decide on the use of school buses to remove
those stranded evacuees. In our context, the design time D2 is two days. However,
as seen on live TV, most school buses were stranded in the flooded parking lots.
FEMA requested over 1000 buses to help out but only a dozen or so arrived the day
after; hence, the deploy lead time D3 was quite long. As a result, New Orleans has
not fully recovered as of this writing; i. e., the recovery time R2 exceeds two years.
The Katrina fiasco suggests that one can reduce the impact – number of deaths,
costs, and recovery time R2 – associated with a disruption by reducing the response
lead time R1 D D1 C D2 C D3.
3.3.1 Response Time and Impact
To understand the importance of shortening the response time, consider the following examples:
Eradicating Med flies in California in 1980. Despite the initial med fly eradication efforts in the mid-70s, med flies were detected in California again in the
early part of 1980. Instead of calling for aerial spray of Malathion in a small area
(30 square miles) that is proven to be effective but costly, Governor Brown approved
the release of sterile male flies and traps. Unfortunately, these methods were not ef-
3 Managing Supply Chain Disruptions via Time-Based Risk Management
33
fective and the area of infestation expanded more than 20-fold from 30 square miles
in June of 1980 to 620 square miles in July of 1981. As Japan and other countries
imposed import restrictions, Governor Brown was under political pressure to approve the aerial spray over an area of 1500 square miles starting July 14, 1981. This
delayed action came at a significant cost: an expenditure of over $ 100 million and
Governor Brown’s political career. See Dawson et al. (1998) and Denardo (2002)
for details.
Ground shipping after September 11. Soon after the 9/11 attacks, Chrysler
requested their logistics providers to switch the mode of transportation from air
to ground. Speedy deployment of this strategy enabled Chrysler to get the parts
from such suppliers as TRW via ground transportation. By the time Ford decided
to switch to ground shipping, all ground transportation capacity has been taken up
and Ford was unable to deploy the same strategy. Facing parts shortages, Ford had
to shut down 5 of the US plants for weeks and reduce its production volume by 13%
in the fourth quarter of 2001 (cf. Hicks, 2002).
Recovering after supply disruption. Both Ericsson and Nokia were facing supply shortage of a critical cellular phone component (radio frequency chips) after
their key supplier, Philip’s Electronics semiconductor plant in New Mexico, caught
on fire in March of 2000. Nokia recovered quickly by doing the following. First,
Nokia immediately sent an executive team to visit Philip’s in New Mexico so as to
assess the situation. Second, Nokia reconfigured the design of their basic phones
so that the modified phones can accept slightly different chips from other Philip’s
plants; and third, Nokia requested Philip’s to produce these alternative chips immediately at other locations. Consequently, Nokia satisfied customer demand smoothly
and obtained a stronger market position mainly due to their speedy deployment of
their recovery plan. On the contrary, Ericsson was unable to deploy a similar strategy
later because all Philip’s production capacity at other plants has been taken up by
Nokia and other existing customers. Facing with supply delay, Ericsson lost $ 400
million in sales (cf. Hopkins, 2005).
The above examples suggest that the recovery lead time R2 is by and large increasing in the response lead time R1. This is mainly because the magnitude of the
problem triggered by the event escalated exponential over time.
3.3.2 Modeling Disruption Impact over Time
To motivate the impact of a risk incident over time, we consider the epidemiological
and the forest fire literature. Specifically, the total impact of a natural disruption
(an epidemic or a forest fire) tends to increase super-linearly or even exponentially
with time initially and then to taper off. Thus, as shown in Fig. 3.1, shortening the
response time R1 (D D1 C D2 C D3) can reduce the total recovery time R2 and
hence the total eventual impact of the disruption.
Epidemic Models. The simplest form of an epidemic model is the exponential
model that can be explained as follows. Let I.t/ be the number of people infected at
34
M.S. Sodhi, C.S. Tang
Impact
Impact reduction
Response Lead Time reduction
Time
R2: Recovery Lead Time
R1 = D1+D2+D3
Response Lead Time
Deployment of a
An event
occurs
recovery plan
Fig. 3.1 The effect of reducing the response lead time R1
time t. In this case, the rate of infection can be defined by the differential equation:
d I.t /
d t D k I.t/, where the parameter k > 0. This differential equation yields: I.t/ D
I0 ekt , where I0 is the number of people infected at time 0. Therefore, the number
of people infected grows exponentially overtime. By contrast, the logistic model is
another simple model that stipulates that the infection rate depends on the number
of people infected and the number of people who is susceptible to the infection. The
number of people infected I.t/ grows exponentially initially and plateaus later on
(Mollison, 2003).
Fire Impact Models. There are many different types of fire models based on
a system of differential equations for estimating the burned areas over time – see,
for example, Richards (1995) and Janssens (2000) for various fire spread models.
The simplest model is the elliptical fire spread model (cf. Arora and Boer, 2005).
that assumes that the burned area takes on the form of an ellipse with the point of
ignition at one of the foci. By assuming that the fire is spread linearly over time
across this two-dimensional space, they show that the total area burned (size of the
ellipse) grows as a squared function of time elapsed since the start of the fire. Thus,
the total area burned grows exponentially over time initially, slowing down later as
the area of the remaining forest decreases.
In addition to these two models, there are hazards analysis reports highlighting
that the magnitude of the problems associated with many hazards (fire, terrorism,
earthquake, etc.) tend to grow super-linearly or exponentially over time (Anderson
et al., 2002).
3 Managing Supply Chain Disruptions via Time-Based Risk Management
35
While we are not aware of any scientific study of modeling impact over time in
the context of supply chain risk, it is plausible that a pattern similar to the logistic
model will emerge (Fig. 3.1). For instance, a week’s supply delay would have caused
little damage to Ericsson but several weeks of supply delay resulted in $ 400 million
loss in sales in the first quarter and $ 2 billion eventually in the first year after the
dust had settled. Based on such examples, we can point to two ideas for investigation
as further research:
(1) The recovery lead time R2 and cost can be significant higher if the deployment
of a recovery plan is delayed; and
(2) The execution of a recovery plan can become much more difficult if its deployment is delayed.
3.3.3 Time-Based Risk Management in Practice
We now present five time-based disruption management activities that would enable
a company to reduce the response time R1 D D1 C D2 C D3 (and consequently
the recovery time R2 and the total impact):
1. Work with suppliers and customers to map risks: Many companies already
identify potential disruptions according to its impact and likelihood as part of
business continuity efforts. They can further that effort in two ways by tracing
the impact of each disruption along the supply chain from upstream partners and
to downstream customers. Doing so requires discussion among supply-chain
partners and therefore creates shared awareness of different types of disruptions
and their impacts on different parties. This generates support for collaborative
efforts for mitigating risks for all parties.
2. Define roles and responsibilities: Companies should work with all key supply
chain partners to define the roles and responsibilities to improve communication
and coordination when responding to a disruption. Van Wassenhove (2006) suggests three forms of coordination for effective response efforts: (1) coordination
by command (central coordination), (2) coordination by consensus (information
sharing), and (3) coordination by default (routine communication). The coordination mechanism, agreed among the parties before a risk event has taken place,
can then be used without further discussion for design and for deployment of solutions after the risk event has occurred. Coordination by command seems to be
appropriate during the design and deployment phases (i. e., during D2 and D3).
This is because, during these two phases, an identified group within the firm
or comprising partners’ representatives as well, needs to take central command
for collecting and analyzing information to design a recovery plan, and then for
disseminating information regarding the deployment of the selected recovery
plan. However, to get to this point of agreed upon procedures, coordination by
consensus is likely more effective in agreeing on detection mechanisms and in
designing pre-packed solutions that anticipate disruptions.
36
M.S. Sodhi, C.S. Tang
3. Develop monitoring/advance warning systems for detection: Companies
need to develop mechanisms to discover a disruption quickly when it occurs
and/or to predict a disruption before it occurs. They must also identify ways
to share the information with their supply-chain partners and to get similar
information from them. Monitoring and advance warning systems can enable
firms to reduce detection time. For instance, many firms have various IT systems for monitoring the material flows (delivery and sales), information flows
(demand forecasts, production schedule, inventory level, quality) along the supply chain on a regular basis. For example, Nike has a “virtual radar screen”
for monitoring the supply chain operations (Hartwigsen, 2005); Nokia monitors the delivery schedule of their suppliers (Hopkins, 2005); and Seven-Eleven
Japan monitors the production/delivery schedule from their vendors (suppliers)
as well as the point of sales data from different stores throughout the day (Lee
and Whang, 2006). These monitoring systems typically use control charts and,
if any anomaly is detected, issue alerts. Hence, these monitoring systems would
reduce the detection time D1. Besides monitoring systems, advance warning
systems are intended to detect an undesirable event before it actually occurs. For
example, Allmendinger and Lombreglia (2005) described how different smart
alert systems enabled GE to conduct remote sensing and diagnostics so that it
can deploy engineers to service their turbines before failures occur.
4. Design recovery plans: Develop contingent recovery plans for different types of
disruptions. Establishing contingent recovery plans for different types of disruptions in advance would certainly reduce the design time D2. Many firms have
developed various recovery plans (or contingency plans) in advance. For example, Li and Fung has different contingent supply plans that will enable them
to switch from one supplier in one country to another supplier in a different
country (St. George, 1998). Also, Seven-Eleven Japan has developed different
contingent delivery plans that will allow them to switch from one transportation
mode (trucks) to a different transportation mode (motorcycles), depending on
the traffic condition (Lee and Whang, 2006).
5. Develop scenario plans and conduct stress tests: Companies need to create
different scenarios and rehearse different simulation runs/drills based on different scenarios with all key supply chain partners. Because the deployment
time D3 accounts for the preparation time to launch the selected recovery plan,
scenario planning and stress tests are effective mechanisms for reducing D3. For
example, by rehearsing different response and recovery plans at each P&G site
under different scenarios annually, P&G managed to restore the operations of its
coffee plant in New Orleans by mid-October 2005 after the Katrina’s landfall in
late August 2005. P&G attributed their quick recovery (R1 C R2 D 2 months)
to its readiness (Contrill, 2006).
3 Managing Supply Chain Disruptions via Time-Based Risk Management
37
3.4 Risk and Reward Considerations
Besides reducing disruption risks, time-based disruption management can increase
a firm’s competitiveness as well. As we mentioned earlier, effective risk reduction
programs must provide strategic value and reduce supply chain risks at the same
time (Tang, 2006). In other words, we should look for ways to mitigate supply chain
risks and increase profits simultaneously so that companies can achieve a higher
level of efficiency by reducing risk while increasing reward (Chopra and Sodhi,
2004). Time-based risk management may help achieve this (Fig. 3.2).
We can use Spanish apparel maker Zara’s success to illustrate how time-based
disruption management can enable firms to increase their competitiveness by responding to dynamic changes quickly (as articulated in the time-based competition
literature). Despite the fact that fashion retailers are susceptible to many supply
chain risks such as uncertain supply, transportation delays, shrinkage and theft, uncertain demand, Zara continues to be a profitable European fashion retailer with
sales and net incoming growing at an annual rate of over 20% as of 2008. Ferdows et al. (2004) attributed Zara’s success to its “rapid fire fulfilment” strategy that
enables Zara to increase its competitiveness while reducing risks (Fig. 3.2). Specifically, Zara’s claim to fame is time reduction: Zara is capable of design, manufacture
and ship a new line of clothing within 2 weeks, while most traditional fashion retailer will take more than 24 weeks.
Zara operates as a vertically integrated supply chain by co-locating designers
and the factory in Spain, by managing their warehouses and distribution centers in
Spain, and by running all Zara stores worldwide (Ghemawat and Nueno, 2003). Not
only does this integrated supply chain provide Zara visibility, it also enables Zara
Risk
Improved Position enabled by
Time Based Management Tools
X
LOW
X
Current
Position
HIGH
Reward
LOW
HIGH
Fig. 3.2 Time Based Disruption Management enables a firm to shift position to a higher efficiency
risk-reward curve. Adapted from Chopra and Sodhi (2004)
38
M.S. Sodhi, C.S. Tang
to facilitate close communication and coordination with all supply chain partners.
By receiving point of sales data from their own stores on a regular basis, Zara has
a well established process for analyzing the sales data to detect sudden changes in
demand and/or fashion trends.
As such, Zara’s detect lead time D1 is short. By managing centrally and by working closely with all partners, Zara can analyze the situation and prescribe a response
should the market change suddenly. By co-locating the designers and the factory,
Zara has the capability to deploy different recovery plans by designing and manufacturing new designed clothes very quickly should the sales of existing designs
are below expectations. Hence, the design time D2 is short. The close proximity
of suppliers, designers, factories, and distribution centres enable Zara to communicate, coordinate, and deploy the selected recovery plan quickly with all supply chain
partners (from suppliers to the stores). Hence, the deploy lead time D3 is also short.
In addition, Zara also has capability to implement recovery plans quickly so as to
reduce the deploy time D3 and recovery time R2: for example, Zara engages in
“flexible supply contracts” with “multiple suppliers” to be able to adjust the order
quantity quickly should a demand disruption occur.
Not only do these mechanisms help Zara to reduce D1, D2, D3 and consequently R2, they enable Zara to increase its competitiveness and profit by: (a) generating more accurate demand forecasts in a timely manner; (b) designing, producing,
and distributing newly designed products in small batches quickly; and (c) reducing
the costs associated with price markdowns (due to over-stocking) and lost sales (due
to under-stocking). Relative to its competitors, the time-based management concept
has enabled Zara to achieve higher profitable growth and lower supply chain disruption risk simultaneously.
3.5 Conclusion
We have used diverse examples and natural disruption models (epidemic model
and fire model) and anecdotal evidence to argue that firms can use the time-based
management concept to reducing the response lead time and recovery lead time,
which will in turn reduce the impact of a disruption. We suggested five activities that would enable a firm to reduce the response lead time R1. Finally, we
suggested using Zara’s example that we may be able to achieve both risk reduction and extra rewards through increased responsiveness enabled by time-based risk
management.
However, we have presented a concept that requires further research. For instance, we presented impact models from the epidemiology literature – we need to
develop similar models for supply chains. Likewise, we need empirical research to
study how and to what extent companies are extending business continuity efforts
to respond to risk events. We believe time-based risk management to be a rich area
for modeling and empirical research.
3 Managing Supply Chain Disruptions via Time-Based Risk Management
39
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Chapter 4
Prioritization of Risks in Supply Chains
Mohd. Nishat Faisal
Abstract Modern supply chains are very complex, with physical, financial, and information flows occurring simultaneously in order to ensure that products are delivered in the right quantities, to the right place in a cost-effective manner. Maintaining uninterrupted supply chain flows is a prerequisite for the success of a supply
chain in the marketplace. But there are always associated risks in each of these
flows which require suitable strategies to mitigate them. The issue of risks in supply chains has assumed importance in wake of the understanding that supply chain
failures are fatal to the existence of all the partners’ in a supply chain. The severity
of supply chain failures are more felt by small and medium enterprises (SMEs) who
form the majority at tier II and tier III levels of a supply chain. This is because of
the limited resources and lack of adequate planning to counter supply chain risks.
Management of risk in supply chains is a multi-criteria decision making problem.
The research presented in this chapter proposes a Fuzzy-AHP based framework to
prioritize various risks in supply chains. An exhaustive literature review complimented with the experts’ opinion was undertaken from the perspective of SMEs to
formulate a hierarchical structure of risks in supply chains. A fuzzy analytic hierarchical process (F-AHP) is then utilized to ascertain the relative weightings which
are subsequently used to prioritize these risks. Understanding the priorities would
help the firms to accord importance and develop suitable strategies to manage supply
chain risks according to their relative importance. This provides effective management of scarce resources available to SMEs to manage risks resident in their supply
chains.
4.1 Introduction
In today’s interconnected and information based economies, there have been dramatic shifts in the way companies interact, driven by both new technologies and
new business models. This has led to firms’ exposure to new forms of risks, many
T. Wu, J. Blackhurst (eds.), Managing Supply Chain Risk and Vulnerability
© Springer 2009
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M.N. Faisal
related to their extended supply chains. Though firms’ recognize that the survival
in the modern business environment is no longer an issue of one firm competing
against another firm but has, instead, become an issue of one supply chain competing against another supply chain the understanding that failure of any one link in the
supply chain would have ripple effect on the overall supply chain has come rather
late. But there is a growing realization among the companies that adopting supply
chain risk management practices can yield continuous improvement of supply chain
operations (Elkins et al., 2005).
The risk in a supply chain is the potential variation of outcomes that influence
the decrease of value added at any activity cell in a chain, where the outcome is
described by the volume and quality of goods in any location and time in a supply
chain flow (Bogataj and Bogataj, 2007). The consequences of failing to manage risk
have also become more severe. In addition to the direct impact on revenue and profit,
disruptions in supply or demand can hurt a firm’s trading partners (e.g. customers
and suppliers), since the interconnectedness of a supply chain has a ripple effect
that affects the entire supply chain ecosystem (Shi, 2004). It is also reported that
companies experiencing such disruptions under-perform their peers significantly in
stock performance as well as in operating performance as reflected in costs, sales,
and profits (Hendricks and Singhal, 2003, 2005). Thus, management of risk is, or
should be, a core issue in the planning and management of any organization (Finch,
2004).
All the parts of supply chain could be impacted by a great variety of risks and the
supply chain risks can have significant impact on the firm’s short-term and long-term
performance. For the success of supply chain, the method to find ways of mitigating
supply chain risks is critical to manage supply chain in unstable environment. In
industries moving towards seamless supply chains the issue of supply chain risk
handling and risk sharing along the supply chain is a topic of growing importance
(Agrell, 2004; Gunasekaran et al., 2004). A key feature of supply chain risk is that,
by definition, it extends beyond the boundaries of the single firm and, moreover, the
boundary spanning flows can become a source of supply chain risks (Jüttner, 2005).
Thus, to assess supply chain risk exposures, companies must identify not only direct
risks to their operations, but also the potential causes or sources of those risks at
every significant link along the supply chain (Christopher et al., 2002; Souter, 2000).
The reasons that make an integrated approach to supply chain risks analysis and
management important are (Harland, 2003; Shi, 2004; Faisal et al., 2006):
• Examining risk factors in isolation makes it difficult to understand their interactions.
• There may be an increase in risk management costs, since firms may unnecessarily hedge certain risks that are in reality offset by others.
• A fragmented approach to risk management also increases the likelihood of ignoring important risks.
• ICT revolution has eliminated the geographical boundaries for developing supply
chain partnerships.
4 Prioritization of Risks in Supply Chains
43
• Even for known risks, it is important to consider their overall impact to the entire
organization. Otherwise mitigation attempts may only introduce new risks, or
shift the risk to less visible parts of the organization.
• Failure to consider risk interactions can also cause firms to grossly underestimate
their risk exposures.
There has been a recent surge in interest and publications from academics and practitioners regarding supply chain disruptions and related issues as supply chain risks
can potentially be harmful and costly for the whole supply chain (Craighead et al.,
2007). One important constituent of risk management process is the prioritization of
risks. Prioritization helps a company to focus the decision making and risk management effort on the most important risks (Hallikas et al., 2002). Prioritization requires
comparisons concerning the relative importance of each of the risk variables.
The purpose of this chapter is to contribute and provide a more complete understanding of risk in supply chains. It seeks to develop a model to assess relative
importance of numerous risks inherent in the supply chain. The primary aim is to
illustrate how organizations can prioritize risks in their supply chains. The main
research problems addressed by the study presented in this chapter are:
(1) What kinds of risks are associated with various supply chain flows?
(2) How these risks can be prioritized?
After introduction, the remainder of this chapter is organized as follows. Sect. 4.2
presents literature review on risk, supply chain risk management, and risk mitigation strategies for supply chains. Risk taxonomy for supply chain is presented in
Sect. 4.3. Next, Sect. 4.4 of the chapter discusses the methodology for prioritizing
supply chain risks. A graphical representation of the model is shown in Fig. 4.1. In
this part the numerical application of the proposed model for small and medium enterprises (SMEs) cluster is also discussed. Finally, Sect. 4.5 presents the concluding
remarks of the chapter.
4.2 Literature Review
4.2.1 Risk
On a very general level, risk is defined as the probability of variance in an expected
outcome and it differs from uncertainty in that risk has associated with it a probability of a loss and uncertainty is an exogenous disturbance (Spekman and Davis,
2004). According to Norrman and Jansson (2004) “risk is the chance, in quantitative
terms, of a defined hazard occurring. It therefore combines a probabilistic measure
of the occurrence of the primary event(s) with a measure of the consequences of
that/those event(s)”. So to manage risk both an assessment of the probability of risk
and its impact is necessary (Hallikas et al., 2002; Zsidisin et al., 2004; Hallikas et al.,
2004).
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M.N. Faisal
As companies increasingly move towards inter-firm co-operation to achieve sustained competitive advantage, research in risk management began to examine risk
management at the level of inter-organizational relationships and more recently at
the level of supply chains and networks (Harland et al., 2003). Risk is perceived to
exist when there is a relatively high likelihood that a detrimental event can occur and
that event has a significant associated impact or cost (Zsidisin et al., 2004). A key
feature of supply chain risk is that, the complexity makes it difficult for the exposed
company to estimate the total financial losses, which contributes to the impediment
in how to design risk mitigation solutions for supply chains. Current business trends
that increase the vulnerability to risks in supply chains are (Harland et al., 2003;
Normann and Jansson, 2004; Christopher and Lee, 2004; Cucchiella and Gastaldi,
2006):
•
•
•
•
•
•
•
•
•
increased use of outsourcing of manufacturing and R&D to suppliers;
globalization of supply chains;
reduction of supplier base;
more intertwined and integrated processes between companies;
reduced buffers;
shorter lead times requirements;
shorter product life cycles and compressed time-to-market;
increased product/service complexity; and
capacity limitation of key components.
4.2.2 Supply Chain Risk Management
The degree of the vulnerability of a supply chain is determined to a large extent by the degree of complexity of the network (Nieger et al., 2008). In recent times the complexity has increased many-fold due to firms’ focus on their
core competence and increased dependence on outsourcing. Top executives at
Global 1000 firms now consider supply chain disruptions and their associated
operational and financial risks to be their single most pressing concern (Craighead et al., 2007). Risk management in supply chain cannot be equated to disaster response. Rather, it means keeping an increasingly complex process moving efficiently at the lowest total cost and without compromising the quality of
the product or customer satisfaction (Hauser, 2003). Supply chain risk management (SCRM) is defined as “the process of risk mitigation achieved through collaboration, co-ordination and application of risk management tools among the
partners, to ensure continuity coupled with long term profitability of the supply
chain” (Faisal et al., 2007a). SCRM is still a fairly new field of research and
studies related to the topic are scarce (Ojala and Hallikas, 2006; Jüttner, 2005).
It should also be noted that risks cannot be completely eliminated from supply
chains but strategies can be developed to manage these risks if the dynamics between the variables related to risks in a supply chain are understood (Faisal et al.,
2006).
4 Prioritization of Risks in Supply Chains
45
It is important for supply chain managers to recognize that in taking action to
reduce known risks, they are changing the risk profile for that organization and for
others in the network (Peck, 2005). Thus, for mitigating risk in supply chains it is
required to expend the risk management focus from the companies’ own sites to suppliers and sub-suppliers. There is a need to work together in risk identification, assessment, management and business continuity planning and also of formal assessment of how suppliers are working with those issues and by putting requirements
into contracts (Normann and Jansson, 2004). Risk management skills which includes, awareness of risk signals, developing risk management plans, and improving
end to end information visibility are essential requirements for supply chain management success (Giunipero and Pearcy, 2000; Christopher and Lee, 2004). While
revisiting single-sourcing decisions and changing inventory management policies
will likely help maintain continuity during future crises, experts have clearly demonstrated, and logistics managers have candidly admitted, that firms need to vastly improve their disaster management planning for managing risk in supply chains (Hale
and Moberg, 2005).
4.2.3 Supply Chain Risk Mitigation Strategies
A risk management system is basically an action plan that specifies which risks can
be addressed, and how to address them (Shi, 2004). Elkins et al. (2005) suggest 18
best practices to mitigate supply chain risks. Companies may not need to implement
all 18 of the best practices to improve supply chain risk management capabilities.
Rather, they should prioritize these 18 best practices as some of these actions can
be taken with a minimal level of investment and should yield immediate benefits.
There should be a plan that identifies the short-term actions that can he deployed
with a minimum of investment and establish a roadmap for deploying intensive
project-team resources, business intelligence systems, and improved supply chain
infrastructure. SAM framework (Kleindorfer and Saad, 2005) for supply chain risk
management comprise three main tasks that have to be practiced continuously and
concurrently as the foundation of disruption risk management. The three tasks are:
Specifying sources of risk and vulnerabilities, Assessment, and Mitigation (SAM).
Further, to implement the three SAM tasks introduced above, the authors have formulated a set of 10 principles, derived from the industrial risk management and
supply chain literatures. Table 4.1 summarizes nine different robust supply chain
strategies that aim to improve a firm’s capability to better manage supply and/or demand under normal circumstances and to enhance a firm’s capability to sustain its
operations under risk (Tang, 2006).
With so many related risks and risk-mitigation approaches to consider, managers must do two things when they begin to construct a supply-chain risk management strategy. First, they must create a shared, organization-wide understanding
of supply-chain risk. Then they must determine how to adapt general risk-mitigation
approaches to the circumstances of their particular company. Managers can achieve
46
M.N. Faisal
Table 4.1 Risk mitigation strategies in supply chains
Robust Supply Chain
Strategy
Main Objective
Benefit(s) under
normal circumstances
Benefit(s) after a major
disruption
Postponement
Increases product
flexibility
Improves capability
to manage supply
Enables a firm to change
the configuration of different products quickly
Strategic Stock
Increases product
availability
Improves capability
to manage supply
Enables a firm to respond to market demand
quickly during a major
disruption
Flexible Supply Base
Increases supply
flexibility
Improves capability
to manage supply
Enables a firm to shift
production among suppliers promptly
Make-and-Buy
Increases supply
flexibility
Improves capability
to manage supply
Enables a firm to shift
production between inhour production facility
and suppliers rapidly
Economic Supply
Incentives
Increases product
availability
Improves capability
to manage supply
Enables a firm to adjust
order quantities quickly
Flexible
Transportation
Increases flexibility
in transportation
Improves capability
to manage supply
Enables a firm to change
the mode of transportation rapidly
Revenue Management Increases control
of product demand
Improves capability
to manage demand
Enables a firm to influence the customer
product selection dynamically
Dynamic Assortment
Planning
Increases control
of product demand
Improves capability
to manage demand
Enables a firm to influence the demands
of different products
quickly
Silent Product
Rollover
Increases control
of product exposure
to customers
Improves capability
to manage supply
and demand
Enables a firm to manage the demands of different products swiftly
Adapted from Tang (2006)
the former through stress testing and the latter through tailoring risk management
approaches (Chopra and Sodhi, 2004).
4.3 Supply Chain Risks Taxonomy
Supply chain structure is made up of interdependent parts that come together to
provide the required products and services to the satisfaction of the customers.
4 Prioritization of Risks in Supply Chains
47
Tied closely to this interdependence is the role of uncertainty within the supply chain (Sounderpandian et al., 2008). The literature in the risk management
field indicates that the primary sources of risk to the business organization may
be categorized into exogenous and endogenous (Ritchie and Brindley, 2000). In
a supply chain, risks can be classified into two types: risks arising from within
the supply chain network and risks external to it. For the former, the attributes
are due to the interaction between firms across the entire supply chain network.
This set of internal risks can encompass supply risk, demand risk, and trade
credit risk for instance. External risks, on the other hand, arise from the interactions between the supply chain network and its environment, such as international terrorism, and natural disasters like SARS (Goh et al., 2007). Jüttner et al.
(2002) suggest organizing risk sources relevant for supply chains into three categories: external to the supply chain, internal to the supply chain, and network related.
Following Cavinato (2004), Spekman and Davis (2004), and Jüttner (2005) risks
in supply chains are classified under four sub-chains, physical, financial, informational, and relational. Physical sub-chain, represent traditionally viewed logistics,
in the form of transportation, warehousing, handling, processing, manufacturing,
and other forms of utility activities. Financial sub-chain working in parallel deals
with the supply chain’s flow of money while informational sub-chains parallel the
physical and financial chains through the processes and electronic systems used for
creating events and triggered product movements and service mobilization. Relational sub-chains relate to the chosen linkages between buyers, sellers, and logistics
parties in between them.
4.3.1 Risks in Physical Sub-Chain
Risks in the actual movements and flows within and between firms, transportation,
service mobilization, delivery movement, storage, and inventories can be termed as
the risk in physical flow of the supply chain (Cavinato, 2004). Traditionally, most of
the earlier definitions of risk in supply chains found in literature took only the physical flow of goods into consideration (Spekman and Davis, 2004). Many of the risk
in the physical flow are difficult to anticipate and consequently formal risk management approaches fails to mitigate them. Prominent among this class are those risk
which have a low probability of occurrence but high impact like disruption risks.
Supplier capacity constraint is a form of risk in physical sub-chain. Constraints exist that restrict a supplier’s ability to make rapid changes to varying demands (Zsidisin et al., 2000). Risk in physical sub-chain can also exist in form of fluctuations
of demand, such as those caused by the “bullwhip effect” and may tax a supplier
beyond its abilities. A supplier may not have extra equipment, available employees, or the ability to obtain necessary inputs to handle rapid spurts in demand. On
the other hand, it may also be difficult for suppliers to utilize excess “slack” during
order declines, which makes it difficult to attain profits from excess capacity. Phys-
48
M.N. Faisal
ical sub-chain is also impacted by quality-related risks that can cause significant
detrimental effects on the purchasing organization, with a cascading effect through
the supply chain to the final consumers. Each link within a supply chain is dependent on the other links to meet product or service requirements. Quality failures can
stem from the failure of suppliers to maintain capital equipment, lack of supplier
training in quality principles and techniques, and damage that occurs in transit (Zsidisin et al., 2000). Risks in physical sub-chain may be further classified as shown
Table 4.2.
Table 4.2 Categories of risk in physical sub-chain
SN
Type of risk
Reference(s)
Remarks
1.
Delays (DL)
Chopra and Sodhi (2004)
Due to high utilization or
another cause of inflexibility
of suppliers
2.
Disruptions (DS)
Very unpredictable but
of high impact.
3.
Supplier capacity constraints (CC)
Chopra and Sodhi (2004);
Finch (2004); Johnson
(2001); Hale and Moberg
(2005); Peck (2005)
Zsidisin et al. (2000); Giunipero and Eltantawy (2004)
4.
Production technological
changes (TC)
Zsidisin et al. (2000); Giunipero and Eltantawy (2004)
Supplier not able to produce
items to necessary demand
level and at a competitive
price
5.
Transportation (TR)
Cavinato (2004); Speckman
and Davis (2004); Svensson,
(2004); Peck (2005)
Pertinent in case of logistics
outsourcing as is the case
of 3PL
6.
Inventory (IN)
Chopra and Sodhi (2004)
Excess inventory for products with high value or short
life cycles can get expensive
7.
Procurement (PR)
Hallikas et al. (2002);
Chopra and Sodhi (2004)
Unanticipated increases
in acquisition costs
8.
Capacity Inflexibility (CI)
Facility fails to respond
to changes in demand
9.
Design (DG)
Chopra and Sodhi (2004);
Johnson (2001); Giunipero
and Eltantawy (2004);
Svensson (2004)
Zsidisin et al. (2000);
Speckman and Davis (2004)
Treleven and Schweikhart
(1988); Zsidisin et al.
(2000); Svensson (2004);
Sounderpandian et al.
(2008)
If suppliers plants don’t
have quality focus
10.
Poor quality (PQ)
Unable to handle sudden
spurt or to utilize excess
slack
Suppliers’ inability to incorporate design changes
4 Prioritization of Risks in Supply Chains
49
4.3.2 Risks in Financial Sub-Chain
Risks in supply chains due to the flows of cash between organizations, incurrence
of expenses, and use of investments for the entire chain/network, settlements, A/R
(accounts receivables) and A/P (accounts payables) processes and systems can be
classified under financial risks. Financial risks also include factors like settlement
process disruption, improper investments, and not bringing cost transparency to the
overall supply chain (Cavinato, 2004). In case of strategic alliances the risk of financial stability of alliance partners is crucial for supply chain success (Giunipero and
Eltantawy, 2004). According to Peck (2005), managing risks in financial sub-chain
is not an easy task as disruptions due to macroeconomic vacillations like currency
fluctuations or due to strained relations among nations are difficult to predict and
are beyond the direct control of supply chain managers and business strategists.
A better understanding of the causal relationship between supply chain performance and financial measures is critical to both supply chain and financial managers
(Tsai, 2008). Financial risks can also present themselves through the risk of reworking stock and penalties for non-delivery of goods (Christopher and Lee, 2004).
When a firm has operations in multiple countries, changes in foreign exchange rates
can have a significant impact on both the income statement and the balance sheet.
Price changes for commodities such as oil and electricity can have an impact on supply chain costs and price changes for commodities like steel and copper can affect
the cost of goods sold. Labor-intensive enterprises in many developing countries
have felt great pressure from the rise of labor-related costs, such as wages and costs
to improve working conditions. A January 2006 report by American Chamber of
Commerce in China found that rising labor costs significantly decreased margins
in 48% of U.S. manufacturers in China (Jiang et al., 2007). Changing economic
scenario in key markets are also a major source of risk in financial sub-chain e.g.
recent recession in US economy has severely dented the profit margins of many of
the firms in India that used to have major chunk of their products being exported to
US markets. Major risks in financial sub-chain are represented in Table 4.3.
4.3.3 Risks in Relational Sub-Chain
This dimension of risk concerns the degree of interdependence among partners and
the tendency of a partner to act in its own self interest to the detriment of other
supply chain members (Spekman and Davis, 2004). Supply chains are entities of interdependent parts which come together to provide the product /service to the final
customer. The type of the relationship is likely to have an effect on the supply chain
risks (Ojala and Hallikas, 2006). Though in supply chain literature long term collaborative relationships are recommended (Mentzer et al., 2000; Barratt and Oliveira,
2001; Callioni and Billington, 2001), companies particularly SMEs competing on
the basis of low cost depend on short term cost based relationships with their part-
50
M.N. Faisal
Table 4.3 Categories of risk in physical sub-chain
SN
Type of risk
Reference(s)
Remarks
1.
Cost/price risk (CR)
Treleven and Schweikhart
(1988); Zsidisin et al. (2000)
Concerns competitive cost
risk
2.
Business risks (BR)
Zsidisin et al. (2000)
Concerns financial stability
of the supplier
3.
Fiscal risks (FR)
Harland et al. (2003)
Arises through changes
in taxation
4.
Untimely payments (UT)
Speckman and Davis
(2004); Shi (2004)
Loss of goodwill and may
impact much on SMEs
5.
Settlement process disruption (SP)
Cavinato (2004)
Leads to delay in payments
and impacts SC profitability
6.
Volatile oil prices (OP)
Faisal et al. (2006)
Impacts inbound
and outbound costs
7.
Lack of hedging (LH)
Speckman and Davis (2004)
Disastrous in case
of bankruptcy of partners
in the SC
8.
Investment risks (IR)
Hallikas et al. (2002); Ojala
and Hallikas (2006)
Caused by economic
fluctuations in the market
9.
Unstable pricing (UP)
Speckman and Davis (2004)
May lead to lack of trust
among SC partners
Exchange rate risks/
currency fluctuations (ER)
Chopra and Sodhi (2004);
Peck (2005)
Impacts the procurement
strategy of the firm
10.
ners. In cost based relationships the firms do not share information and partners are
switched frequently thus giving rise to risks in relational sub-chains as enunciated
below.
4.3.3.1 Reputational Risk (RR)
Outsourcing from low cost destinations is fraught with dangers of associated risks
arising from moral issues like child labor, labor health, safety, and welfare in developing countries. Consumers are shunning products that contain materials manufactured under sweatshop labor conditions (Jiang et al., 2007). The cases of labor abuse
in the sporting goods and apparel industry, recent being that of Primark show that
such negative publicity can damage brands and erode market positions substantially
(Zadek, 2004; Harland et al., 2003; Frenkel and Scott, 2002).
4 Prioritization of Risks in Supply Chains
51
4.3.3.2 Lack of Trust and Opportunism Risk (TOR)
One of the most important factors affecting the entire process of supply chain management is the trust among the trading partners (Sinha et al., 2004). Trust may concern a partner’s willingness to perform according to agreements, or the intention to
do so. Risks exist if the party is not competent to act or if the party chooses not to
act (Spekman and Davis, 2004). Lack of trust may also lead to opportunism, where
one supply chain partner acts in its own self-interest to the detriment of others.
4.3.3.3 Legal Risk (LR)
These risks expose the firms to litigation with action arising from customers, suppliers, shareholders, and employees (Harland et al., 2003).
4.3.3.4 Intellectual Property Rights Risk (IPR)
Increased reliance on outsourcing creates a loss of control and a risk of losing proprietary information shared between parties (Giunipero and Eltantawy, 2004). If
there are no predefined rules and the organizations are not careful regarding the dissemination of information to its suppliers, the probability of losing the proprietary
information is high. Today suppliers may work for different organizations at the
same time and in general the enforcement mechanisms related to intellectual property are weak in many developing countries and thus there is a risk that proprietary
information may be leaked to competitors.
4.3.4 Risks in Informational Sub-Chain
Risks associated with materials flows are not unrelated to the risks associated with
information flows. Orders that are transmitted incorrectly, a lack of transparency
and visibility in the supply chain, or hesitancy in sharing accurate and timely information with partners, all contribute to a supply chain’s inability to perform as
intended (Spekman and Davis, 2004). So based on the type of impact that different
information risks have on the supply chain, they can be broadly classified as (Faisal
et al., 2007b):
4.3.4.1 Information Security/Breakdown Risks (SR)
Today computer based information systems are central to the supply chain and thus
their failure can result in a substantial cost. In general this cost can be immediate lost
sales, emergency service cost, cost of restoring data, and long-term loss of customer
goodwill (Cardinali, 1998). Security is defined as the protection of data against accidental or intentional disclosure to unauthorized persons, or unauthorized modifications or destruction. It is a careful balance between information safeguard and user
52
M.N. Faisal
access (McFadden, 1997). Information security risks arise from hackers, viruses and
worms, distributed denial of service attacks or even the internal employee frauds of
the organization. Terrorist attacks like 9/11 and natural disasters like Hurricanes,
Tsunami have made organizations to rethink their information security strategies.
4.3.4.2 Forecast Risks (FR)
Forecast risks results from a mismatch between a company’s projections and actual
demand (Chopra and Sodhi, 2005). All kinds of information distortions in a supply
chain, often lead to the risks of bullwhip (Piplani and Fu, 2005). It creates situations
where the orders to the supplier tend to have larger fluctuations than sales to the
customer.
4.3.4.3 Information Systems/Information Technology Outsourcing Risk (OR)
IS/IT outsourcing is broadly defined as a decision taken by an organization to
contract-out or sell the organization’s IT assets, people and/or activities to a third
party supplier, who in exchange provides and manages assets and services for monetary returns over an agreed time period (Kern and Willcocks, 2000). IT outsourcing
risks include opportunism by vendors, hidden costs, loss of control, poaching, and
information security apprehensions.
4.4 Methodology
The analytic hierarchy process (AHP) developed by Saaty (1980) is a multi-criteria
decision-making tool that can handle unstructured or semi-structured decisions with
multi-person and multi-criteria inputs. It also allows users to structure complex
problems in the form of a hierarchy or a set of integrated levels. In addition to
this, AHP is easier to understand and can effectively handle both qualitative and
quantitative data (Durán and Aguilo, 2008). The AHP attracted the interest of many
researchers for long because of its easy applicability and interesting mathematical
properties (Sasamal and Ramanjaneyulu, 2008). AHP involves the principles of decomposition, pair wise comparisons, and priority vector generation and synthesis.
Though the purpose of AHP is to capture the expert’s knowledge, the conventional AHP still cannot reflect the human thinking style. In spite of its popularity,
this method is often criticized because of a series of pitfalls associated with the AHP
technique which can be summarized as follows (Durán and Aguilo, 2008):
• Its inability to adequately handle the inherent uncertainty and imprecision associated with the mapping of the decision-maker’s perception to exact numbers.
• In the traditional formulation of the AHP, human’s judgments are represented
as exact (or crisp, according to the fuzzy logic terminology) numbers. However,
in many practical cases the human preference model is uncertain and decision-
4 Prioritization of Risks in Supply Chains
53
makers might be reluctant or unable to assign exact numerical values to the comparison judgments.
• Although the use of the discrete scale of 1–9 has the advantage of simplicity, the
AHP does not take into account the uncertainty associated with the mapping of
one’s judgment to a number.
A good decision-making models needs to tolerate vagueness or ambiguity since
fuzziness and vagueness are common characteristics in many decision-making problems (Yu, 2002). Due to the fact that uncertainty should be considered in some or all
of the pairwise comparison values, the pairwise comparison under traditional AHP,
which needs to select arbitrary values in the process, may not be appropriate (Yu,
2002). Thus the use of fuzzy numbers and linguistic terms may be more suitable,
and the fuzzy theory in AHP should be more appropriate and effective than traditional AHP in an uncertain pairwise comparison environment (Kang and Lee, 2007).
Fuzzy set theory bears a resemblance to the logical behavior of human brain when
faced with imprecision (Cakir and Canbolat, 2008). It has the advantage of mathematically representing uncertainty and vagueness and provides formalized tools for
dealing with the imprecision intrinsic to many problems (Chan and Kumar, 2007).
Although the purpose of the original AHP was to capture expert knowledge,
conventional AHP did not truly reflect human cognitive processes-especially in the
context of problems that were not fully defined and/or problems involving uncertain
data (so-called “fuzzy” problems) (Fu et al., 2006). Laarhoven and Pedrycz (1983)
therefore introduced the concept of “fuzzy theory” to AHP assessments. This socalled “fuzzy analytic hierarchical process” (fuzzy AHP) was able to solve uncertain “fuzzy” problems and to rank excluded factors according to their weight ratios. The research presented in this chapter prefers Chang’s extent analysis method
(Chang 1992, 1996) since the steps of this approach are relatively easier than the
other fuzzy AHP approaches and similar to the conventional AHP (Büyüközkan
et al., 2008; Bozbura et al., 2007; Büyüközkan, 2008; Chan and Kumar, 2007).
Fuzzy-AHP has been widely used for prioritization purposes like prioritization of
organizational capital (Bozbura and Beskese, 2007), key capabilities in technology
management (Erensal et al., 2006), prioritization of human capital measurement indicators (Bozbura et al., 2007), adoption of electronic marketplaces (Fu et al., 2006),
and supply base reduction (Sarkar and Mohapatra, 2006).
A fuzzy number is a special fuzzy set F D fx 2 RjF .x/g, where x takes its
values on the real line R1 W 1 < x < C1 and F .x/ is a continuous mapping
from R1 to the close interval Œ0; 1. A triangular fuzzy number can be denoted as
M D .l; m; u/. Its membership function M .x/ W R ! Œ0; 1 is equal to:
8
0;
x < l or x > u ;
<
l x m;
M .x/ D .x l/=.m l/ ;
(4.1)
:
.x u/=.m u/ ;
m x u:
Where l m u, l and u stand for the lower and upper value of the support of M ,
respectively, and m is the mind-value of M . When l D m D u, it is a non fuzzy
number by convention. The main operational laws for two triangular fuzzy numbers
54
M.N. Faisal
M1 and M2 are as follows (Kauffman and Gupta, 1991):
M1 C M2 D .l1 C l2 ; m1 C m2 ; u1 C u2 / ;
M1 ˝ M2 .l1 l2 ; m1 m2 ; u1 u2 / ;
˝ M1 D .l1 ; m1 ; u1 /; > 0; M11 .1=u1 ; 1=m1 ; 1= l1 / :
(4.2)
Let X D fx1 ; x2 ; : : :; xn g be an object set, and U D fu1 ; u2 ; : : :; um g be a goal set.
According to the method of Chang’s extent analysis model, each object is taken and
extent analysis for each goal, gi , is performed respectively (Chang, 1992, 1996).
Therefore, m extent analysis values for each object can be obtained with the following signs:
(4.3)
Mg1 i ; Mgmi ; i D 1; 2; : : : ; n :
Where all the Mgj i .j D 1; 2; : : :; m/ are triangular fuzzy numbers. A triangular
fuzzy number can be denoted as M D .l; m; u/ where l m u, l and u stand for
the lower and upper value of the support of M , respectively, and m is the mid-value
of M .
The steps of the improved Chang’s extent analysis model, which is applied in
this chapter, can be given as follows:
Step 1: The value of fuzzy synthetic extent with respect to the i th object is defined
as:
31
2
m
m
n X
X
X
j
j
Mg i ˝ 4
Mg i 5 :
(4.4)
Si D
j D1
i D1 j D1
Pm
j
j D 1 Mg i ,
To obtain
perform the fuzzy addition operation of m extent analysis
values for a particular matrix such that
0
1
m
m
m
m
X
X
X
X
Mgj i D @
lj ;
mj ;
uj A
(4.5)
j D1
and to obtain
Mgj i .j
hP
n
j D1
Pm
i D1
j
j D1
j D1
i1
j D 1 Mg i
, perform the fuzzy addition operation of
D 1; 2; : : :; m/ values such that
m
n X
X
i D1 j D1
Mgj i
D
n
X
i D1
li ;
n
X
i D1
mi ;
n
X
i D1
!
ui
(4.6)
4 Prioritization of Risks in Supply Chains
55
and then compute the inverse of the vector in (4.6) such that
0
1
2
31
B
C
n X
m
X
B 1
1
1 C
C:
4
Mgj i 5 D B
;
;
BX
C
n
n
n
X
X
@
A
i D1 j D1
ui
mi
li
i D1
i D1
(4.7)
i D1
The principles for the comparison of fuzzy numbers were introduced to derive the
weight vectors of all elements for each level of the hierarchy with the use of fuzzy
synthetic values. We now discuss these principles that allow the comparison of fuzzy
numbers. (Zhu et al., 1999).
Step 2: The degree of possibility of M2 M1 is defined as
V .M2 M1 / D sup Œmin .M1 .x/; M2 .y// ;
(4.8)
y x
where sup represents supremum (i.e., the least upper bound of a set) and when a pair
(x; y) exists such that y x and M1 .x/ D M2 .y/, then we have V .M2 M1 / D 1.
Since M1 D .l1 ; m1 ; u1 / and M2 D .l2 ; m2 ; u2 / are convex fuzzy number it
follows that:
V .M2 M1 / D hgt.M1 \ M2 / D M2 .d /
(where the term hgt is the height of fuzzy numbers on the intersection of M1 and M2 )
8
< 1; if m2 m1
M 2.d / D 0; if l1 u2
:
(4.9)
:
l1 u2
.m1 u2 /.m1 l1 /
Where d is the crossover point’s abscissa of M1 and M2 . To compare M1 and M2; we
need both the values of V .M1 M2 / and V .M2 M1 /.
Step 3: The degree of possibility for a convex fuzzy number to be greater than k
convex fuzzy numbers Mi (i D 1, 2, : : :, k) can be defined by
V .M M1 ; M2 ; : : :; Mk /
D V Œ.M M1 / and M M2 and : : : and .M Mk /
D min V .M Mi /;
i D 1; 2; 3; : : :; k
Assume that
d 0 .Ai / D min V .Si Sk / ;
(4.10)
for k D 1; 2; : : :; n; k ¤ i . Then the weight vector is obtained as follows:
W 0 D .d 0 .A1 /; d 0 .A2 /; : : :; d 0 .An //T :
(4.11)
Where Ai (i D 1; 2; : : :; n) are n elements.
Step 4: After normalization, the normalized weight vectors are,
W D .d.A1 /; d.A2 /; : : :; d 0 .An //T :
Where W is not a fuzzy number.
(4.12)
56
M.N. Faisal
4.4.1 A Numerical Application
As previously mentioned, in the third step of the framework, fuzzy AHP methodology is applied for weight determination. The sub-chains together with related risks
are represented in Fig. 4.1.
In order to perform a pairwise comparison among the requirements, the linguistic
scale as proposed by Büyüközkan (2008) and Büyüközkan et al. (2008) is adopted in
this chapter. The scale is depicted in Fig. 4.2 and the corresponding explanations are
provided in Table 4.4. Figure 4.2 shows the triangular fuzzy numbers M = (l; m; u/
where l m u, l and ustand for the lower and upper value of the support
of M , respectively, and m is the mid-value of M . Similar to the importance scale
defined in Saaty’s classical AHP (Saaty, 1980), five main linguistic terms are used to
compare the criteria: “equal importance (EI)”, “moderate importance (MI)”, “strong
importance (SI)”, “very strong importance (VSI)” and “demonstrated importance
(DI)”. Further, their reciprocals: “equal unimportance (EUI)”, “moderate unimportance (MUI)”, “strong unimportance (SUI)”, “very strong unimportance (VSUI)”
and “demonstrated unimportance (DUI)” have also been considered. For instance,
if criterion A is evaluated “strongly important” than criterion B, then this answer
means that criterion B is “strongly unimportant” than criterion A.
Level 1:
Objective
Level 2:
Sub-chains
Level 3:
Sub-chain
risks
Prioritization of Supply Chain Risks
Physical
Sub-chain
Financial
Sub-chain
Relational
Sub-chain
Informational
Sub-chain
DL
CR
RR
SR
DS
BR
LR
OR
CC
FR
TOR
FR
TC
UT
IPR
TR
SP
IN
OP
PR
LH
CI
IR
DG
UP
PQ
ER
Fig. 4.1 A hierarchy based model of supply chain risks
4 Prioritization of Risks in Supply Chains
57
µx
MI
SI
VSI
DI
1
x
1/2
1
3/2
2
5/2
3
Fig. 4.2 Triangular fuzzy importance scale
Table 4.4 Triangular fuzzy importance scale
Linguistic Scale
Explanation
Triangular
fuzzy Scale
Triangular fuzzy
reciprocal scale
Equal Importance (EI)
Moderate Importance (MI)
Strong Importance (SI)
Very Strong Importance (VSI)
Two requirements are the same importance
(1, 1, 1)
(1, 1, 1)
Experience and judgement slightly favor
one requirement over another
Experience and judgement strongly favor
one
A requirement is favored very strongly
over another; its dominance demonstrated
in practice
The evidence favoring one requirement
over another is the highest possible order
of affirmation
( 1/2, 1, 3/2)
(2/3, 1, 2)
(1, 3/2, 2)
(1/2, 2/3, 1)
(3/2, 2, 5/2)
(2/5, 1/2, 2/3)
(2, 5/2, 3)
(1/3, 2/5, 1/2 )
Demonstrated
Importance (DI)
Adapted from Büyüközkan (2008)
The proposed model was evaluated for small and medium enterprises (SMEs)
cluster. A group of experts consisting of academics and professionals were asked
to make pairwise comparisons for the sub-chains and their related risks mentioned
in Sect. 4.5. A questionnaire (see Appendix A) is provided to get the evaluations.
The overall results could be obtained by taking the geometric mean of individual
Table 4.5 Fuzzy evaluation matrix with respect to goal
Physical sub-chain (PSC)
Financial sub-chain (FSC)
Relational sub-chain (RSC)
Informational sub-chain (ISC)
(PSC)
(FSC)
(RSC)
(ISC)
(1, 1, 1)
(1, 3/2, 2)
(2/3, 1, 2)
(2/5, 1/2, 2/3)
(1/2, 2/3, 1)
(1, 1, 1)
(1/2, 2/3, 1)
(2/5, 1/2, 2/3)
(1/2, 1, 3/2)
(1, 3/2, 2)
(1, 1, 1)
(2/3, 1, 2)
(3/2, 2, 5/2)
(3/2, 2, 5/2)
(1/2, 1, 3/2)
(1, 1, 1)
58
M.N. Faisal
evaluations. However, since the group of experts came up with a consensus by the
help of the Delphi Method in this case, a single evaluation could be obtained to represent the group’s opinion (Bozbura et al., 2007; Büyüközkan, 2008) as represented
in Table 4.5 for relative importance of sub-chain risks.
The values of fuzzy synthetic extents with respect to the sub-chain are calculated
by applying formula (4.1) as below
RPSC D .3:5; 4:66; 6/ ˝ .0:0428; 0:0577; 0:0762/
RFSC
D .0:1498; 0:2688; 3:4572/ ;
D .4:5; 6; 7:5/ ˝ .0:0428; 0:0577; 0:0762/
D .0:1926; 0:3462; 0:5715/ ;
RRSC D .2:66; 3:66; 5:5/ ˝ .0:0428; 0:0577; 0:0762/
RISC
D .0:1138; 0:2111; 0:4191/ ;
D .2:46; 3; 4:33/ ˝ .0:0428; 0:0577; 0:0762/
D .0:1052; 0:1731; 0:3299/ :
The degrees of possibility are calculated using these values and formula (4.5) as
below:
V .RPSC RFSC / D 0:1926 0:4572=.0:2688 0:4572/ .0:3462 0:1926/
D 0:7736 ;
V .RPSC RRSC / D 1:00 ;
V .RPSC RISC / D 1:00 ;
V .RFSC RPSC / D 1:00 ;
V .RFSC RRSC / D 1:00 ;
V .RFSC RISC / D 1:00 ;
V .RRSC RPSC / D 0:1498 0:4191=.0:2111 0:4191/ .0:2688 0:1498/
D 0:8235 ;
V .RRSC RFSC / D 0:1926 0:4191=.0:2111 0:4191/ .0:3462 0:1926/
D 0:3289 ;
V .RRSC RISC / D 1:00 ;
V .RISC RPSC / D 0:1498 0:3299=.0:1731 0:3299/ .0:2688 0:1498/
V .RISC
D 0:6530 ;
RFSC / D 0:1926 0:3299=.0:1731 0:3299/ .0:3462 0:1926/
D 0:4423 ;
V .RISC RRSC / D 0:1138 0:3299=.0:1731 0:3299/ .0:2111 0:1138/
D 0:8504 :
4 Prioritization of Risks in Supply Chains
59
The weight vector of the main factors of the hierarchy can be calculated by using
the formulas (4.10) and (4.6) as below:
d 0 (PhysicalSC) D V .RPSC RFSC ; RRSC ; RISC /
D min.0:7736; 1; 1/ D 0:7736 ;
d 0 (FinancialSC) D V .RFSC RPSC ; RRSC ; RISC /
D min.1; 1; 1/ D 1 ;
d 0 (RelationalSC) D V .RRSC RPSC ; RFSC ; RISC /
D min.0:8235; 0:3289; 1/ D 0:3289 ;
d 0 (InformationalSC) D V .RISC RPSC ; RFSC ; RISC /
D min.0:6530; 0:4423; 0:8504/ D 0:4423 ;
0
W D .0:7736; 1; 0:3289; 0:4423/T :
Hence, via normalization, the normalized vectors of Physical, Financial, Relational,
and Informational sub-chains risks are obtained as below:
Wobjective D .0:3039; 0:3929; 0:1292; 0:1738/T
In a similar way, the importance weights of the risks within physical sub-chain are
calculated as follows
W D.d.DL/; d.DS/; d.CC/; d.TC/; d.TR/; d.IN/; d.PR/; d.CI/;
WPhysical
d.DG/; d.PQ//T
D.0:1123; 0:0679; 0:1231; 0:0697; 0:1298; 0:0753; 0:0526; 0:1336;
0:0579; 0:1666/T :
It is observed that for the physical sub-chain poor quality, capacity inflexibility,
transportation risks, product technological changes are more important than other
risks.
In a similar way, the importance weights of the risks within financial sub-chain
are calculated as follows
W D.d.CR/; d.BR/; d.FR/; d.UT/; d.SP/; d.OP/; d.LH/; d.IR/;
WFinancial
d.UP/; d.ER//T ;
D.0:1121; 0:0893; 0:0547; 0:1443; 0:0582; 0:1204; 0:1318; 0:0357;
0:1158; 0:1377/T :
It can be concluded that for financial sub-chain untimely payments, lack of hedging,
and volatile oil prices emerge as the most important risks. In a similar way, the
60
M.N. Faisal
importance weights of the risks within relational sub-chain are calculated as follows
W D .d.RR/; d.TOR/; d.LR/; d.IPR//T ;
WRelational D .0:2881; 0:2493; 0:2712; 0:1924/T :
For relational sub-chain, reputational risks and lack of trust and opportunism risk
seem to appear more important than other risks. In a similar way, the importance
weights of the risks within informational sub-chain are calculated as follows
W D .d.SR/; d.FR/; d.OR//T
WInformational D .0:3799; 0:3761; 2440:/T :
It can be concluded that for informational sub-chain forecast risks emerges as the
most important risk.
Finally, considering the obtained results, composite priority weights for supply
chain risks can be calculated as given in Table 4.6.
Table 4.6 Composite priority weights for supply chain risks
Sub-chain
Local
weights
Sub-chain
risks
Local
weights
Global
weights
Physical
0.3039
DL
DS
CC
TC
TR
IN
PR
CY
DG
PQ
0.1123
0.0679
0.1231
0.0697
0.1298
0.0753
0.0526
0.1336
0.0579
0.1666
0.0341
0.0206
0.0374
0.0212
0.0394
0.0229
0.0159
0.0406
0.0176
0.0506
Financial
0.3929
CR
BR
FR
UT
SP
OP
LH
IR
UP
ER
0.1121
0.0893
0.0547
0.1443
0.0582
0.1204
0.1318
0.0357
0.1158
0.1377
0.0440
0.0351
0.0215
0.0567
0.0229
0.0473
0.0518
0.0140
0.0455
0.0541
Relational
0.1292
RR
LR
TOR
IPR
0.2881
0.2493
0.2712
0.1924
0.0372
0.0322
0.0350
0.0248
Informational
0.1738
SR
FR
OR
0.3799
0.3761
0.2440
0.0660
0.0653
0.0424
4 Prioritization of Risks in Supply Chains
61
Based on the values in Table 4.6 it can be concluded that forecast risks, system
breakdown/security risks, untimely payment risks, exchange rate risks, lack of hedging risks, quality risks are the most important risks in supply chains as perceived by
small and medium enterprises.
4.5 Concluding Remarks
A very important task in risk management is to establish those risk factors that are
important to a particular company. With the help of this assessment the company
is able to focus its resources more efficiently. The model presented in this chapter
would help the practitioners to assign relative importance to various risks in a supply
chain and develop plans accordingly to mitigate them.
Despite the recent surge in academic and practitioner publications regarding supply chain risks, the research presented in this chapter provides an additional value to
the body of knowledge and consequently to managerial decision making. Because
of the subjective and intangible nature of the risk variables considered in the model,
the proposed methodology based on fuzzy-AHP framework provides a systematic
method and is more capable of capturing a human’s appraisal of ambiguity when
complex multi-attribute decision-making problems are considered.
For further research, the model developed in this chapter can be evaluated for
supply chains for large corporations. Also, other fuzzy multi-attribute approaches
such as fuzzy TOPSIS and fuzzy outranking methods can be used for the prioritization of supply chain risks. In future models we can also consider the interdependence
among various supply chain risks and in that case analytic network process (ANP)
approach that takes into account the dependence and feedback can be applied to
evaluate the model.
As risk is inherent in every link within a firm’s supply chain it is impossible to
completely insulate a supply chain from risks. But by understanding the sources of
risk and prioritizing them, firms can take a proactive view for reducing and managing these risks.
Appendix
Sample questions from the questionnaire used to facilitate comparisons of sub-chain
risks
Questionnaire
Read the following questions and put check marks on the pairwise comparison matrices. If an attribute on the left is more important than the one matching on the
right, put your check mark to the left of the “Equal importance” column, under the
62
M.N. Faisal
importance level (column) you prefer. On the other hand, if an attribute on the left is
less important than the one matching on the right, put your check mark to the right
of the importance “Equal Importance” column, under the importance level (column)
you prefer.
Questions
With respect to the overall goal “prioritization of the supply chain risks”,
2
3
4
5
6
p
RSR
Sub-chain risks
Demonstrated unimportance
RSR
p
ISR
PSR
FSR
p
FSR
PSR
Very Strong unimportance
PSR
Strong unimportance
Sub-chain risks
1
Moderate unimportance
Questions
Q6.
Equal Importance
Q5.
Moderate Importance
Q4.
Strong Importance
Q3.
Very Strong Importance
Q2.
How important are physical sub-chain risks (PSR) when compared with financial sub-chain risks (FSR)?
How important are financial sub-chain risks (FSR) when compared with relational sub-chain risk (RSR)?
How important are informational sub-chain risks (ISR) when compared with
financial sub-chain risks (FSR)?
How important are physical sub-chain risks (PSR) when compared with informational sub-chain risks (ISR)?
How important are physical sub-chain risks (PSR) when compared with relational sub-chain risks (RSR)?
How important are relational sub-chain risks (RSR) when compared with
informational sub-chain risks (ISR)?
Demonstrated Importance
Q1.
p
FSR
ISR
p
p
RSR
ISR
4 Prioritization of Risks in Supply Chains
63
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Chapter 5
A Generalized Simulation Framework
for Responsive Supply Network Management
Jin Dong, Wei Wang, and Teresa Wu
Abstract Firms are under the pressure to explore various strategies to improve the
supply network performance so that customers’ demands can be met more responsively. Many of the challenges from implementing the strategies lie in the distributed
and dynamic nature of the network where geographically dispersed entities may
have different goals and objectives. Additionally, irregularities and disruptions occurring at any point in the network may propagate through the network and amplify
the negative impact. These disruptions, often occurring without warning due to the
dynamic nature of a supply network, can lead to poor performance of the supply
network. A key component in responsive supply network management is to proactively assess the robustness and resilience to disruption of a supply network. Discrete
Event Simulation (DES) can achieve this. In this chapter, we introduce a simulation
tool developed by IBM China Research Lab, named General Business Simulation
Environment (GBSE). It can capture supply network dynamics with a fine level of
granularity and provide useful insights to supply network’s real operations. GBSE is
designed for tactical-level decision making, and may be useful for supply network
what-if analysis and risk analysis. The architecture of GBSE is detailed in this chapter followed by several scenarios in an automobile supply network to demonstrate
the applicability of GBSE to assess the responsiveness of a supply network.
5.1 Introduction
Supply network management focuses on integrating material flows and information
flows to increase the value and responsiveness for the customer. However, such integration is not an easy task due to the diversity of the participants in terms of size,
technological capabilities, culture differences and efficiencies (Blackhurst et al.,
2004). One additional difficulty is the risk inherent in the network, which refers
to the potential deviations from the original objectives. This can cause decreases in
value added activities at different levels in the netowrk. Therefore, to have a comT. Wu, J. Blackhurst (eds.), Managing Supply Chain Risk and Vulnerability
© Springer 2009
67
68
J. Dong, W. Wang, T. Wu
plex supply network with stable performance, risk assessment is an integral part of
the management process. A large number of analytical models (deterministic optimization, stochastic optimization) have been developed to study supply network
for profit maximization and risk minimization. However, these models suffer from
some shortfalls that limit their applications to supply network risk management:
(1) the size and complexity of a typical network means that the mathematical models can involve a very large number of variables and constraints. Maintaining such
models can be difficult while the computational burden can be heavy. (2) Many assumptions, such as the linearity assumption, to simplify the model may not hold
(Wu and O’Grady, 2004). On the other hand, discrete event simulation (DES) has
been proven valuable to be a practical tool for representing complex interdependencies, evaluating alternative designs and policies, and analyzing performance tradeoffs for supply chain systems (Hennessee, 1998; Chwif et al., 2002; Jain et al., 2002;
Venkateswaran et al., 2002; Enns and Suwanruji, 2003; Gan et al., 2000).
However, simulation is not without limitations. First, it is a challenge for the
analyst to determine the proper level of granularity. Secondly, many skills are required to create a simulation model, and sometimes it is necessary to write programming codes for special scenarios. Thirdly, a large volume data is required to
develop realistic simulation models. Lastly, it is time-consuming to run some simulations, for instance, it takes several hours to run one medium-size scenario (Dong
et al. (2006)). To address these issues, IBM China Research Lab developed a supply
chain simulation tool, named General Business Simulation Environment (GBSE),
which is a flexible and powerful software tool to help supply chain practitioners to
model, simulate and analyze their supply networks. GBSE is previously a part of
IBM SmartSCOR (Dong et al. (2006)), and it is usually used for making tactic-level
decisions. However, it does have the ability for developing interfaces, linking external tools for strategic and/or operational level models. GBSE has been applied to
study various supply networks such as wholesale industry and automobile industry,
just to name a few. In this study, of particular interest is the application of GBSE to
assess the robustness of a supply network, specifically, an automobile supply network. We first review supply chain simulation tools and framework followed by
detailed description of GBSE architecture. We then explain the development of the
supply chain simulation model developed using GBSE. Four scenarios are studied to
assess the supply chain performance with respect to varied demand forecasts, varied
selections of supplier, shipment and production.
5.2 Review of Supply Chain Simulation
Simulation has been commonly used tool to supply network management and several comprehensive surveys have been conducted to summarize the applications of
simulation. For instance, Kleijnen (2003) provides a survey of simulation in supply chain management and categorizes the simulation into four types: spreadsheet
simulation, system dynamics, discrete event simulation (DES) and business games.
5 A Generalized Simulation Framework for Responsive Supply Network Management
69
Terzi and Cavalieri (2004) focus on the architecture of the simulation and conduct
comparison studies between local monolithic simulation, parallel and distributed
simulation paradigms. Compared to local simulation, distributed simulation can
leverage computation resources from multiple machines to handle larger problems
within a shorter time. However, in supply chain simulation area, local simulation
is still popular because of its simplicity. In local simulation, Monte Carlo Simulation (MCS) and DES are two important methods. MCS is a light-weight static
method which can be implemented with spreadsheet based tools. It is very useful
for creating high-level models for preliminary results. DES is more computational
intensive methodology with the capability to handle the modeling and decisions in
great details.
Applicability of simulation for supply network decision-making has been well
studied. For instance, Lendermann et al. (2001) demonstrate the use of simulation
in semiconductor manufacturing. Its popularity is also reflected in industry applications. As early as in late last century, IBM developed a supply chain simulator, which
has a mix of simulation and optimization functions to model and analyze IBM supply chains (Bagchi et al., 1998). In 1999, IBM employed its own simulation-based
supply chain analyzer to visualize and quantify the effects of making changes on
a hypothetical supply chain, and the impact of the changes on system performance
(Archibald et al., 1999). Further, the need for executing supply chain simulations
based on a full-detailed model has also been pointed out: Jain et al. (1999) compare
two models with different levels of detail for semiconductor manufacturing supply
chains and concluded that simulations incorporating detailed models are required
when attempting to determine the correct inventory levels for maintaining desired
customer responsiveness. In these studies, abstracted models may result in inaccurate solutions that subsequently lead to erroneous decisions. Similar conclusions are
draw by Venkateswaran et al. (2002). Thus, it is necessary to develop a simulation
tool with fine granularity which enables accurate assessment of the supply network.
There exist a number of general purpose simulation tools for supply network
modeling including Arena, AnyLogic, AutoMod, just to name a few. When using
these tools, analysts usually create supply chain models with a set of pre-defined
logic elements, like CreateNode, DecisionNode, DisposeNode, etc. Most existing
tools have separate views for logic and presentation where logic view presents the
internal simulation logic with flow charts, decision trees, and presentation view
shows animations, charts, maps. While promising, the importance of the supply
network drives the effort to develop specific packages to simulate supply chain.
Swaminathan et al. (1998) propose a supply chain modeling framework, in which
supply chain models are composed from software components that represent types
of supply chain agents, their constituent control elements, and their interaction protocols. Rossetti and Chan (2003) discuss the design, development and testing of an
object-oriented prototype framework for supply chain simulation. Later on, Rossetti et al. (2006) develop a JSL (Java Simulation Library) based object-oriented
framework for simulating multi-echelon inventory systems. EasySC is a simulation
platform for understanding supply chains through studying the impact of stochastic
demands, logistics decisions and production policies on key performance measures
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J. Dong, W. Wang, T. Wu
(Liu et al., 2004). Supply Chain Guru (Supply Chain Guru, 2008) is a supply chain
simulation and optimization tool for enterprise strategic planning and targeted supply chain performance improvements. Other than these full scale frameworks and
systems reviewed above, numerous simulation libraries are available to facilitate
building simulation tools. Repast (Repast, 2008) and Scalable Simulation Framework (SSF, 2008) is one such example. As a leading firm in studying supply network
perfoamance, IBM China Research Lab recently developed a large scale Discrete
Event Simulation package, named GBSE which is extensible and flexible with user
friendly interfaces. This package has been applied to provide consulting solutions
to various industries ranging from wholesale industry, financial services to automobile industry. In the following section, the framework and architecture of GBSE is
explained in details.
5.3 GBSE: A Supply Chain Simulation Environment
Figure 5.1 illustrates a typical supply chain system modeled by GBSE. The supply
chain operation consists of two processes: planning and execution. The planning
process includes demand forecasting which is mainly based on historical order data
and supply planning which creates a supply commitment from components suppliers. The execution process starts at the order processing once the orders are received
from customers. The order fulfillment and scheduling module generates the pur-
Fig. 5.1 Functional components of a supply chain model
5 A Generalized Simulation Framework for Responsive Supply Network Management
71
chase orders to the suppliers as well as the premium shipping approvals which authorize the use of shipment modes (air vs. ocean in this study). The network process
models a general supply network consisting of supplier, manufacturing, distribution
and customers.
The simulation engine models six important components/functions of a supply
chain network including:
• Customer: representing external customers that issue orders to the supply chain,
based on demand forecast. GBSE also allows the user to set the desired service
level and priority for the customer.
• Manufacturing: modeling assembly process and keeping raw materials and finished goods inventory.
• Distribution: modeling distribution centers, including finished goods inventory
and material handling.
• Transportation: modeling transportation time, vehicle loading, and transportation costs.
• Forecasting: modeling demand forecast of products, including promotional and
stochastic demand.
• Inventory planning: modeling periodic setting of inventory target levels. Underlying this process is the GSBE optimization engine that computes recommended
inventory levels at various locations in the supply chain based on desired customer serviceability.
In addition, the simulation engine provides an animation module that allows users
to see how materials and information flow through the supply chain.
5.3.1 GBSE Architecture
As a flexible framework that can be extended to be compatible with other existing
system, GBSE is designed to have layered architecture (Fig. 5.2): data layer, controller layer, service layer, and presentation layer. The Data Layer manages all the
data in simulation; the Service Layer defines all the simulation processes; the ConFig. 5.2 GBSE architecture
Presentation Layer
Controller Layer
Service Layer
Data Layer
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J. Dong, W. Wang, T. Wu
troller Layer implements the simulation engine; and the Presentation Layer is the
interface to simulation analyst.
5.3.1.1 Data Layer
The Data layer manages all the simulation data, including configuration data, runtime data and report data. A non-trivial simulation model in general involves large
volume data. It is time-consuming to access and handle all the data, which prohibits the detailed study of a supply network. Thus, an efficient data access solution
is important to the success of simulation study. In GBSE, the data access layer is
built upon a relational database system which caches the data to manage the out-ofmemory issue. Data can be imported and exported to files with different formats, for
instance, Microsoft Excel files and CSV (Comma Separated Version) files.
5.3.1.2 Service Layer
The Service layer contains simulation services which are the finest unit in a simulation execution. Four types of data are associated with a service: configuration data,
input data, output data, and state data. Each service has its internal transactions to
operate on inputs and generate outputs. The behavior of services is controlled by the
configuration data with the runtime status being stored in state data. Note that the
Data layer is leveraged by Service layer to manage these four types of data. Simulation logic is implemented as one service or a combination of several services.
Services can be grouped as service bundles.
5.3.1.3 Controller Layer
The Controller layer is responsible for scheduling service events and dispatching
messages between services. A discrete event simulation (DES) engine and a simulation bus are implemented in this layer. The DES engine is the heart of the controller
layer. An event list is maintained in the engine, and events are scheduled to occur at
certain time point as services request. In a non-trivial simulation study, millions of
events can be in place at the same time, so it could be a big challenge for the DES
engine to handle them effectively. GBSE implements a built-in high-performance
DES engine. Meanwhile, it provides the interface to other external DES engines
which can leverage the usages between internal and external engines to optimize
the simulation executions upon design request. The simulation bus is the backbone
of the controller layer. All services are connected to the service bus and exchange
messages through it.
5 A Generalized Simulation Framework for Responsive Supply Network Management
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5.3.1.4 Presentation Layer
The Presentation layer is the interface to the end users. It helps users to build the
model, run the simulation, and perform analysis with reports. There are two perspectives: the modeling perspective (Fig. 5.3a) is used to create simulation model,
and the running perspective (Fig. 5.3b) is used to launch the simulation and monitor the process. In addition, we have implemented five functions in the presentation
layer: (1) create and edit the simulation model; (2) import and export the simulation
data; (3) control the simulation running; (4) monitor the simulation running status;
(5) generate and check the simulation report.
Fig. 5.3 a Modeling perspective. b Running perspective
5.3.2 GBSE for Supply Chain Simulation
The four layers explained above are leveraged to create simulation models through
the use of templates. A template is a module which consists of (1) simulation elements and (2) customized user interfaces. Each simulation element consists of data
definitions and services. Services can be reused in several simulation elements. As
an example, in GBSE we can have a template for a distribution network, and another
template for a banking system. In the distribution network template, simulation elements are distribution centers, warehouses, hubs, retails, routes, etc. In the banking system template, simulation elements are banking branches, ATMs, customers,
etc. GBSE provides different palettes for different templates. After applying a template to a model, analysts can drag elements from the palette and drop them to the
model. A uniform table editor is provided for editing data associated with each element. The particular interest in this study is the Supply Chain Simulation Template.
It implements supply chain model at tactical level, and allows analysts to create
a multi-period and multi-echelon supply chain model. The data structure, modeling
processes and performance measurement for a supply network are described.
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J. Dong, W. Wang, T. Wu
5.3.2.1 Data Structure
All data is managed in data layer and stored in database. Collecting and cleaning
up data is the one of the most time-consuming part of simulation modeling, and the
success of a simulation study depends on the quality of data directly. In GBSE, four
types of data are considered: Calendar, Product, Network and Configuration.
Calendar Data
GBSE adopts a multi-period simulation model. A period can be modeled as a day,
a week, a month, a quarter, or even a year. Depending on the expected granularity
of the model, different period definitions can be selected accordingly. Smaller period lengths mean finer granularity and thus more requirements on the data. Note
the simulation configuration data (discussed in Sect. 5.3.2.1) can be different for
different periods. This is useful to model time-changing parameters like seasonality
demand. The simulation outputs of different periods can be collected separately so
as to show the trends to the analysts. Supply chain planning is heavily relied on the
calendar data to define the planning horizons.
Product Data
The Product data represents the physical components flowing through the network
including finished goods, raw materials and intermediate products. It is not practical
to have the information of all the components in the network recorded, so analysts
need to select a proper subset since most configuration data is specific to certain
kinds of products. General information for products should be provided, such as
weight, dimension and brand. If manufacturing processes are taken into account,
analysts will need to determine bill of material (BOM), which defines the composition relationships between different levels of products. Again, analysts should make
the selection of the parts based on certain rules, such as selecting most expensive or
heaviest parts.
Network Data
A supply chain network consists of nodes and links. In GBSE simulation model, we
define three types of nodes (Customer, Supplier, and Facility) and one type of link
(Lane). Supplier nodes are the source of supply, and they are the origins of a supply
chain. Since there are no upstream nodes for suppliers, we assume the inventories
are replenished by rules. In addition, supply capacity is taken into consideration,
that is, the supply volume within specified periods can not exceed the allowed capability. Customer nodes are the source of demand, and they are final destinations of
a supply chain. Depending on the size of the supply chain, customers can be clus-
5 A Generalized Simulation Framework for Responsive Supply Network Management
75
tered to generate the demands at various levels ranging from a country to a shop.
Facility nodes are internal sites including warehouses, distribution centers, factories, retailers, wholesalers, etc. In GBSE, facilities are modeled with more details
than suppliers and customers to assist the study. Lanes are physical directed connections between nodes. Inbound lanes connect suppliers and facilities; outbound lanes
connect facilities and customers; inter-facility lanes connect facilities and facilities.
There should be no more than one lane between two nodes, but there can be multiple transportation modes associated with one lane. If geographical information is
provided, such as latitude and longitude, the supply chain network can be displayed
in a geographic information system (GIS) embedded in GBSE. This gives analysts
an intuitive view of the entire network.
Configuration Data
Configuration data refers to demand data, cost data, capacity data, lead time data,
policy data. Demand data is defined for Customer Nodes. Usually only aggregated
demand are available. GBSE can split the aggregated demand into a number of
orders. Cost data includes one-time transition cost, fixed cost and variable cost.
One-time transition cost is considered only under the situation that some existing
facilities are closed or some potential facilities are opened. Fixed cost applies for
specific products (defined by the analyst) while variable cost depends on product
volume. In a multiple period model, both fixed cost and variable cost are related
to periods, that is, for different periods, the costs can be different. Capacity data
consists of supply capacity, manufacturing capacity, storage capacity, handling capacity, transportation capacity. Lead time data represents manufacturing lead time,
transportation lead time, handling lead time, etc. Usually lead time is defined as
a random number. Policy data is parameters to different policies, for instance, the
batch size in transportation policy. There also exists other data such as customer
order interval, shipping shrinkage, manufacturing yield, budget, time threshold in
GBSE.
5.3.2.2 Supply Chain Modeling Processes
A process is a working unit at operational level which has its inputs and outputs, as
well as internal logic to handle inputs and generate outputs. Meanwhile, processes
can be controlled by local parameters and global parameters. In GBSE, all processes
are implemented as services in service layer.
Resource Management
In supply chain context, resources can be workers, trucks, drivers, and handling
equipment with limited capacities. GBSE implements a generic resource manage-
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J. Dong, W. Wang, T. Wu
ment framework in which the key components are resources in a resource pool.
A simulation task can request a resource from the pool, and return the resource to
the pool when the task is terminated. There are also cases that tasks can consume
specific resources, as a result, the resource pool will manage the replenishment.
Customer Order Generating Process
The Customer Order Generating Process applies to Customer Node. Usually, aggregated demand data is available for the customers. In the simulation, the aggregated
demand will be split into several waves. In each wave, one or more customer orders are generated and sent to corresponding facilities. Forecast errors are applied
to order quantity which reflects the demand uncertainty. Since the demand is split
into a few waves, the forecast error can be applied to either the total demand of the
period, or the order quantity in one wave.
Order Process
Once an order enters a facility, it will be first pre-processed followed by putting into
a prioritized order queue. The order queue will be checked periodically. For each
round, some orders will be released and leave the order queue to get processed. Orders with higher priority will leave the queue earlier than orders with lower priority.
An availability check is performed for each order to determine whether it can be
released. In GBSE, the on-hand stock is checked first. If the order can not be fulfilled at the on-hand stock level, the in-transit stock will be checked. At this step,
the due time needs to be estimated and compared with the arrival time of in-transit
shipments. In the cases that in-transit stock can not fulfill the order, special arrangements have to be made such as placing urgent purchase orders. If still unsuccessful,
the order will stay in the order queue and waiting for the next round.
Inventory Process
Inventory is considered as the control center as it triggers the events such as procurement when the inventory level is low than required. As a matter of fact, products fall
into two categories: in-source and out-source. For in-source products, the replenishment is built from the manufacturing process in the same facility; for out-source
products, the replenishment is from external suppliers via procurement process. Inventory control is applied to each product in each facility. Analysts can specify
periodical review or continuous review. Several typical inventory control policies
are implemented including (R, Q) and (s, S). These parameters can be set for each
product and each period. If required, handling process can be modeled, which represents the tasks to move products into the storage area or move them out. This will
involve resource framework to manage the handling equipments.
5 A Generalized Simulation Framework for Responsive Supply Network Management
77
Procurement Process
The Procurement process is in charge of purchasing products from upstream facilities or suppliers. We model two procurement policies: single sourcing and multiple sourcing. In single sourcing policy, the analyst needs to locate the supplier
for each product in each period. As for multiple sourcing policy, a set of methods
are defined in GBSE for supplier selection. As an example, analysts can define the
volume proportion for each supplier for each product. Procurement process can be
triggered by procurement plan and inventory signals. Procurement plan defines the
time and quantity of each procurement task, which allows analysts the complete
control of procurement process. Meanwhile, inventory control process can trigger
procurement tasks for out-source products when the inventory level is lower than
a predefined reorder point. GBSE consolidates the procurement tasks by grouping
the orders to the same suppliers based on the desired delivery date.
Manufacturing Process
GBSE focuses on discrete-manufacturing. An assembly process is implemented to
model the consumption of raw materials and create intermediate and finished goods.
Similar to the procurement process, the manufacturing process can be triggered by
manufacturing plan and inventory signals. A Manufacturing plan consists of a set
of manufacturing tasks; each task has its time and quantity. An Inventory signal is
sent from inventory process for in-source products. Manufacturing capacities are
defined to restrict the maximum manufacturing volume for specified products and
periods. On the other hand, analysts are allowed to define manufacturing resources
such as machines, workers, etc. Note that the manufacturing process will halt in the
circumstances that corresponding resources are not available. GBSE will calculate
the overall manufacturing cost consisting of direct labor cost, in-direct labor cost,
energy consumption, and all other variable costs during manufacturing.
Transportation Process
The Transportation process happens on inbound, outbound, and inter-facility lanes.
Several types of transportation modes are supported in GBSE, like LTL (Lessthan-Truckload), TL (Truckload), ocean, train, and air shipping, other transportation
modes, if not available, can be added by the analysts. Transportation time, cost, as
well as the desired service level, are defined for each mode. GBSE can consolidate
the transportation tasks which can save the transportation expenses. These consolidated tasks are grouped based on customers and due time, and the fulfilled orders
are sent to customers in batches.
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J. Dong, W. Wang, T. Wu
Planning Process
To enable BTP (Build-to-Plan) process, it is necessary to run MRP process during
the simulation. Several parameters and system status will be taken into account by
MRP process (1) for demand, average customer demands in the next several periods should be provided; (2) for inventory, backlog, in-transit inventory, and on-hand
inventory should be calculated together; (3) for time, supply lead time and delivery lead time should be estimated. With all the three kinds of data as input, procurement quantity and procurement time can be determined. A planning engine is
implemented in GBSE which provides the interfaces to external engines.
5.3.2.3 Performance Measurement
One important target of GBSE is to balance service level and total cost. Service
Level is measured by time and percentage. Time related metrics show supply chain
responsiveness. Some important metrics may be of interest to analysts are order cycle time, average assembling time, average transportation time, etc. It is also useful
to check the average waiting time for an order queue or a resource pool. Percentage related metrics represent supply chain effectiveness. Some metrics of interest
are the order fill rates, procurement fulfill rates, out-of-stock rates, etc. GBSE can
record the related metric to enable the study of the supply network performance
quantitatively. Due to the fact that (1) GBSE considers uncertain inputs (2) various
what-if setting can be easily modeled in GBSE, in this chapter, we assess the supply
network performance under different demand forecast, different supplier selection,
different shipment selection and different production selection. This will provide the
insights to design a more responsive supply network.
5.4 Experiments
In this section, we present a case study for an automotive manufacturer with GBSE.
Simulation has been applied at three different levels: production line level, individual plant level, and supply chain level. In production line level, simulation can be
used for product design; analysts create continuous model for physical systems and
evaluate the performances. In plant level, simulation can be used to design the layout
of the shop floor. This study will be focused on supply chain level. Current practices
of automotive industry indicate the main challenges are:
• The Bill-of-Material (BOM) is very complex: 1) The number of components
is usually quite large: thousands of components are required to produce a car.
2) A substitute BOM is very common in the automotive industry. Some components can be replaced by other components. 3) Components have a life cycle. Some components will not be used any more after the specified time point.
5 A Generalized Simulation Framework for Responsive Supply Network Management
79
4) During the manufacturing process, some by-products can be created, and they
can be used as components in the other BOM. All the issues above increase the
complexity of component management and simulation modeling.
• Highly configurable customer orders. It is common for customers to choose different options and customize their automobiles. For manufacturers, each order
can be different. Usually the customized cars are more expensive than standard
ones. This is an opportunity, as well as a big challenge to the decision makers.
• Service level is critical. From the inbound side, the error of component supply
time is not allowed to be longer than a few minutes; from the outbound side, it
is mandatory for multi-national automotive manufacturers to deliver a high value
product portfolio to the global market at the right time and in the right place.
• In different types of manufacturing supply chain, the decision trade-offs are different. For instance, Swaminathan et al. (1998) study three distinct domains
which differ in terms of centers of decision making, heterogeneity in the supply chain, and relationship with suppliers.
We study a general four-tier automotive industry supply chain (Fig. 5.4) which consists of three suppliers, two manufacturing facilities, four distribution centers, and
four customers. Figure 5.5 illustrates the snapshot of GBSE implementation of the
supply chain. The main area is the logic diagram of the entire supply chain. Users
can modify the diagram by dragging and dropping elements from the toolbar to the
diagram. Project Navigator is in the left side of the tool, users can manage their
model files and resource files in the navigator. In the left bottom, the Database Navigator is provided for checking the data in database. In the right bottom, users can
modify data in the Properties Panel.
In the following sections, we describe four simulation scenarios. Each of them
illustrates a typical supply chain. Twenty experiments are conducted for the four
scenarios. In the model, one period is defined as one week, twelve periods are simu-
Supplier1
Manufacturing
facility1
DC1
Customer1
DC2
Customer2
DC3
Customer3
DC4
Customer4
Supplier2
Manufacturing
facility2
Supplier3
Fig. 5.4 The structure of the studied supply network
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J. Dong, W. Wang, T. Wu
Fig. 5.5 GBSE snapshot
lated in total. A two-tier BOM is modeled. There are five finished goods with three
components for each.
5.4.1 Notation
˛W
d W
d W
ro W
rm W
b
csp
W
clpm W
t
ckp
W
cpv W
Cb W
Cm W
Ct W
Cv W
qivp W
forecast accuracy,
standard deviation of the customer demand,
mean demand,
fill rate,
manufacturing failure rate,
unit procurement cost for product p from supplier s,
unit manufacturing cost for product p at production line l,
unit transportation cost for product p with mode k,
unit inventory carrying cost for product p,
procurement cost,
manufacturing cost,
transportation cost,
inventory carrying cost,
inventory quantity during time section i for product p,
5 A Generalized Simulation Framework for Responsive Supply Network Management
b
qsp
W
m
qi W
qlpm W
t
qkp
W
qio W
Qim W
Qio W
ti p W
81
manufacturing quantity of product p from supplier s,
number of qualified products for manufacturing shift i ,
manufacturing quantity of product p at production line l,
transportation quantity of product p with mode k,
fulfilled quantity for order i ,
total number of products for manufacturing shift i ,
ordered quantity of order i ,
length of time section i of product p.
5.4.2 Scenario I: Impact of Demand Forecast Accuracy
Given different forecast accuracy levels, the fill rate of each distribution center will
change accordingly. The sensitivity of GBSE can help the manager to decide if it is
necessary to invest more to improve the forecast accuracy.
The forecast accuracy is defined as:
˛ D1
d
;
d
where ˛ is the forecast accuracy, d is the standard deviation of the customer demand
and d is the mean demand.
During the simulation, a set of random numbers in normal distribution is generated to represent the customer demands. According to the definition of forecast
accuracy, the standard deviation of customer demand is determined as:
d D d .1 ˛/ :
We run different experiments with respect to different forecast errors. Two performance metrics are collected for the study: fill rate and inventory carrying cost. The fill
rate is defined as:
P o
q
o
r D P i io ;
i Qi
where r denotes the fill rate, qio denotes the fulfilled quantity for order i and Qio
denotes the ordered quantity of order i .
In all the rest scenarios, we will use the same definition of fill rate.
For calculating the inventory carrying cost, we need to split the simulation time
into a set of time sections. During each time section, the inventory keeps no change.
This means each time we change the inventory, we start a new time section. The
inventory carrying cost is defined as:
XX
cpv qivp ti p :
Cv D
p
i
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J. Dong, W. Wang, T. Wu
Where C v denotes the inventory carrying cost, cpv denotes the unit inventory carrying cost for product p, qivp denotes the inventory quantity during time period i for
product p, ti p denotes the length of time period i of product p.
The AS-IS forecast accuracy is 60 %. We change the forecast accuracy from 60 %
to 90 %. Table 5.1 and Fig. 5.6 show the overall and individual fill rates for different
values of forecast accuracy.
Table 5.1 Simulation results of scenario S1
Experiments
Forecast
Accuracy(%)
Inventory Carrying
Cost (K$)
Fill
Rate
(%)
Exp1
Exp2
Exp3
Exp4
Exp5
Exp6
Exp7
Exp8
60
65
70
75
80
85
90
95
37,412
31,856
27,301
25,609
21,923
21,266
21,010
20,726
57.5
65.8
68.8
78.8
88.4
89.7
91.8
92.0
Fig. 5.6 Simulation results of
scenario I
40,000
100.0%
35,000
90.0%
80.0%
30,000
70.0%
25,000
60.0%
20,000
50.0%
15,000
40.0%
30.0%
10,000
20.0%
5,000
10.0%
0.0%
0
60% 65% 70% 75% 80% 85% 90% 95%
Inventory Carrying Cost
Fill Rate
The results indicate that with an increase of forecast accuracy, the fill rate is improved significantly and, the inventory carrying cost decreases. Because less inventory is needed to ensure safety stock, lower average inventory levels are achieved.
It is interesting to note that 80 % is the break point. When the forecast accuracy is
lower than 80 %, the fill rate and inventory carrying cost are changed significantly.
When the forecast accuracy is higher than 80 %, the magnitude of the changes diminishes. We conclude that improving the forecast accuracy is important, however,
in certain extent, when the watershed is reached, forecast accuracy improvement
will be more costly with considerable less return.
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5.4.3 Scenario II: Impact of Supplier Selection
In automobile industry, supplier selection is very important because thousands of
components are included in the BOMs. In the competitive market, each component can be supplied by different suppliers, e. g. local suppliers can supply products
quickly while oversea suppliers may provide less expensive components due to low
labor and raw material cost. In this example, there are three suppliers. Assume the
suppliers have different procurement costs and supply lead times. Since procurement time is uncertain in nature, we will study the use of GBSE to assess how
different suppliers impact the fill rate and the total procurement cost.
In this scenario, there are fifteen types of components among which ten can only
be supplied by one of the three suppliers and the rest five can be supplied by all three
suppliers. Supplier 3 has lowest procurement cost, however the longest lead time.
Compared to Supplier 1, Supplier 2 has less lead time and relatively higher cost.
We conduct four experiments for the 3 suppliers with Supplier 3 being rejected for
the first two experiments and Supplier 3 being selected for the last two experiments.
The proportions of procurement volume for the suppliers are different. For each
experiment, fill rate and procurement cost are calculated. The procurement cost is
defined as:
XX
b b
csp
qsp :
Cb D
s
p
b
b
denotes the unit procurement cost for
Where C denotes the procurement cost, csp
b
product p from supplier s, qsp denotes the manufacturing quantity of product p from
supplier s. Table 5.2 and Fig. 5.7 show the simulation results.
The result shows that if Supplier 3 is selected to provide some proportion of
the supplies, the total cost decreases dramatically with the scarifying of the service
level.
5.4.4 Scenario III: Impact of Different Transportation Mode
In a typical supply chain, there are usually several types of transportation modes,
like air, ocean, TL (truck load), LTL (less than truck load), etc. Each transportation
Table 5.2 Simulation Results of Scenario II
Experiments
Supplier 1
%
Supplier 2
%
Supplier 3
%
Procurement
Cost (K$)
Fill
Rate %
Exp9
Exp10
Exp11
Exp12
60
40
50
30
40
60
30
50
0
0
20
20
54,897
55,104
50,741
51,211
96.8
92.7
86.0
81.3
84
J. Dong, W. Wang, T. Wu
Fig. 5.7 Simulation results of
scenario II
100.0%
56,000
55,000
95.0%
54,000
90.0%
53,000
52,000
85.0%
51,000
80.0%
50,000
75.0%
49,000
48,000
70.0%
Exp9
Exp10
Exp11
Procurement Cost
Exp12
Fill Rate
mode has different elements of uncertainty. The decision makers need to answer
questions like what transportation modes should be selected, how to assign usage
ratio for each transportation mode, etc. There are three types of transportation in
each supply chain: inbound transportation time, internal transportation time, and
outbound transportation time. Inbound transportation is from suppliers to internal
facilities; outbound transportation is from internal facilities to customers or from
customer to other customers; internal transportation is between internal facilities.
In this example, air and ocean modes are supported for inbound transportation.
Since the air transportation is expensive, it is used for high priority or urgent orders
only. The cost of ocean transportation is much lower, and it is proper for normal
shipping. But the lead time of ocean mode is usually several weeks, so it’s not flexible and a precise procurement plan needs to be made in advance. Truck and train
modes are supported for internal and outbound transportation. Both modes need
to follow transportation schedules, but the truck mode is more flexible. Table 5.3
summarizes the characteristics of the transportation modes.
Table 5.3 Comparison of different transportation modes
Transportation Mode
Cost
Transportation Time
Air
Ocean
Truck
Train
Very high
Very low
High
Low
A few days
Several weeks
Several days
Several days
We conduct four experiments for this scenario and calculate the transportation
cost and fill rate. The transportation cost is defined as:
XX
t
t
ckp
qkp
:
Ct D
k
p
5 A Generalized Simulation Framework for Responsive Supply Network Management
85
t
Where C t denotes the transportation cost, ckp
denotes the unit transportation cost
t
denotes the transportation quantity of product p with
for product p with mode k, qkp
mode k. Table 5.4 and Fig. 5.8 show the simulation results.
Table 5.4 Simulation results of scenario III
Experiments
Air
%
Ocean
%
Truck
%
Train
%
Transportation
Cost (K$)
Fill Rate
%
Exp13
Exp14
Exp15
Exp16
10
10
20
20
90
90
80
80
30
70
30
70
70
30
70
30
38,322
39,210
43,687
44,471
82.3
85.5
91.1
96.3
Fig. 5.8 Simulation Results
of Scenario III
100.0%
45,000
44,000
43,000
42,000
41,000
40,000
39,000
38,000
37,000
36,000
35,000
95.0%
90.0%
85.0%
80.0%
75.0%
Exp13
Exp14
Transportation Cost
Exp15
Exp16
Fill Rate
From the results, we conclude that the use of air transportation instead of ocean
for the inbound will encounter higher cost, and same for the use of truck instead of
train, however, the fill rate will be improved significantly.
5.4.5 Scenario IV: Impact of Quality Uncertainty
There are usually multiple production lines in an automotive manufacturing facility.
Two key attributes of production lines are failure rate and unit production cost. The
failure rate is related to product quality, it is defined as:
P m
q
m
r D 1 P i im :
i Qi
Where r m denotes the failure rate, qim denotes the number of qualified products for
manufacturing shift i , Qim denotes the total number of products for manufacturing
shift i .
86
J. Dong, W. Wang, T. Wu
In this experiment, we focus on manufacturing facility1 which consists of three
existing production lines (PL1, PL2, and PL3). PL1 and PL2 are the same. PL3
has lower failure rate, while the operation cost is relatively higher than PL1 and
PL2. Meanwhile, the management team is considering if it’s required to purchase
two new production lines (PL4 and PL5). They have lowest failure rate and highest
operation cost.
Four experiments are designed for this study in which PL4 and PL5 are not purchased with only PL1, PL2 and PL3 are used for the first two experiments, all give
production lines are used for the last two experiments. Manufacturing cost and fill
rate are calculated for each experiment
XX
clpm qlpm :
Cm D
p
l
Where C m denotes the manufacturing cost, clpm denotes the unit manufacturing cost
for product p at production line l, qlpm denotes the manufacturing quantity of product p at production line l. Table 5.5 and Fig. 5.9 summarize the simulation results.
Table 5.5 Simulation results of scenario IV
Experiments
PL1
%
PL2
%
PL3
%
PL4
%
PL5
%
Manufacturing
Cost (K$)
Fill
Rate %
Exp17
Exp18
Exp19
Exp20
40
30
20
10
40
30
20
10
20
40
20
20
0
0
20
30
0
0
20
30
46,732
47,561
48,785
49,760
82.3
86.0
93.1
95.9
Fig. 5.9 Simulation results of
scenario IV
50,000
49,500
49,000
48,500
48,000
47,500
47,000
46,500
46,000
45,500
45,000
100.0%
95.0%
90.0%
85.0%
80.0%
75.0%
Exp17
Exp18
Exp19
Manufacturing Cost
Exp20
Fill Rate
As shown by the results, after introducing two new production lines, although
the total cost increases, the fill rates are improved significantly. In addition to this,
if more products are produced with PL3, the fill rate will also get improved.
5 A Generalized Simulation Framework for Responsive Supply Network Management
87
5.5 Conclusion
In this chapter, we introduce GBSE, an integrated supply chain simulation environment developed by IBM China Research Lab. It has been applied for both IBM
internal and external supply chains to evaluate several key performance metrics and
optimize supply network operations. The tool is designed for tactical-level of decision making, and it supports wide range of supply chain processes. Simulation
analysts can use it to conduct several kinds of what-if analysis and risk analysis
in supply chain context, so as to make correct decisions more effectively. In this
study, we demonstrate the applicability of GBSE to responsive supply chain management by presenting four scenarios to study varied uncertainties in forecasting,
various decisions in selecting suppliers, transportation modes and production lines.
We conclude that GBSE can facilitate the decision making by analyzing the impact of different uncertainties in details quantitatively. While promising, we will
design experiments with more impacting factors being considered and further indepth analysis will be conducted.
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Section II
Decision Making and Risk Mitigation
in the Supply Chain
Chapter 6
Modeling of Supply Chain Risk
Under Disruptions with Performance
Measurement and Robustness Analysis
Qiang Qiang, Anna Nagurney, and June Dong
Abstract In this chapter, we develop a new supply chain network model with multiple decision-makers associated at different tiers and with multiple transportation
modes for shipment of the good between tiers. The model formulation captures
supply-side risk as well as demand-side risk, along with uncertainty in transportation and other costs. The model also incorporates the individual attitudes towards
disruption risks among the manufacturers and the retailers, with the demands for
the product associated with the retailers being random. We present the behavior of
the various decision-makers, derive the governing equilibrium conditions, and establish the finite-dimensional variational inequality formulation. We also propose
a weighted supply chain performance and robustness measure based on our recently
derived network performance/efficiency measure and provide supply chain examples for which the equilibrium solutions are determined along with the robustness
analyses. This chapter extends previous supply chain research by capturing supplyside disruption risks, transportation and other cost risks, and demand-side uncertainty within an integrated modeling and robustness analysis framework.
6.1 Introduction
Supply chain disruptions and the associated risk are major topics in theoretical
and applied research, as well as in practice, since risk in the context of supply
chains may be associated with the production/procurement processes, the transportation/shipment of the goods, and/or the demand markets. In fact, Craighead,
et al. (2007) have argued that supply chain disruptions and the associated operational
and financial risks are the most pressing issue faced by firms in today’s competitive global environment. Notably, the focus of research has been on “demand-side”
risk, which is related to fluctuations in the demand for products, as opposed to the
“supply-side” risk, which deals with uncertain conditions that affect the production
and transportation processes of the supply chain. For a discussion of the distinction
between these two types of risk, see Snyder (2003).
T. Wu, J. Blackhurst (eds.), Managing Supply Chain Risk and Vulnerability
© Springer 2009
91
92
Q. Qiang, A. Nagurney, J. Dong
For example, several recent major disruptions and the associated impacts on the
business world have vividly demonstrated the need to address supply-side risk with
a case in point being a fire in the Phillips Semiconductor plant in Albuquerque, New
Mexico, causing its major customer, Ericsson, to lose $ 400 million in potential
revenues. On the other hand, another major customer, Nokia, managed to arrange
alternative supplies and, therefore, mitigated the impact of the disruption (cf. Latour, 2001). Another illustrative example concerns the impact of Hurricane Katrina,
with the consequence that 10 %–15 % of total U.S. gasoline production was halted,
which not only raised the oil price in the U.S., but also overseas (see, e.g., Canadian
Competition Bureau, 2006). Moreover, the world price of coffee rose 22 % after
Hurricane Mitch struck the Central American republics of Nicaragua, Guatemala,
and Honduras, which also affected supply chains worldwide (Fairtrade Foundation,
2002). As summarized by Sheffi (2005) on page 74, one of the main characteristics
of disruptions in supply networks is “the seemingly unrelated consequences and vulnerabilities stemming from global connectivity.” Indeed, supply chain disruptions
may have impacts that propagate not only locally but globally and, hence, a holistic,
system-wide approach to supply chain network modeling and analysis is essential
in order to be able to capture the complex interactions among decision-makers.
Indeed, rigorous modeling and analysis of supply chain networks, in the presence of possible disruptions is imperative since disruptions may have lasting major
financial consequences. Hendricks and Singhal (2005) analyzed 800 instances of
supply chain disruptions experienced by firms whose stocks are publicly traded.
They found that the companies that suffered supply chain disruptions experienced
share price returns 33 % to 40 % lower than the industry and the general market
benchmarks. Furthermore, share price volatility was 13.5 % higher in these companies in the year following a disruption than in the prior year. Based on their
findings, it is evident that only well-prepared companies can effectively cope with
supply chain disruptions. Wagner and Bode (2007), in turn, designed a survey to
empirically study the responses from executives of firms in Germany regarding
their opinions as to the factors that impact supply chain vulnerability. The authors
found that demand-side risks are related to customer dependence while supplyside risks are associated with supplier dependence, single sourcing, and global
sourcing.
The goal of supply chain risk management is to alleviate the consequences of
disruptions and risks or, simply put, to increase the robustness of a supply chain.
However, there are very few quantitative models for measuring supply chain robustness. For example, Bundschuh, et al. (2003) discussed the design of a supply
chain from both reliability and robustness perspectives. The authors built a mixed
integer programming supply chain model with constraints for reliability and robustness. The robustness constraint was formulated in an implicit form: by requiring
the suppliers’ sourcing limit to exceed a certain level. In this way, the model built
redundancy into a supply chain. Snyder and Daskin (2005) examined supply chain
disruptions in the context of facility location. The objective of their model was to
select locations for warehouses and other facilities that minimize the transportation
costs to customers and, at the same time, account for possible closures of facilities
6 Modeling of Supply Chain Risk
93
that would result in re-routing of the product. However, as commented in Snyder
and Shen (2006), “Although these are multi-location models, they focus primarily
on the local effects of disruptions.” Santoso, et al., 2005 applied a sample average
approximation scheme to study the stochastic facility location problem by considering different disruption scenarios.
Tang (2006a) also discussed how to deploy certain strategies in order to enhance
the robustness and the resiliency of supply chains. Kleindorfer and Saad (2005),
in turn, provided an overview of strategies for mitigating supply chain disruption
risks, which were exemplified by a case study in a chemical product supply chain.
For a comprehensive review of supply chain risk management models to that date,
please refer to Tang (2006b).
To-date, however, most supply disruption studies have focused on a local point of
view, in the form of a single-supplier problem (see, e. g., Gupta, 1996; Parlar, 1997)
or a two-supplier problem (see, e. g., Parlar and Perry, 1996). Very few papers have
examined supply chain risk management in an environment with multiple decisionmakers and in the case of uncertain demands (cf. Tomlin, 2006). We believe that it
is imperative to study supply chain risk management from a holistic point of view
and to capture the interactions among the multiple decision-makers in the various
supply chain network tiers. Indeed, such a perspective has also been argued by Wu
et al. (2006), who focused on inbound supply risk analysis. Towards that end, in this
chapter, we take an entirely different perspective, and we consider, for the first time,
supply chain robustness in the context of multi-tiered supply chain networks with
multiple decision-makers under equilibrium conditions. For a plethora of supply
chain network equilibrium models and the associated underlying dynamics, see the
book by Nagurney (2006a).
Of course, in order to study supply chain robustness, an informative and effective
performance measure is first required. Beamon (1998, 1999) reviewed the supply
chain literature and suggested directions for research on supply chain performance
measures, which should include criteria on efficient resource allocation, output maximization, and flexible adaptation to the environmental changes (see also, Lee and
Whang, 1999; Lambert and Pohlen, 2001; Lai et al., 2002). We emphasize that different supply performance measures can be devised based on the specific nature of
the problem. In any event, the discussion here is not meant to cover all the existing
supply chain performance measures. Indeed, we are well aware that it is a daunting
task to propose a supply chain performance measure that covers all aspects of supply chains. We believe that such a discussion will be an ongoing research topic for
decades to follow. In this chapter, we study supply chain robustness based on a novel
network performance measure proposed by Qiang and Nagurney (2008), which captures the network flows, the costs, and the decision-makers’ behavior under network
equilibrium conditions.
In particular, the model developed in this chapter extends the supply chain model
of Nagurney et al. (2002) with consideration of random demand (cf. Nagurney et al.,
2005). In order to study supply chain robustness, the new model contains the following novel features:
94
Q. Qiang, A. Nagurney, J. Dong
• We associate each process in a supply chain with random cost parameters to
represent the impact of disruptions to the supply chain.
• We extend the aforementioned supply chain models to capture the attitude of the
manufacturers and the retailers towards disruption risks.
• We propose a weighted performance measure to evaluate different supply chain
disruptions.
• Different transportation modes are considered in the model (see also, e. g., Dong
et al., 2002; Dong et al., 2005). In the multimodal transportation supply chain,
alternative transportation modes can be used in the case of the failure of a transportation mode. Indeed, many authors have emphasized that redundancy needs
to be considered in the design of supply chains in order to prevent supply chain
disruptions. For example, Wilson (2007) used a system dynamic simulation to
study the relationship between transportation disruptions and supply chain performance. The author found that the existence of transportation alternatives significantly improved supply chain performance in the case of transportation disruptions.
In this chapter, we assume that the probability distributions of the disruption related cost parameters are known. This assumption is not unreasonable given today’s
advanced information technology and increasing awareness of the risks among managers. A great deal of disruption related information can be obtained from a careful
examination and abstraction of the relevant data sources. Specifically, as indicated
by Sheffi (2005, p. 55), “. . . as investigation boards and legal proceedings have revealed, in many cases relevant data are on the record but not funneled into a useful
place or not analyzed to bring out the information in the data”. Moreover, Holmgren (2007) also discussed ways to improve prediction of disruptions, using, for
example: historical data analysis, mathematical modeling, and expert judgments.
Furthermore, we assume that the random cost parameters are independent.
The organization of this chapter is as follows. In Sect. 6.2, we present the model
of a supply chain network faced with (possible) disruptions and in the case of random demands and multiple transportation modes. In Sect. 6.3, we provide a definition of a weighted supply chain performance measure with consideration of robustness. In Sect. 6.4, we present numerical examples in order to illustrate the model
and concepts introduced in this chapter. The chapter concludes with Sect. 6.5, which
summarizes the results obtained and provides suggestions for future research.
6.2 The Supply Chain Model with Disruption Risks
and Random Demands
The topology of the supply chain network is depicted in Fig. 6.1.
The supply chain model consists of m manufacturers, with a typical manufacturer
denoted by i , n retailers with a typical retailer denoted by j , and o demand markets
with a typical demand market denoted by k. Furthermore, we assume that there are
6 Modeling of Supply Chain Risk
95
Fig. 6.1 The multitiered network structure of the supply chain
g transportation modes from manufacturers to retailers, with a typical mode denoted
by u and there are h transportation modes between retailers and demand markets,
with a typical mode denoted by v. Typical transportation modes may include trucking, rail, air, sea, etc. By allowing multiple modes of transportation between successive tiers of the supply chain we also generalize the earlier models of Dong et al.
(2002) and Dong et al. (2005).
Manufacturers are assumed to produce a homogeneous product, which can be
purchased by retailers, who, in turn, make the product available to demand markets.
Each process in the supply chain is associated with some random parameters that
affect the cost functions. The relevant notation is summarized in Table 6.1.
Table 6.1 Notation for the supply chain network model
Notation
Definition
q
m-dimensional vector of the manufacturers’ production outputs with components: q1 , . . . , qm
Q1
mng-dimensional vector of product shipments between manufacturers and
u
retailers via the transportation modes with component ij u denoted by qij
Q2
noh-dimensional vector of product shipments between retailers and demand
markets via the transportation modes with component j kv denoted by qjvk
˛
m-dimensional vector of nonnegative random parameters with being the
random parameter associated with the product cost of manufacturer i and the
corresponding cumulative distribution function is given by Fi .˛i /
ˇ
u
mng-dimensional vector of nonnegative random parameters with ˇij
being
the random parameter associated with the transportation cost of manufacturer i
and retailer j via mode u and the corresponding cumulative distribution
u
/
function is given by Fiju .ˇij
96
Q. Qiang, A. Nagurney, J. Dong
Table 6.1 (continued)
Notation
Definition
n-dimensional vector of nonnegative random parameters with j being the
random parameter associated with the handling cost of retailer j and the
corresponding cumulative distribution function is given by Fj .j /
n-dimensional vector of shadow prices associated with the retailers with
component j denoted by j
m-dimensional vector of nonnegative weights with i reflecting manufacturer
i ’s attitude towards disruption risks
$
n-dimensional vector of nonnegative weights with $j reflecting retailer j ’s
attitude towards disruption risks
fi .q;
˛i / fi Q1 ; ˛i
FO .q/ FO .Q1 /
Production cost of manufacturer i with random parameter
VFi .Q1 /
u
u
u
qij
Cij
; ˇij
u
u
qij
CO ij
u
u
qij
V Cij
Expected production cost function of manufacturer i with marginal production
@FOi .Q1 /
u
cost with respect to qij
denoted by
u
@qij
Variance of the production cost of manufacturer i with marginal with respect
@VFi .Q1 /
u
denoted by
to qij
u
@qij
Transaction cost between manufacturer i and retailer j via transportation
u
mode u with the random parameter ˇij
Expected transaction cost between manufacturer i and retailer j via
trans
u
u
@CO ij
qij
portation mode u with marginal transaction cost denoted by
u
@qij
Variance of the transaction cost between manufacturer i and retailer j via
u
u
qij
@V Cij
transportation mode u with marginal denoted by
u
@qij
Cj Q1 ; Q2 ; j Handling cost of retailer j with random parameter j
CO j1 Q1 ; Q2
Expected handling cost of retailer j with marginal handling cost with respect
@CO j1 Q1 ; Q2
u
and the marginal handling cost with respect
to qij denoted by
u
@qij
@CO j1 Q1 ; Q2
to qjvk denoted by
@qjvk
1
1
u
2
V Cj Q ; Q
Variance of the handling cost of retailer j with marginal with respect to qij
1
1
2
@V Cj Q ; Q
denoted by
and the marginal with respect to qjvk denoted
u
@qij
@V Cj1 Q1 ; Q2
by
@qjvk
cjvk Q2
Unit transaction cost between retailer j and demand market k via transportation mode v
dk .3 /
Random demand at demand market k with expected value dOk .3 /
3
Vector of prices of the product at the demand markets with 3k denoting the
demand price at demand market k
6 Modeling of Supply Chain Risk
97
6.2.1 The Behavior of the Manufacturers
We assume a homogeneous product economy meaning that all manufacturers produce the same product which is then shipped to the retailers, who, in turn, sell the
product to the demand markets.
Since the total amount of the product shipped from a manufacturer via different transportation modes has to be equal to the amount of the production of each
manufacturer, we have the following relationship between the production of manufacturer i and the shipments to the retailers:
qi D
g
n X
X
qiju ;
i D 1; : : : ; m :
(6.1)
j D1 uD1
We assume that disruptions will affect the production processes of manufacturers,
the impact of which is reflected in the production cost functions. For each manufacturer i , there is a random parameter ˛i that reflects the impact of disruption
to his production cost function. The expected production cost function is given
by:
Z
FOi .Q1 / fi Q1 ; ˛i dFi .˛i /; i D 1; : : : ; m :
(6.2)
˛i
We further denote the variance of the above production cost function as VFi .Q1 /
where i D 1, . . . , m.
As noted earlier, we assume that each manufacturer has g types of transportation
modes available to ship the product to the retailers, the cost of which is also subject
to disruption impacts. The expected transportation cost function is given by:
Z
ciju qiju ; ˇiju dFiju ˇiju ;
CO iju qiju u
ˇij
i D 1; : : : ; mI
j D 1; : : : ; nI
u D 1; : : : ; g :
(6.3)
We further denote the variance of the above transportation cost function as V Ciju .Q1 /
where i D 1, . . . , m; j D 1, . . . , n; u D 1, . . . , g.
It is well-known in economics that variance may be used to measure risk (see,
e. g., Silberberg and Suen, 2000; Tomlin, 2006 using such an approach to study
risks in applications to supply chains). Therefore, we assign a nonnegative weight
i to the variance of the cost functions for each manufacturer to reflect his attitude
towards disruption risks. The larger the weight is, the larger the penalty a manufacturer imposes on the risk, and, therefore, the more risk-averse the manufacturer is.
u
denote the price charged for the product by manufacturer i to retailer j
Let 1ij
when the product is shipped via transportation mode u. Hence, manufacturers can
price according to their locations as well as according to the transportation modes
utilized. Each manufacturer faces two objectives: to maximize his expected profit
98
Q. Qiang, A. Nagurney, J. Dong
and to minimize the disruption risks adjusted by his risk attitude. Therefore, the
objective function for manufacturer i ; i D 1, . . . , m can be expressed as follows:
Maximize
g
n X
X
u u
1ij
qij FOi .Q1 /
j D1 uD1
2
g
n X
X
CO iju qiju
j D1 uD1
i 4VFi .Q1 / C
g
n X
X
3
V Ciju qiju 5
(6.4)
j D1 uD1
subject to:
qiju 0;
for all i; j; and u :
The first term in (6.4) represents the revenue. The second term is the expected disruption related production cost. The third term is the expected disruption related
transportation cost. The fourth term is the cost of disruption risks adjusted by each
manufacturer’s attitude.
We assume that, for each manufacturer, the production cost function and the
transaction cost function without disruptions are continuously
differentiable
and
1
1
u
u
u
u
O
O
convex. It is easy to verify thatFi .Q /,VFi .Q /, Cij qij , and V Cij qij are also
continuously differentiable and convex. Furthermore, we assume that manufacturers
compete in a non-cooperative fashion in the sense of Nash (1950, 1951). Hence, the
optimality conditions for all manufacturers simultaneously (cf. Bazaraa et al., 1993;
Nagurney, 1999) can be expressed as the following variational inequality: determine
mng
satisfying:
Q1 2 RC
m
X
n
X
g
X
i D1 j D 1 u D 1
"
1 O u q u
@
C
O
@Fi Q
ij
ij
C
u
u
@qij
@qij
1
0
3
@V Ciju qiju
@VFi Q1
u 5
A 1ij
Ci @
C
@qiju
@qiju
mng
qiju qiju 0; 8Q1 2 RC
:
(6.5)
6.2.2 The Behavior of the Retailers
The retailers, in turn, are involved in transactions both with the manufacturers and
the demand markets since they must obtain the product to deliver to the consumers
at the demand markets.
v
denote the price charged for the product by retailer j to demand market
Let 2jk
k when the product is shipped via transportation mode v. Hence, retailers can price
6 Modeling of Supply Chain Risk
99
according to their locations as well as according to the transportation modes utilized.
This price is determined endogenously in the model along with the prices associated
u
with the manufacturers, that is, the 1ij
, for all i , j and u. We assume that certain
disruptions will affect the retailers’ handling processes (e. g., the storage and display
processes). An additional random risk/disruption related random parameter j is
associated with the handling cost of retailer j . Recall that we also assume that there
are h types of transportation modes available to each retailer for shipping the product
to the demand markets. The expected handling cost is given by:
Z
1 2
1
O
(6.6)
Cj Q ; Q cj Q1 ; Q2 ; j dFj j ; j D 1; : : : ; n :
j
We further denote the variance of the above handling cost function as V Cj1 Q1 ; Q2
where j D 1, . . . , n.
Furthermore, similar to the case for the manufacturers, we associate a nonnegative weight $j to the variance of each retailer’s handling cost according to his
attitude towards risk. Each retailer faces two objectives: to maximize his expected
profit and to minimize the disruption risks adjusted by his risk attitude. Therefore,
the objective function for
retailer j ; j D 1, . . . , n can be expressed as follows:
Maximize
o X
h
X
g
m X
X
v v
u u
2jk
qjk CO j1 Q1 ; Q2 1ij
qij $j V Cj1 Q1 ; Q2
(6.7)
i D1 uD1
k D 1 vD1
subject to:
o X
h
X
k D 1 vD1
v
qjk
g
m X
X
qiju
(6.8)
i D1 uD1
v
and the nonnegativity constraints: qiju 0 for all i , j , and u; qjk
0 for all j , k,
and v.
Objective function (6.7) expresses that the difference between the revenues minus the expected handling cost, the payout to the manufacturers and the weighted
disruption risk is to be maximized. Constraint (6.8) states that retailers cannot purchase more product from a retailer than is available in stock.
As noted in Table 6.1, j is the Lagrange multiplier associated with constraint
(6.6) for retailer j . Furthermore, we assume that, for each retailer, the handling
cost without disruptions
differentiable
and convex. It is easy to
is continuously
verify that CO j1 Q1 ; Q2 and V Cj1 Q1 ; Q2 are also continuously differentiable
and convex. We assume that retailers compete with one another in a noncooperative manner, seeking to determine their optimal shipments from the manufacturers
and to the demand markets. The optimality conditions for all retailers simultaneously coincide with the solution of the following variational inequality: determine
1 2 mngCnohCn
satisfying:
Q ; Q ; 2 RC
100
Q. Qiang, A. Nagurney, J. Dong
g
m X
n X
X
"
@CO j1 Q1 ; Q2
@qiju
i D1 j D1 uD1
C
u
1ij
C $j
@V Cj1 Q1 ; Q2
@qiju
#
j
qiju qiju
"
1 2 #
n X
o X
h
1
O 1 Q1; Q2
X
Q ;Q
@
C
@V
C
j
j
v
C
2jk
C j C
C $j
v
v
@qjk
@qjk
j D1 k D1 vD1
h
i
v
v
qjk
qjk
" m g
#
n
o X
h
X
XX
X
u
v
qij qjk j j
C
j D1
0;
i D1 uD1
kD1vD1
mngCnohCn
8 Q1 ; Q2 ; 2 RC
:
(6.9)
6.2.3 The Market Equilibrium Conditions
We now turn to a discussion of the market equilibrium conditions. Subsequently, we
construct the equilibrium condition for the entire supply chain network.
The equilibrium conditions associated with the product shipments that take place
between the retailers and the consumers are the stochastic economic equilibrium
conditions, which, mathematically, take on the following form: for any retailer with
associated demand market k; k D 1, . . . , o:
8
o
h
P
P
ˆ
v
ˆ
ˆ
qjk
; if 3k
D 0;
<
j D1 vD1
O
(6.10a)
dk 3
o
h
ˆ
ˆ D P P q v ; if > 0;
:̂
jk
3k
j D1 vD1
v
2jk
2 v
Q
C cjk
(
3k
;
D 3k
;
v
if qjk
D 0;
v
if qjk
> 0:
(6.10b)
Conditions (6.10a) state that, if the expected demand price at demand market k is
positive, then the quantities purchased by consumers at the demand market from the
retailers in the aggregate is equal to the demand at demand market k. Conditions
(6.10b) state, in turn, that in equilibrium, if the consumers at demand market k purchase the product from retailer j via transportation mode v, then the price charged
by the retailer for the product plus the unit transaction cost is equal to the price that
the consumers are willing to pay for the product. If the price plus the unit transaction cost exceeds the price the consumers are willing to pay at the demand market
then there will be no transaction between the retailer and demand market via that
transportation mode.
Equilibrium conditions (6.10a) and (6.10b) are equivalent to the following variational inequality problem, after summing over all demand markets: determine
6 Modeling of Supply Chain Risk
101
nohCo
satisfying:
Q2 ; 3 2 RC
o
X
k D1
C
0
h
n X
X
@
1
v
qjk
dOk 3 A 3k 3k
j D1 vD1
o
X
h n X
h
i
X
v
v
v
Cvjk Q2 3k
qjk
2jk
qjk
0;
k D1 j D1 vD1
o
83 2 RC
;
noh
8Q2 2 RC
;
(6.11)
where 3 is the o-dimensional vector with components: 31 , . . . , 30 and Q2 is the
noh-dimensional vector.
Remark: In this chapter, we are interested in the cases where the expected deo
mands are positive, that is, dOk .3 / > 0,83 2 RC
for k D 1, . . . , o. Furthermore,
v
2
we assume that the unit transaction costs: cjk Q > 0; 8j; k; 8Q2 ¤ 0:
P
P
Under the above assumptions, we have that 3k
> 0 and dOk 3 D nj D 1 ok D 1
Ph
v
N
v D 1 qjk ; 8k: This can be shown by contradiction. If there exists a k where
P
P
P
v
dOkN 3
N D 0, then according to (6.10a) we have that nj D 1 ok D 1 hv D 1 qjk
3k
> 0. Hence, there exists at least a j=kN pair such that q vN > 0, which means
jk
that c v N Q2 > 0 by assumption. From conditions (6.10b), we have that v N C
2j k
jk c v N Q2 D 3kN > 0, which leads to a contradiction.
jk
6.2.4 The Equilibrium Conditions of the Supply Chain
In equilibrium, we must have that the optimality conditions for all manufacturers, as
expressed by (6.4), the optimality conditions for all retailers, as expressed by (6.9),
and as well as the equilibrium conditions for all the demand markets, as expressed
by (6.9), must hold simultaneously (see also Nagurney, et al., 2005). Hence, the
product shipments of the manufacturers with the retailers must be equal to the product shipments that retailers accept from the manufacturers. We now formally state
the equilibrium conditions for the entire supply chain network as follows:
Definition 5.1: Supply Chain Network Equilibrium with Uncertainty and Random Demands
The equilibrium state of the supply chain network with disruption risks and random
demands is one where the flows of the product between the tiers of the decisionmakers coincide and the flows and prices satisfy the sum of conditions (6.4), (6.9),
and (6.11).
The summation of inequalities (6.4), (6.9), and (6.11), after algebraic simplification, yields the following result (see also Nagurney, 1999, 2006a).
102
Q. Qiang, A. Nagurney, J. Dong
Theorem 5.1: Variational Inequality Formulation
mngCnohCnCo
A product shipment and price pattern Q1 ; Q2 ; ; 3 2 RC
is an
equilibrium pattern of the supply chain model according to Definition 1, if and only
if it satisfies the variational inequality problem:
1
2
0
1 1 u
u
g
O u q u
n X
m X
q
@
C
@V
C
O
X
@F Q
@VFi Q
ij
ij
ij
ij
4 i
A
C
C i @
C
u
u
u
u
@q
@q
@q
@q
ij
ij
ij
ij
i D1j D1uD1
#
@CO j1 Q1 ; Q2
@V Cj1 Q1 ; Q2
C
C $j
j qiju qiju
u
u
@qij
@qij
" 1 1 2 g
o
n
X X X @CO j Q ; Q
@V Cj1 Q1 ; Q2
C $j
v
v
@qjk
@qjk
j D1 k D1 vD1
#
i
h
v
v
v
Q2 3k
Cj C cjk
qjk
qjk
C
n
X
j D1
"
g
m X
X
i D1 uD1
dOk 3
!
qiju o X
h
X
k D1 vD1
#
v
qjk
0
o
n X
h
X
X
v
@
j j C
qjk
kD1
j D1 vD1
3k 3k
0;
mngCnohCnCo
8 Q1 ; Q2 ; ; 3 2 RC
:
(6.12)
For easy reference in the subsequent sections, variational inequality problem (6.12)
can be rewritten in standard variational inequality form (cf. Nagurney, 1999) as
follows: determine X 2 K:
˛
˝ mngCnohCnCo
;
(6.13)
F X ; X X 0; 8X 2 K RC
where
X Q1 ; Q2 ; ; 3 ;
F .X / Fij u ; Fjkv ; Fj ; Fk i D1; ::: ; mIj D1; ::: ; nI kD1; ::: ; oI uD1; ::: ; gI vD1; ::: ; h ;
and the specific components of F are given by the functional terms preceding
the multiplication signs in (6.12). The term h;i denotes the inner product in
N-dimensional Euclidean space.
Note that the equilibrium values of the variables in the model (which can be
determined from the solution of either variational inequality (6.12) or (6.13)) are:
the equilibrium product shipments between manufacturers and the retailers given
by Q1 , and the equilibrium product shipments transacted between the retailers and
the demand markets given by Q2 , as well as the equilibrium prices: 3 and . We
6 Modeling of Supply Chain Risk
103
now discuss how to recover the prices 1 associated with the top tier of nodes of the
supply chain network and the prices 2 associated with the middle tier.
@FO .Q1 /
u
First, note that, from (6.5), we have that if qiju > 0, then price 1ij
D i@q u C
ij
!
u q u
u q u
1
@CO ij
@V
C
@VF
Q
.
/
ij
ij
ij
i
. On the other hand, from (6.9), it follows
Ci
C
@q u
@q u
@q u
ij
ij
ij
that, if qijv > 0, the price 2j
D j C
@CO j1 .Q1 ;Q2 /
@qjvk
C$j
@V Cj1 .Q1 ;Q2 /
@qjvk
. These ex-
pressions can be utilized to obtain all such prices for all modes and decision-makers.
6.3 A Weighted Supply Chain Performance Measure
In this section, we first propose a supply chain network performance measure. Then,
we provide the definition of supply chain network robustness, and follow with the
definition for a weighted supply chain performance measure.
6.3.1 A Supply Chain Network Performance Measure
Recently, Qiang and Nagurney (2008) (see also Nagurney and Qiang, 2007a,b,c)
proposed a network performance measure, which captures flows, costs, and behavior under network equilibrium conditions. Based on the measure in the above paper(s), we propose the following definition of a supply chain network performance
measure.
Definition 5.2: The Supply Chain Network Performance Measure
The supply chain network performance measure,", for a given supply chain, and
expected demands: dOk I k D 1, 2, . . . , o, is defined as follows:
Po
"
dOk
k D 1 3k
o
;
(6.14)
where o is the number of demand markets in the supply chain network, and dOk and
3k denote, respectively, the expected equilibrium demand and the equilibrium price
at demand market k.
Note that the equilibrium price is equal to the unit production and transaction
costs plus the weighted marginal risks for producing and transacting one unit from
the manufacturers to the demand markets (see also Nagurney, 2006b). According to
the above performance measure, a supply chain network performs well in network
equilibrium if, on the average, and across all demand markets, a large demand can
be satisfied at a low price. Therefore, in this chapter, we apply the above performance measure to assess the robustness of particular supply chain networks. From the
104
Q. Qiang, A. Nagurney, J. Dong
discussion in Sect. 5.2.3, we have that 3k > 0; 8k. Therefore, the above definition
is well-defined.
Furthermore, since each individual may have different opinions as to the risks,
we need a “basis” to compare supply chain performance under different risk attitudes and to understand how risk attitudes affect the performance of a supply chain.
Hence, we define"0as the supply chain performance measure where the dOk and the
3k ; k D 1, . . . , o, are obtained by assuming that the weights that reflect the manufacturers and the retailers’ attitudes towards the disruption risks are zero. This definition excludes individuals’ subjective differences in a supply chain and, with this
definition, we are ready to study supply chain network robustness.
6.3.2 Supply Chain Robustness Measurement
Robustness has a broad meaning and is often couched in different settings. Generally speaking, robustness means that the system performs well when exposed to
uncertain future conditions and perturbations (cf. Bundschuh et al., 2003; Snyder,
2003; Holmgren 2007).
Therefore, we propose the following rationale to assess the robustness of a supply
chain: assume that all the random parameters take on a given threshold probability
value; say, for example, 95 %. Moreover, assume that all the cumulative distribution
functions for random parameters have inverse functions. Hence, we have that: ˛i D
Fi1 .0:95/, for i D 1, . . . , m; ˇiju D Fiju1 .0:95/, for i D 1, . . . , m; j D 1, . . . ,
n, and so on. With the disruption related parameters given, we can calculate the
supply chain performance measure according to the definition given by (6.14). Let
"w denote the supply chain performance measure with random parameters fixed at
a certain level as described above. For example, when w D 0.95, "w is the supply
chain performance with all the random risk parameters fixed at the value of a 95 %
probability level. Then, the supply chain network robustness measure, R, is given
by the following:
(6.15)
R D "0 "w ;
where "0 gauges the supply chain performance based on the model introduced in
Sect. 6.2, but with weights related to risks being zero.
"0 examines the “base” supply chain performance while "w assesses the supply
chain performance measure at some pre-specified uncertainty level. If their difference is small, a supply chain maintains its functionality well and we consider the
supply chain to be robust at the threshold disruption level. Hence, the lower the
value of R, the more robust a supply chain is. Note that since the random parameters are fixed at certain threshold level when we compute "w , the corresponding
cost variances are equal to zero. Therefore, "w does not consider individual’s risk
attitude either as in the definition of "0 .
Notably, the above robustness definition has implications for network resilience
as well. Resilience is a general and conceptual term, which is hard to quantify.
6 Modeling of Supply Chain Risk
105
McCarthy (2007) defined resilience “. . . as the ability of a system to recover from
adversity, either back to its original state or an adjusted state based on new requirements, . . . ”. For a comprehensive discussion of resilience, please refer to the Critical Infrastructure Protection Program (2007). Because our supply chain measure is
based on the network equilibrium model, a network that is qualified as being robust
according to our measure is also resilient provided that its performance after experiencing the disruption(s) is close to the “original value.” Interestingly, this idea is in
agreement with Hansson and Helgesson (2003), who proposed that robustness can
be treated as a special case of resilience.
6.3.2.1 A Weighted Supply Chain Performance Measure
Note that different supply chains may have different requirements regarding the
performance and robustness concepts introduced in the previous sections. For example, in the case of a supply chain of a toy product one may focus on how to
satisfy demand in the most cost efficient way and not care too much about supply chain robustness. A medical/healthcare supply chain, on the other hand, may
have a requirement that the supply chain be highly robust when faced with uncertain conditions. Hence, in order to be able to examine and to evaluate the different
application-based supply chains from both perspectives, we now define a weighted
supply chain performance measure as follows:
"O D .1 2/ "0 C 2 .R/ ;
(6.16)
where " 2[0, 1] is the weight that is placed on the supply chain robustness.
When " is equal to 1, the performance of a supply chain hinges only on the
robustness measure, which may be the case for a medical/healthcare supply chain,
noted above. In contrast, when " is equal to 0, the performance of the supply chain
depends solely on how well it can satisfy demands at low prices. The supply chain
of a toy product in the above discussion falls into this category.
6.4 Examples
The supply chain network topology for the numerical examples is depicted in
Fig. 6.2 below. There are assumed to be two manufacturers, two retailers, and
two demand markets. There are two modes of transportation available between
each manufacturer and retailer pair and between each retailer and demand market
pair. These examples are solved by the modified projection method of Korpelevich
(1977); see also, e. g., Nagurney (2006a). Furthermore, for completeness, in the following examples, I also reported different variance functions for the general purpose
of computing supply chain equilibrium solutions though they are not necessarily
needed for determining the supply chain performance.
106
Q. Qiang, A. Nagurney, J. Dong
Fig. 6.2 The supply chain
network for the numerical
examples
Example 6.1
In the first example, for illustration purposes, we assumed that all the random parameters followed uniform distributions. The relevant parameters are as follows:
˛i [0, 2]
for i D 1; 2I
ˇiju [0, 1]
for i D 1; 2I
j [0, 3]
for j D 1; 2 :
j D 1; 2I
u D 1; 2I
We further assumed that the demand functions followed a uniform distribution given
by Œ200 23k ; 600 23k , for k D 1, 2. Hence, the expected demand functions
are:
dOk .3 / D 400 23k ; for k D 1; 2 :
The production cost functions for the manufacturers are given by:
12 0
10
1
0
2
2
2
2 X
2 X
2 X
X
X
X
1 u A
u A@
u A
q1j
C@
q1j
q2j
f1 Q ; ˛1 D 2:5 @
j D1uD1
0
C 2˛1 @
2
2 X
X
1
j D1 uD1
j D1 uD1
u A
;
q1j
j D1 uD1
12 0
10
1
2
2
2
2 X
2 X
2 X
X
X
X
1 u A
u A@
u A
f2 Q ; ˛2 D 2:5 @
q2j
C@
q1j
q2j
0
j D1uD1
0
C 2˛2 @
2
2 X
X
j D1 uD1
1
u A
q2j
:
j D1 uD1
j D1 uD1
6 Modeling of Supply Chain Risk
107
The expected production cost functions for the manufacturers are given by:
FO1 Q
1
0
D 2:5 @
0
C2@
0
2
2 X
X
2
2 X
X
j D1 uD1
0
C2@
2 X
2
X
0
u A
q1j
C@
j D1 uD1
j D1 uD1
FO2 .Q1 / D 2:5 @
12
2 X
2
X
10
2 X
2
X
u A@
q1j
j D1 uD1
1
1
2 X
2
X
u A
q2j
j D1 uD1
u A
q1j
;
12
0
u A
q2j
C@
2
2 X
X
10
u A@
q1j
j D1 uD1
1
2
2 X
X
1
u A
q2j
j D1 uD1
u A
q2j
:
j D1 uD1
The variances of the production cost functions for the manufacturers are given by:
12
0
2
2 X
X
4
u A
q1j
;
VF1 .Q1 / D @
3
j D1 uD1
12
0
2
2 X
X
4
u A
VF2 .Q1 / D @
q2j
:
3
uD1
j D1
The transaction cost functions faced by the manufacturers and associated with transacting with the retailers are given by:
2
cij1 qij1 ; ˇij1 D 0:5 qij1 C 3:5ˇij1 qij1 ; for i D 1; 2I j D 1; 2 ;
2
cij2 qij2 ; ˇij2 D qij2 C 5:5ˇij2 qij2 ; for i D 1; 2I j D 1; 2 :
The expected transaction cost functions faced by the manufacturers and associated
with transacting with the retailers are given by:
2
CO ij1 qij1 D 0:5 qij1 C 1:75qij1 ;
2
CO ij2 qij2 D 0:5 qij2 C 2:75qij2 ;
for i D 1; 2I j D 1; 2;
for i D 1; 2I j D 1; 2 :
The variances of the transaction cost functions faced by the manufacturers and associated with transacting with the retailers are given by:
2
V Cij1 qij1 D 1:0208 qij1 ;
2
V Cij2 qij2 D 2:5208 qij2 ;
for i D 1; 2I j D 1; 2;
for i D 1; 2I j D 1; 2:
108
Q. Qiang, A. Nagurney, J. Dong
The handling costs of the retailers, in turn, are given by:
2 X
2
X
cj Q1 ; Q2 ; j D 0:5
qiju
!2
C j
i D1 uD1
2 X
2
X
!
qiju
;
for j D 1; 2 :
i D1 uD1
The expected handling costs of the retailers are given by:
1
CO j Q1 ; Q
2
D 0:5
2 X
2
X
!2
qiju
C 1:5
i D1 uD1
2 X
2
X
!
qiju
;
for j D 1; 2 :
i D1uD1
The variance of the handling costs of the retailers are given by:
V Cj Q 1 ; Q
2
3
D
4
2
2 X
X
!2
qiju
;
for j D 1; 2 :
i D1 uD1
The unit transaction costs from the retailers to the demand markets are given by:
2
1
1
cjk
Q D 0:3qjk
; for j D 1; 2I k D 1; 2;
2
2
2
cjk Q D 0:6qjk ; for j D 1; 2I k D 1; 2 :
We assumed that the manufacturers and the retailers placed zero weights on the
disruption risks as discussed in Sect. 6.3.1 to compute "0 .
In the equilibrium, under the expected costs and demands, we have that the
equilibrium shipments between manufacturers and retailers are: qij1 D 8.5022, for
i D 1, 2; j D 1, 2; qij2 D 3.7511, for i D 1, 2; j D 1, 2; whereas the equilib1
D 8.1767,
rium shipments between the retailers and the demand markets are: qjk
2
for j D 1, 2; k D 1, 2; qjk D 4.0767, for j D 1, 2; k D 1, 2. Finally, the
equilibrium prices are: 31
D 32
D 187.7466 and the expected equilibrium deO
O
mands are: d1 D d2 D 24.5068. The supply chain performance measure is equal to
"0 D 0.1305. Now, assume that w D0.95; that is, all the random cost parameters are
fixed at a 95 % probability level. The resulting supply chain performance measure is
computed as "w D 0.1270. If we let " D 0:5 (cf. (6.12)), which means that we place
equal emphasis on performance and robustness of the supply chain, the weighted
supply chain performance measure is "O D 0.0635.
Example 5.2
For the same network structure and cost and demand functions, we now assume
that the relevant parameters are changed as follows: ˛i [0, 4] for i D 1, 2; ˇiju [0, 2] for i D 1, 2; j D 1, 2; u D 1, 2; j [0, 6] for j D 1, 2.
In the equilibrium, under the expected costs and demands, we have that the equilibrium shipments between manufacturers and retailers are now: qij1 D 8.6008, for
i D 1, 2; j D 1, 2; qij2 D 3.3004, for i D 1, 2; j D 1, 2; whereas the equilib-
6 Modeling of Supply Chain Risk
109
1
rium shipments between the retailers and the demand markets are: qjk
D 7.9385,
2
for j D 1, 2; k D 1, 2; qjk D 3.9652, for j = 1, 2; k = 1, 2. Finally, the
equilibrium prices are: 31
D 32
D 188.0963 and the expected equilibrium demands are: dO1 D dO2 D 23.8074. The supply chain performance measure is equal to
"0 D 0.1266. Similar to the above example, let us assume that w D 0:95; that is,
all the random cost parameters are fixed at a 95 % probability level. The resulting
supply chain performance measure is now: "w D 0.1194. If we let " D 0:5, the
weighted supply chain performance measure is "O D 0.0597.
Observe that first example leads to a better measure of performance since the
uncertain parameters do not have as great of an impact as in the second one for the
cost functions under the given threshold level.
6.5 Summary and Conclusions
In this chapter, we developed a novel supply chain network model to study the
demand-side as well as the supply-side risks, with the demand being random and the
supply-side risks modeled as uncertain parameters in the underlying cost functions.
This supply chain model generalizes several existing models by including multiple
transportation modes from the manufacturers to the retailers, and from the retailers
to the demand markets. We also proposed a weighted supply chain performance and
robustness measure based on our recently derived network performance/efficiency
measure and illustrated the supply chain network model through numerical examples for which the equilibrium prices and product shipments were computed and
robustness analyses conducted. For future research, we plan on constructing further
comprehensive metrics in order to evaluate supply chain network performance and
to also apply the results in this chapter to empirically-based supply chain networks
in different industries.
Acknowledgements The research of the first two authors was supported by the John F. Smith
Memorial Fund at the Isenberg School of Management. This support is gratefully appreciated.
The authors would like to thank Professor Teresa Wu of Arizona State University and Professor
Jennifer Blackhurst of Iowa State University for the invitation to contribute this chapter to the volume Managing Supply Chain Risk and Vulnerability: Tools and Methods for Supply Chain
Decision Makers, Springer.
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Chapter 7
The Effects of Network Relationships
on Global Supply Chain Vulnerability
Jose M. Cruz
Abstract In this chapter, we analyze the effects of levels of social relationship on
the global supply chain networks vulnerability. Relationship levels in our framework
are assumed to influence transaction costs as well as risk for the decision-makers.
We propose a network performance measure for the evaluation of the global supply chain networks efficiency and vulnerability. The measure captures risk, transaction cost, price, transaction flow, revenue, and demand information in the context
of the decision-makers behavior the network. The network consists of manufacturers, retailers, and consumers. Manufacturers and retailers are multicriteria decisionmakers who decide about their production and transaction quantities as well as the
level of social relationship they want to pursue in order to maximize net return and
minimize risk. The model allows us to investigate the interplay of the heterogeneous decision-makers in the supply chain and to compute the resultant equilibrium
pattern of product outputs, transactions, product prices, and levels of social relationship. The results show that high levels of relationship can lead to lower overall
cost and therefore lower price and higher product transaction. Moreover, we use the
performance measure to assess which nodes in the supply networks are the most vulnerable in the sense that their removal will impact the performance of the network
in the most significant way.
7.1 Introduction
In recent years, growing competition and emphasis on efficiency and cost reduction, as well as the satisfaction of consumer demands, have brought new challenges
for businesses in the global marketplace. As a result companies are outsourcing
and offshoring large portions of manufacturing, sourcing in low-cost countries,
reducing inventories, streamlining the supply base, and collaborating more intensively with other supply chain actors [12, 19]. However, the increase in interfirm
dependence as well as longer and more complex supply chain setups with globeT. Wu, J. Blackhurst (eds.), Managing Supply Chain Risk and Vulnerability
© Springer 2009
113
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J.M. Cruz
spanning operations have increased the vulnerability of supply chains to unexpected
events [6, 17, 18, 36]. For example, recently, the threat of illness in the form of
SARS (see [10]) has disrupted supply chains, as have terrorist threats (cf. [34]) and
the natural disaster of Hurricane Katrina in 2005. Indeed, at the same time that supply chains have become increasingly globalized, their operation environment has
become unpredictable and filled with uncertainty.
Supply chain disruptions can materialize from various areas internal and external to a supply chain. The main supply chain vulnerability drivers can be divided
in three groups, demand-side, supply-side, and Catastrophic events. The demandside drivers would include demand uncertainty, customer dependence, and disruptions in the physical distribution of products to the end-customers. The supply-side
drivers include supplier business risks, production capacity constraints on the supply
market, quality problems, technological changes, and product design changes [39].
Moreover these drivers would increase supply chain vulnerability even more if the
firm uses single sourcing or fewer suppliers. Catastrophic events refer to natural
hazards, socio-political instability, civil unrest, economic disruptions, and terrorist
attacks [26, 24]. Therefore we believe that firms should proactively assess and manage the uncertainties in supply chain by creating a portfolio of relationships with
their suppliers and demand markets in order to guard against costly supply chain
disruptions.
The value of relationship is not only economical but also technical and social [14]. Strong supply chain relationships enable firms to react to changes in
the market, create customer value and loyalty, which lead to improve profit margins [11]. The benefits are reduction of production, transportation and administrative
costs. On the technical development the greatest benefit is the possibility of sharing
the resources of suppliers and shortening the lead-times. Spekman and Davis [35]
found that supply chain networks that exhibit collaborative behaviors tend to be
more responsive and that supply chain-wide costs are, hence, reduced. These results
are also supported by Dyer [9] who demonstrated empirically that a higher level of
trust (relationship) lowers transaction costs (costs associated with negotiating, monitoring, and enforcing contracts). Baker and Faulkner [1] present an overview of
papers by economic sociologists that show the important role of relationships due to
their potential to reduce risk and uncertainty. Uzzi [37] and Gadde and Snehota [14]
suggest that multiple relationships can help companies deal with the negative consequences related to dependence on supply chain partners. Krause et al. [25] found
that buyer commitment and social capital accumulation with key suppliers can improve buying company performance. However, Christopher and Jüttner [5] indicate
that the value of the relationship depends on the substitutability of the buyers or
sellers, the indispensability of goods, savings resulting from partner’s practices and
the degree of common interest.
In this chapter, we analyze the effects of relationships on a multitiered global
supply chain network efficiency and vulnerability. Wakolbinger and Nagurney [38]
and Cruz et al. [8] developed a framework for the modeling and analysis of supply
chains networks that included the role that relationships play. Their contribution was
apparently the first to introduce relationship levels in terms of flows on networks,
7 The Effects of Network Relationships on Global Supply Chain Vulnerability
115
along with logistical flows in terms of product transactions, combined with pricing.
However, their models did not considerer the effects of relationship levels on supply
chain efficiency and vulnerability.
This chapter models the multicriteria decision-making behavior of the various
decision-makers in a multitiered global supply chain network, which includes the
maximization of profit and the minimization of risk through the inclusion of the social relationship, in the presence of both business-to-business (B2B) and businessto-consumer (B2C) transactions. We describe the role of relationships in the global
supply chain networks. Decision-makers in a given tier of the network can decide
on the relationship levels that they want to achieve with decision-makers associated
with the other tiers of the network. Establishing/maintaining a certain relationship
level induces some costs, but may also lower the risk and the transaction costs. We
explicitly describe the role of relationships in influencing transaction costs and risk.
Both the risk functions and the relationship cost functions are allowed to depend on
the relationship levels. In addition, we analyze the effects of the levels of social relationship on the supply chain efficiency and vulnerability. Hence, we truly capture
the effects of networks of relationships in the global supply chain framework.
This chapter is organized as follows. In Sect. 7.2, we develop the multitiered,
multiperiod supply chain network model. We describe decision-makers’ optimizing
behavior and establish the governing equilibrium conditions along with the corresponding variational inequality formulation. In Sect. 7.3, we present the supply
chain network efficiency and vulnerability measures. In Sect. 7.4, we present numerical examples. Section 7.5 provides managerial implications. We conclude the
chapter with Sect. 7.6 in which we summarize our results and suggest directions for
future research.
7.2 The Global Supply Chain Networks Model
In this Section, we develop the network model with manufacturers, retailers, and
demand markets in a global context. We assume that the manufacturers are involved
in the production of a homogeneous product and we consider L countries, with
I manufacturers in each country, and J retailers, which are not country-specific
but, rather, can be either physical or virtual, as in the case of electronic commerce.
There are K demand markets for the homogeneous product in each country and H
currencies in the global economy. We denote a typical country by l or lO, a typical
manufacturer by i , and a typical retailer by j . A typical demand market, on the
other hand, is denoted by k and a typical currency by h. We assume that each
manufacturer can conduct transactions with the retailers in different currencies. The
demand for the product in a country can be associated with a particular currency.
The network in Fig. 7.1 represents the global supply chain network consisting of
three tiers of decision-makers. The top tier of nodes consists of the manufacturers
in the different countries, with manufacturer i in country l being referred to as
116
J.M. Cruz
Fig. 7.1 The structure of the global supply chain network
manufacturer i l and associated with node i l. There are, hence, IL top-tiered nodes
in the network. The middle tier of nodes of the network consists of the retailers
(which recall need not be country-specific) and who act as intermediaries between
the manufacturers and the demand markets, with a typical retailer j associated with
node j in this (second) tier of nodes. The bottom tier in the supply chain network
consists of the demand markets, with a typical demand market k in currency h and
O being associated with node khlO in the bottom tier of nodes. There are, as
country l,
depicted in Fig. 7.1, J middle (or second) tiered nodes corresponding to the retailers
and KHL bottom (or third) tiered nodes in the global supply chain network.
We have identified the nodes in the network and now we turn to the identification of the links joining the nodes in a given tier with those in the next tier. We
assume that each manufacturer i in country l involved in the production of the
homogeneous product can transact with a given retailer in any of the H available
currencies, as represented by the H links joining each top tier node with each middle tier node j ; j D 1, . . . , J . Furthermore, each retailer (intermediate) node j ;
j D 1, . . . , J , can transact with each demand market denoted by node khlO. The
product transactions represent the flows on the links of the supply chain network in
Fig. 7.1.
We also assume that each manufacturer i in country l can establish a portfolio of relationships with retailers. Furthermore, each retailer (intermediate) node j ;
j D 1, . . . , J , can establish a relationship level with a demand market denoted by
7 The Effects of Network Relationships on Global Supply Chain Vulnerability
117
node khlO and with manufacturers. We assume that the relationship levels are nonnegative and that they may attain a value from 0 through 1. A relationship level of 0
indicates no relationship and a relationship of 1 indicates the highest possible relationship. These relationship levels are associated with each of nodes of the first two
tiers of the network in Fig. 7.1.
Note that there will be prices associated with each of the tiers of nodes in the
global supply chain network. The model also includes the rate of appreciation of
currency h against the basic currency, which is denoted by eh (see [28]). These
“exchange” rates are grouped into the column vector e 2 RH . The variables for this
model are given in Table 7.1. All vectors are assumed to be column vectors.
Table 7.1 Variables in global supply chain networks
Notation
Definition
q
IL-dimensional vector of the amounts of the product produced by the manufacturers
in the countries with component i l denoted by q il
Q1
ILJH -dimensional vector of the amounts of the product transacted between the
manufacturers in the countries in the currencies with the retailers with component il
jh
denoted by qjilh
Q2
JKHL-dimensional vector of the amounts of the product transacted between the
retailers and the demand markets in the countries and currencies with component j
denoted by q j
khlO
khlO
1
IL-dimensional vector of the relationships levels of manufacturers with component il
denoted by il
2
J -dimensional vector of the relationship levels of retailers with component j denoted
by j
il
1j
h
Price associated with the product transacted between manufacturer i l and retailer j
in currency h
j
Price associated with the product transacted between retailer j and demand market k
in currency h and country lO
3
KHL-dimensional vector of the demand market prices of the product at the demand
markets in the currencies and in the countries with component khl denoted by 3khl
2khlO
We now turn to the description of the functions and assume that they are measured in the base currency (dollar). We first discuss the production cost, transaction
cost, handling, and unit transaction cost functions given in Table 7.2. Each manufacturer is faced with a certain production cost function that may depend, in general, on
the entire vector of production outputs. Furthermore, each manufacturer and each retailer are faced with transaction costs. The transaction costs are affected/influenced
by the amount of the product transacted and the relationship levels. As indicated in
the introduction, relationship levels affect transaction costs [9, 35]. This is especially
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J.M. Cruz
Table 7.2 Production, handling, transaction, and unit transaction cost functions
Notation
Definition
f il .q/ D f il .q il /
The production cost function of manufacturer i in country l
cj .Q1 /
cjilh qjilh ; il
The handling/conversion cost function of retailer j
cOjilh qjilh ; j
cj
khlO
qj O; j
khl
cO j O .Q2 ; 2 /
khl
The transaction cost function of manufacturer i l transacting
with retailer j in currency h
The transaction cost function of retailer j transacting
with manufacturer i l in currency h
The transaction cost function of retailer j transacting
with demand market khlO
The unit transaction cost function associated with consumers
at demand market khl in obtaining the product from retailer j
important in international exchanges in which transaction costs may be significant.
Hence, the transaction cost functions depend on flows and relationship levels.
Each retailer is also faced with what we term a handling/conversion cost (cf. Table 7.2), which may include, for example, the cost of handling and storing the product plus the cost associated with transacting in the different currencies. The handling/conversion cost of a retailer is a function of how much he has obtained of the
product from the various manufacturers in the different countries and what currency
the transactions took place. For the sake of generality, however, we allow the handling functions to depend also on the amounts of the product held and transacted by
other retailers.
The consumers at each demand market are faced with a unit transaction cost. As
in the case of the manufacturers and the retailers, higher relationship levels may potentially reduce transaction costs, which mean that they can lead to quantifiable cost
reductions. The unit transaction costs depend on the amounts of the product that the
retailers and the manufacturers transact with the demand markets as well as on the
vectors of relationships established with the demand markets. The generality of the
unit transaction cost function structure enables the modeling of competition on the
demand side. Moreover, it allows for information exchange between the consumers
at the demand markets who may inform one another as to their relationship levels
which, in turn, can affect the transaction costs.
We now turn to the description of the relationship production cost functions and,
finally, the risk functions and the demand functions. We assume that the relationship
production cost functions as well as the risk functions are convex and continuously
differentiable. The demand functions are assumed to be continuous.
We start by describing the relationship production cost functions that are given in
Table 7.3. We assume that each manufacturer may actively try to achieve a certain
relationship level with a retailer as proposed in Golicic et al. [15]. Furthermore, each
retailer may actively try to achieve a certain relationship level with a manufacturer
7 The Effects of Network Relationships on Global Supply Chain Vulnerability
119
Table 7.3 Relationship productions cost functions
Notation
b il il
bj j
Definition
The relationship production cost function associated with manufacturer i l
The relationship production cost function associated with retailer j
and/or demand market. These relationship production cost functions may be distinct
for each such combination. Their specific functional forms may be influenced by
such factors as the willingness of retailers or demand markets to establish/maintain
a relationship as well as the level of previous business relationships and private relationships that exist. Hence, we assume that these production cost functions are also
affected and influenced by the relationship levels. Crosby and Stephens [7] indicate
that the relationship strength changes with the amount of buyer-seller interaction
and communication. In a global setting, cultural differences, difficulties with languages, and distances, may also play a role in making it more costly to establish
(and to maintain) a specific relationship level (cf. [20]).
The concept of relationship levels was inspired by a paper by Golicic et al. [15]
who introduced the concept of relationship magnitude. That research strongly suggested that different relationship magnitudes lead to different benefits and those
different levels of relationship magnitudes can be achieved by putting more or
less time and effort into the relationship. The idea of a continuum of relationship
strength is also supported by several theories of relationship marketing that suggest
that business relationships vary on a continuum from transactional to highly relational (cf. [13]). The model by Wakolbinger and Nagurney [38] operationalized the
frequently mentioned need to create a portfolio of relationships (cf. [4, 15]). The
optimal portfolio balanced out the various costs and the risk, against the profit and
the relationship value and included the individual decision-makers preferences and
risk aversions.
We now describe the risk functions as presented in Table 7.4. We note that the
risk functions in our model are functions of both the product transactions and the
relationship levels. Jüttner et al. [21] suggest that supply chain-relevant risk sources
falls into three categories: environmental risk sources (e. g., fire, social-political actions, or “acts of God”), organizational risk sources (e. g., production uncertainties),
and network-related risk sources. Johnson [22] and Norrman and Jansson [31] argue
that network related risk arises from the interaction between organizations within the
supply chain, e. g., due to insufficient interaction and cooperation. Here, we model
Table 7.4 Risk funktions
Notation
r il Q1 ; 1
r j Q1 ; Q2 ; 2
Definition
The risk incurred by manufacturer i l in his transactions
The risk incurred by retailer j in his transactions
120
J.M. Cruz
supply chain organizational risk and network-related risk by defining the risk as
a function of product flows as well as relationship levels. We use relationship levels (levels of cooperation) as a way of possibly mitigating network-related risk. We
also note that by including the currency appreciation rate (eh ) in our model, in order
to convert the prices to the base currency (dollar), we are actually mitigating any
exchange rate risk. Of course, in certain situations; see also Granovetter [16], the
risk may be adversely affected by higher levels of relationships. Nevertheless, the
functions in Table 7.4 explicitly include relationship levels and product transactions
as inputs into the risk functions and reflect this dependence.
The demand functions as given in Table 7.5 are associated with the bottom-tiered
nodes of the global supply chain network. The demand of consumers for the product
at a demand market in a currency and country depends, in general, not only on the
price of the product at that demand market (and currency and country) but also on
the prices of the product at the other demand markets (and in other countries and
currencies). Consequently, consumers at a demand market, in a sense, also compete
with consumers at other demand markets.
Table 7.5 Demand functions
Notation
Definition
dkhlO .3/
The demand for the product at demand market k transacted in currency h
in country lO as a function of the demand market price vector
We now turn to describing the behavior of the various economic decision-makers.
The model is presented, for ease of exposition, for the case of a single homogeneous
product. It can also handle multiple products through a replication of the links and
added notation. We first focus on the manufacturers. We then turn to the retailers,
and, subsequently, to the consumers at the demand markets.
7.2.1 The Behavior of the Manufacturers
The manufacturers are involved in the production of a homogeneous product and
in transacting with the retailers. Furthermore, they are also involved in establishing the corresponding relationship levels. The quantity of the product produced by
manufacturer i l must satisfy the following conservation of flow equation:
qi l D
H
J X
X
il
qjh
;
(7.1)
j D1 hD1
which states that the quantity of the product produced by manufacturer i l is equal
to the sum of the quantities transacted between the manufacturer and all retailers.
7 The Effects of Network Relationships on Global Supply Chain Vulnerability
121
Hence, in view of (7.1), and as noted in Table
7.2, we have that for each manufacturer i l the production cost f i l .q/ D f i l q i l .
Each manufacturer i l tries to maximize his profits. He faces total costs that equal
the sum of his production cost plus the total transaction costs and the costs that
he incurs in establishing and maintaining his relationship levels. His revenue, in
turn, is equal to the sum of the price that he can obtain times the exchange rate
multiplied by quantities of the product transacted. Furthermore, each manufacturer
tries to minimize his risk generated by interacting with the retailers subject to his
individual weight assignment to this criterion.
7.2.2 The Multicriteria Decision-Making Problem
Faced by a Manufacturer
We can now construct the multicriteria decision-making problem facing a manufacturer which allows him to weight the criteria of profit maximization and risk minimization in an individual manner. Manufacturer i l’s multicriteria decision-making
objective function is denoted by U i l . Assume that manufacturer i l assigns a nonnegative weight ˛ i l to the risk generated. The weight associated with profit maximization serves as the numeraire and is set equal to 1. The nonnegative weights
measure the importance of the risk and, in addition, transform it value into monei l
denote the actual price charged by manufacturer i l for the
tary units. Let now 1jh
product in currency h to retailer j . We later discuss how such price is recovered. We
can now construct a value function for each manufacturer (cf. [8, 23]) using a constant additive weight value function. Therefore, the multicriteria decision-making
problem of manufacturer i l can be expressed as:
Maximize U i l D
J X
H
X
i l
il
.1jh
eh /qjh
f i l .q i l / j D1 hD1
J X
J
X
il
il
cjh
.qjh
; i l /
j D1 hD1
b i l .i l / ˛ i l r i l .Q1 ; 1 /
(7.2)
subject to:
il
qjh
0; 8j; h ;
(7.3)
0 i l 1 :
(7.4)
The first four terms on the right-hand side of the equal sign in (7.2) represent the
profit which is to be maximized, the next term represents the weighted total risk
which is to be minimized. The relationship values lie in the range between 0 and 1
and, hence, we need constraint (7.4).
122
J.M. Cruz
7.2.3 The Optimality Conditions of Manufacturers
Here we assume that the manufacturers compete in a noncooperative fashion following Nash [29, 30]. Hence, each manufacturer seeks to determine his optimal strategies, that is, product transactions, given those of the other manufacturers. The optimality conditions of all manufacturers i ; i D 1, . . . , I ; in all countries: l; l D 1, . . . ,
L simultaneously, under the above assumptions (cf. [2, 8, 27]), can be compactly expressed as: determine .Q1 ; 1 / 2 k 1 , satisfying
"
il
i l i l
L X
H
I X
J X
il
1 1
X
.qjh
; /
@cjh
@f i l .q i l /
i l @r .Q ; /
C
C
˛
il
il
il
@qjh
@qjh
@qjh
i D1 l D 1 j D 1 h D 1
i h
i
i l
il
i l
1jk
eh qjh
qjh
C
L X
H
I X
J X
X
"
il
i l i l
@cjh
.qjh
; /
i D1 l D1 j D1 hD1
@i l
C
@b i l .i l /
@i l
#
i
h
@r i l .Q1 ; 1 /
il
i l
0;
C˛
@i l
il
8.Q1 ; 1 / 2 k 1 ;
(7.5)
where
h
il
k 1 .Q1 ; 1 /jqjh
0; 0 i l 1;
i
8i; l; j; h :
(7.6)
The inequality (7.5), which is a variational inequality (cf. [27]) has a meaningful
economic interpretation. From the first term in (7.5) we can see that, if there is a positive volume of the product transacted from a manufacturer to a retailer, then the
marginal cost of production plus the marginal cost of transacting plus the weighted
marginal cost of risk must be equal to the price (times the exchange rate) that the
retailer is willing to pay for the product. If that sum, in turn, exceeds that price then
there will be no product transacted.
The second term in (7.5) show that if there is a positive relationship level (and
that level is less than one) then the marginal cost associated with the level is equal
to the marginal reduction in transaction costs plus the weighted marginal reduction
in risk.
7.2.4 The Behavior of the Retailers
The retailers (cf. Fig. 7.1), in turn, are involved in transactions both with the manufacturers in the different countries, as well as with the ultimate consumers associated
with the demand markets for the product in different countries and currencies and
7 The Effects of Network Relationships on Global Supply Chain Vulnerability
123
represented by the bottom tier of nodes in both the global supply chain network and
the social network.
As in the case of manufacturers, the retailers have to bear some costs to establish
and maintain relationship levels with manufacturers and with the consumers, who
are the ultimate purchasers/buyers of the product. Furthermore, the retailers have
associated transaction costs in regards to transacting with the manufacturers, which
we assume can be dependent on the type of currency as well as the manufacturer.
Retailers also are faced with risk in their transactions. As in the case of the manufacturers, the transaction cost functions and the risk functions depend on the amounts
of the product transacted as well as the relationship levels.
Each retailer j tries to maximize profits and to minimize his individual risk associated with his transactions with these criteria weighted in an individual fashion.
7.2.5 A Retailer’s Multicriteria Decision-Making Problem
Retailer j assigns a nonnegative weight ı j to his risk. The weight associated with
profit maximization is set equal to 1 and serves as the numeraire (as in the case of
the manufacturers). The actual price charged for the product by retailer j is denoted
by j O , and is associated with transacting with consumers at demand market k
2khl
O Later, we discuss how such prices are arrived at. We
in currency h and country l.
are now ready to construct the multicriteria decision-making problem faced by a retailer which combines the individual weights with the criteria of profit maximization
and risk minimization. Let U j denote the multicriteria objective function associated
with retailer j with his multicriteria decision-making problem expressed as:
Maximize
U D
j
K X
H X
L
X
.
2khlO
k D 1 h D 1 lO D 1
K
X
H
X
j
L
X
eh /q
j
khlO
cj .Q / 1
khl
I X
L X
H
X
ı r .Q ; Q ; /
1
2
i l
il
.1jh
eh /qjh
i D1 l D1 hD1
k D 1 h D 1 lO D 1
j j
il
il
cOjh
.qjh
; j /
i D1 l D1 hD1
c j O .q j O ; j / b j .j / khl
I X
L X
H
X
2
(7.7)
subject to:
K X
H X
L
X
q
j
khlO
k D 1 h D 1 lO D 1
il
qjh
0; q j
khlO
0;
0 j 1; 8j :
L X
I X
H
X
il
qjh
;
(7.8)
i D1 l D1 hD1
8i; l; k; h; lO ;
(7.9)
(7.10)
124
J.M. Cruz
The first six terms on the right-hand side of the equal sign in (7.7) represent the
profit which is to be maximized, the next term represents the weighted risk which
is to be minimized. Constraint (7.8) states that consumers cannot purchase more of
the product from a retailer than is held “in stock”.
7.2.6 The Optimality Conditions of Retailers
We now turn to the optimality conditions of the retailers. Each retailer faces the
multicriteria decision-making problem (7.7), subject to (7.8), the nonnegativity assumption on the variables (7.9), and the assumptions for the relationship values
(7.10). As in the case of the manufacturers, we assume that the retailers compete in
a noncooperative manner, given the actions of the other retailers. Retailers seek to
determine the optimal transactions associated with the demand markets and with the
manufacturers. In equilibrium, all the transactions between the tiers of the decisionmakers will have to coincide, as we will see later in this section.
If one assumes that the handling, transaction cost, and risk functions are continuously differentiable and convex, then the optimality conditions for all the retailers
satisfy the variational inequality: determine .Q1 ; Q2 ; 2 ; / 2 k 2 , such that
"
#
I X
L X
J X
il
i l j H
j
X
@cOjh
.qjh
; /
@cj .Q1 /
j @r
i l
C
C 1jh eh C
j
ı
il
il
il
@qjh
@qjh
@qjh
j D1 i D1 l D1 hD1
h
i
il
i l
qjh
qjh
C
h
K X
J X
H X
L
X
4ı j
j D 1 k D 1 h D 1 lO D 1
qj
khlO
C
2
q j O
i
@r j @q j
C
@c
j
.q
O
khl
j
; j /
O
khl
@q j
khlO
3
C j O eh C j 5
2khl
khlO
khl
K X
J X
H X
L
X
j D 1 k D 1 h D 1 lO D 1
2
j
4ı j @r C
@j
@c
j
khlO
.q
j
khlO
@j
; j /
C
il
i l j @cOjh
.qjh
; /
@j
@b j .j /
j j C
@j
C
J
X
j D1
"
L X
I X
H
X
i l
qjh
i D1 l D1 hD1
8.Q1 ; Q2 ; 2 ; / 2 k 2 ;
K X
H X
L
X
#
q
j
khlO
j j 0 ;
k D1 hD1 l D1
(7.11)
7 The Effects of Network Relationships on Global Supply Chain Vulnerability
where r j D r j .Q1 ; Q2 ; 2 / and
h
ˇ il
k 2 .Q1 ; Q2 ; 2 ; /ˇqjh
0; q j
125
i
O :
8i;
l;
j;
h;
k;
l
khlO
(7.12)
Here j denotes the Lagrange multiplier associated with constraint (7.8) and is the
column vector of all the retailers’ Lagrange multipliers. These Lagrange multipliers
can also be interpreted as shadow prices. Indeed, according to the fourth term in
(7.11), j serves as the price to “clear the market” at retailer j .
The economic interpretation of the retailers’ optimality conditions is very interesting. The first term in (7.11) states that if there is a positive amount of product
i l
> 0,
transacted between a manufacturer/retailer pair and currency h, that is, qjh
then the shadow price at the retailer, j , is equal to the price charged for the product plus the various marginal costs and the associated weighted marginal risk. In
addition, the second term in (7.11) shows that, if consumers at demand market khlO
purchase the product from a particular retailer j , which means that, if the q j O is
0; 0 j 1; j 0;
khlm
j
positive, then the price charged by retailer j , O , is equal to j plus the marginal
2khl
transaction costs in dealing with the demand market and the weighted marginal costs
for the risk that he has to bear. One also obtains interpretations from (7.11) as to the
economic conditions at which the relationship levels associated with retailers interacting with either the manufacturers or the demand markets will take on positive
values.
7.2.7 The Consumers at the Demand Markets
We now describe the consumers located at the demand markets. The consumers can
transact through with the retailers. The consumers at demand market k in country lO take into account the price charged for the product transacted in currency h
j
by retailer j , which is denoted by O and the exchange rate, plus the transac2khl
tion costs, in making their consumption decisions. The equilibrium conditions for
O thus, take the form: for all retailers: j D 1, . . . , J , demand
demand market khl,
markets k; k D 1, . . . , K; and currencies: h; h D 1, . . . , H
(
j
D O ; if q O > 0 ;
j
j
2 2
khl
3khl
O eh C cO O .Q ; /
(7.13)
j
2khl
khl
O ; if q O D 0 ;
3khl
In addition, we must have that for all k; h; lO
8
J
P
ˆ
j
ˆ
ˆD
q O;
<
j D 1 khl
dkhlO .3 /
J
ˆ
ˆ P qj ;
:̂
O
j D 1 khl
if 3khlO
if
O
3khl
khl
> 0;
(7.14)
D 0;
126
J.M. Cruz
Conditions (7.13) state that consumers at demand market khlO will purchase the
product from retailer j , if the price charged by the retailer for the product times the
exchange rate plus the transaction cost (from the perspective of the consumer) does
not exceed the price that the consumers are willing to pay for the product in that
currency and country, i. e., O . Note that, according to (7.13), if the transaction
3khl
costs are identically equal to zero, then the price faced by the consumers for a given
product is the price charged by the retailer for the particular product.
Condition (7.14), on the other hand, states that, if the price the consumers are
willing to pay for the product at a demand market is positive, then the quantity of
the product at the demand market is precisely equal to the demand.
In equilibrium, conditions (7.13) and (7.14) will have to hold for all demand
markets and these, in turn, can be expressed also as an inequality analogous to those
in (7.5) and (7.11) and given by:
.J C1/KHL
determine .Q2 ; 3 / 2 RC
; such that
K X
J X
H X
L h
X
j
j
O eh C cO O .Q2 ; 2 / j D 1 k D 1 h D 1 lO D 1
C
K X
H X
L
X
2
4
k D 1 h D 1 lO D 1
2khl
J
X
j D1
3khlO
khl
h
j
q
3
h
q j O dkhlO.3 /5 3khlO khl
.J C1/KHL
8.Q2 ; 3 / 2 RC
i
3khlO
:
q
O
khl
i
i
j
khlO
0;
(7.15)
In the context of the consumption decisions, we have utilized demand functions,
whereas profit functions, which correspond to objective functions, were used in the
case of the manufacturers and the retailers. Since we can expect the number of
consumers to be much greater than that of the manufacturers and retailers we believe
that such a formulation is more natural. Also, note that the relationship levels in
(7.15) are assumed as given. They are endogenous to the integrated model as is
soon revealed.
7.2.8 The Equilibrium Conditions of the Network
In equilibrium, the product flows that the manufacturers in different countries transact with the retailers must coincide with those that the retailers actually accept from
them. In addition, the amounts of the product that are obtained by the consumers in
the different countries and currencies must be equal to the amounts that the retailers actually provide. Hence, although there may be competition between decisionmakers at the same level of tier of nodes of the network there must be cooperation
between decision-makers associated with pairs of nodes. Thus, in equilibrium, the
prices and product transactions must satisfy the sum of the optimality conditions
7 The Effects of Network Relationships on Global Supply Chain Vulnerability
127
(7.5) and (7.11) and the equilibrium conditions (7.15). We make these statements
rigorous through the subsequent definition and variational inequality derivation.
Definition 1 (Network Equilibrium). The equilibrium state of the global supply
chain network is one where the product transactions and relationship levels between
the tiers of the network coincide and the product transactions, relationship levels,
and prices satisfy the sum of conditions (7.5), (7.11), and (7.15).
The equilibrium state is equivalent to the following:
Theorem 1 (Variational Inequality Formulation). The equilibrium conditions
governing the global supply chain network model according to Definition 1 are
equivalent to the solution of the variational inequality given by:
determine .Q1 ; Q2 ; 1 ; 2 ; ; 3 / 2 k, satisfying:
"
L X
H
I X
J X
X
@f i l .q i l /
il
@qjh
i D1 l D1 j D1 hD1
C˛
il
@r i l .Q1 ; 1 /
il
@qjh
Cı
j
C
il
i l i l
@cjh
.qjh
; /
il
@qjh
@r j .Q1 ; Q2 ; 2 /
il
@qjh
2
K X
J X
H X
L
X
il
i l j @cOjh
.qjh
; /
C
il
@qjh
#
j
C
@cj .Q1 /
il
@qjh
i
h
il
i l
qjh
qjh
j
j
j
1
2 2
@c O .q O ; j /
l
j @r .Q ; Q ; /
4
C
C khl kh
ı
j
j
@q
@q
j D 1 k D 1 h D 1 lO D 1
khlO
khlO
#
i
h
j
j
j
C cO O .Q2 ; 2 /Cj O q O q O
3khl
khl
C
L X
H
I X
J X
X
"
il
i l i l
@cjh
.qjh
; /
@i l
i D1 l D1 j D1 hD1
h
i
khl
khl
il
1 1
@b i l .i l /
i l @r .Q ; /
C
C
˛
@i l
@i l
#
2
j
1
2 2
@c j O .q j O ; j /
j @r .Q ; Q ; /
4
C khl khj l
C
ı
@j
@
j D 1 k D 1 h D 1 lO D 1
#
" I L H
il
i l j J
XXX
@cOjh
.qjh
; / @b j .j /
X
j
j
i l
C
C
C
qjh
j
j
@
@
il
i l
K X
J X
H X
L
X
j D1
K X
H X
L
X
3
q
j
khlO
3khlO
5 j j C
k D 1 h D 1 lO D 1
h
3khlO K X
H X
L
X
k D 1 h D 1 lO D 1
i
0;
i D1 l D1 hD1
2
4
J
X
j D1
8.Q1 ; Q2 ; 1 ; 2 ; ; 3 / 2 k ;
3
q
j
khlO
dkhlO .3 /5
(7.16)
128
where
J.M. Cruz
h
il
k .Q1 ; Q2 ; 1 ; 2 ; ; 3 /jqjh
0; q j
0; 0 i l 1 ;
i
0; j 0; 8i; l; j; h; k; lO :
khlO
0 j 1; 3khlO
(7.17)
Proof. Summation of inequalities (7.5), (7.11), and (7.14), yields, after algebraic
simplification, the variational inequality (7.15).
We now put variational inequality (7.15) into standard form which will be utilized
in the subsequent sections. For additional background on variational inequalities
and their applications, see the book by Nagurney [27]. In particular, we have that
variational inequality (7.15) can be expressed as:
hF .X /; X X i 0;
8X 2 k ;
(7.18)
Where
X .Q1 ; Q2 ; 1 ; 2 ; ; 3 / and F .X / .Fi ljh ; FjkhlO ; FOi ljh ; FOjkhlO ; Fj ; FkhlO /
With indices: i D 1, . . . , I ; l D 1, . . . , L; j D 1, . . . , J ; h D 1, . . . , H ; lO D 1, . . . ,
L;, and the specific components of F given by the functional terms preceding the
multiplication signs in (7.14), respectively. The term h; i denotes the inner product
in N -dimensional Euclidean space.
We now describe how to recover the prices associated with the first two tiers of
nodes in the global supply chain network. Such a pricing mechanism guarantees
that the optimality conditions (7.5) and (7.11) as well as the equilibrium conditions
(7.14) are satisfied individually through the solution of variational inequality (7.16).
Clearly, the components of the vector 3 are obtained directly from the solution
of variational inequality ((7.16) as will be demonstrated explicitly through several
numerical examples in Sect. 7.5). In order to recover the second tier prices associated with the retailers and the appreciation/exchange rates one can (after solving
variational inequality (7.16)hfor the particular numerical
i problem) either (cf. (7.13)
or (7.15)) set j O eh D O cOj O .Q2 ; 2 / , for any j; k; h; lO; m such that
q
j
2khl
3khl
j
khl
> 0 or (cf. (7.11)) for any q O > 0, set
khlO
khl
j
j
@c O .q O ; j /
j
j @r j .Q1 ;Q2 ; 2 /
khl m khl
C
C
O eh D ı
j
j
j .
2khl
@q
@q
khlO
khlO
Similarly, from (7.5) we can infer that the top tier prices can be recovered (once
the variational inequality (7.16) is solved with particular data) thus:
for any i; l; j; h; m, such that i l i l
il
1 1
i l
i l
> 0, set 1jh
eh D @f .qi l / C ˛ i l @r .Q i l ; / C
qjh
@qj h
@qj h
i l /
@cji lh .qji l
h ;
@qji lh
, or
7 The Effects of Network Relationships on Global Supply Chain Vulnerability
equivalently, (cf. (7.11)), to j ı j @r
j .Q1 ;Q2 ; 2 /
@qji lh
@cj .Q1 /
@qji lh
129
@cOji lh .qji l
; j /
h
@qji lh
.
Under the above pricing mechanism, the optimality conditions (7.5) and (7.11)
as well as the equilibrium conditions (7.15) also hold separately (as well as for each
individual decision-maker) (see also, e. g., [8, 28]).
Existence of a solution to variational inequality (7.16) follows from the standard
theory of variational inequalities, under the assumption that the functions are continuous, since the feasible set k is compact (cf. [27]). Also, according to the theory of
variational inequalities, uniqueness of solution, in turn, is then guaranteed, provided
that the function F .X / that enters variational inequality (7.16) is strictly monotone
on k.
Note that, if the equilibrium values of the flows (be they product or relationship
levels) on links are identically equal to zero, then those links can effectively be
removed from the network (in equilibrium). Moreover, the size of the equilibrium
flows represents the “strength” of the respective links. In addition, the solution of the
model reveals the true network structure in terms of the optimal relationships (and
their sizes) as well as the optimal product transactions, and the associated prices.
7.2.9 Remark
We note that manufacturers as well as retailers may be faced with capacity constraints. Capacity limitations can be handled in the above model since the production cost functions, as well as the transaction cost functions and the handling cost
functions can assume nonlinear forms (as is standard in the case of modeling capacities on roads in congested urban transportation networks (cf. [33])). Of course, one
can also impose explicit capacity constraints and this would then just change the
underlying feasible set(s) so that k would need to be redefined accordingly. However, the function F .X / in variational inequality (7.18) would remain the same (see,
e. g., [27]). Finally, since we consider a single homogeneous product the exchange
rates eh are assumed fixed (and relative to a base currency). Once can, of course,
investigate numerous exchange rate and demand scenarios by altering the demand
functions and the fixed exchange rates and then recomputing the new equilibrium
product transaction, price, and relationship level equilibrium patterns.
7.3 The Supply Chain Network Efficiency
and Vulnerability Measures
In this section, we propose the global supply chain network efficiency measure and
the associated network component importance definition.
130
J.M. Cruz
Definition 2 (The global supply chain network efficiency measure). The global
supply chain network efficiency measure, ", for a given network topology G, and
demand price 3khlO , and available product from manufacturer i l and retailer j , is
defined as follows:
PH
PK
".G/ D
kD1
hD1
PL
lO D 1
K H L
dkhlO .3 /
O
3khl
;
(7.19)
where K H L is the number of demand markets in the network, and dkhlO .3 / and
O denote the equilibrium demand and the equilibrium price for demand market
3khl
khlO, respectively.
The global supply chain network efficiency measure, " defined in (7.19) is actually the average demand to price ratio (cf. [32]). It measures the overall (economic)
functionality of the global supply chain network. When the network topology G, the
demand price functions, and the available product are given, a global supply chain
network is considered to be more efficient if it can satisfy higher demand at lower
prices.
By referring to the equilibrium conditions (7.13), we assume that if there is a positive transaction between a retailer with a demand market at the equilibrium, the
price charged by the retailer plus the respective unit transaction costs is always positive. Hence, the prices paid by the demand market will always be positive and the
above network efficiency measure is well-defined.
The importance of the network components is analyzed, in turn, by studying their
impact on the network efficiency through their removal. The network efficiency of
a global supply chain network can be expected to deteriorate when a critical network component is eliminated from the network. Such a component can include
a link or a node or a subset of nodes and links depending on the network problem
under study. Furthermore, the removal of a critical network component will cause
more severe damage than that of a trivial one. Hence, the importance of a network
component is defined as follows (cf. [32]):
Definition 3 (Importance of a global supply chain network component). The
importance of network component g of global supply chain network G, I.g/, is
measured by the relative global supply chain network efficiency drop after g is removed from the network:
I.g/ D
".G/ ".G g/
;
".G/
(7.20)
where ".G g/ is the resulting global supply chain network efficiency after component g is removed.
It is worth pointing out that the above importance of the network components is well-defined even in a supply chain network with disconnected manufacturer/demand market pairs. In our supply chain network efficiency measure, the
elimination of a transaction link is treated by removing that link from the network
7 The Effects of Network Relationships on Global Supply Chain Vulnerability
131
while the removal of a node is managed by removing the transaction links entering or exiting that node. The above procedure(s) to handle disconnected manufacturer/demand market pairs will be illustrated in the numerical examples in Sect. 7.4,
when we compute the importance of the supply chain network components and their
rankings.
Supply chain vulnerability arises from two sources, the risk within the supply
chain and the external risk. The risk within the supply chain network is caused
by sub-optimal interaction and co-operation between the entities along the chain.
Such supply chain risks result from a lack of visibility, lack of ’ownership’ and
inaccurate forecasts. External risks are risks that arise from interactions between the
supply chain and its environment. Such interactions include disruptions caused by
strikes, terrorism and natural catastrophes. These risks impact the vulnerability of
the supply chain. Thus, supply chain vulnerability can be defined as an exposure
to serious disturbance, arising from risks within the supply chain as well as risks
external to the supply chain.
Hence, vulnerability ("A ) is a measure of the average decrease in efficiency of the
network over the time horizon after attack and takes into account the entire history
of the attack and the rapidity of the decline [3].
Pm
"n
(7.21)
"A D nD1
N
Let "1 , "2 , . . . , "N , be the efficiency the network after the elimination of 1, 2, up
to N nodes. "A measures the average loss of efficiency during N attacks so that
networks with a more rapid decline will have higher "A scores.
Consequently, supply chain risk management should aims at identifying the areas
of potential risk and implementing appropriate actions to contain that risk. Therefore, we believe that the best way to mitigate supply chain risk and to reduce supply
chain vulnerability as a whole is through coordinated and relationship approach
amongst supply chain members.
7.4 Numerical Examples
In this section, we analyze the global supply chain networks efficiency and vulnerability. For each example, our network efficiency and vulnerability measures are
computed and the importance and the rankings of nodes are also reported.
Example 1
The first set of numerical examples consisted of one country, two manufacturers, two
currencies, two retailers, and two demand markets for the product. Hence, L D 1,
I D 2, H D 2, J D 2, and K D 2, for this and the subsequent two numerical exam-
132
J.M. Cruz
Fig. 7.2 Global supply chain network for Example 1
ples. The global supply chain network for the first example is depicted in Fig. 7.2.
The examples below were solved using the Euler method (see [8, 28]).
The data for the first example were constructed for easy interpretation purposes
(cf. Tables 7.2, 7.3, 7.5)
The transaction cost functions faced by the manufacturers associated with transacting with the retailers were given by:
2
il
il
il
il
.qjh
; i l / D 0:5 qjh
C 3:5qjh
i l ; for i D 1; 2I l D 1I j D 1; 2I h D 1; 2 :
cjh
The production cost functions faced by the manufacturers were
0
f i l .q i l / D 0:5 @
2
2 X
X
12
il A
qjh
;
for i D 1; 2I l D 1; 2 :
j D1 hD1
The handling costs of the retailers were given by:
0
cj .Q1 / D :5 @
2
2 X
X
j D1 hD1
12
il A
qjh
;
for j D 1; 2 :
7 The Effects of Network Relationships on Global Supply Chain Vulnerability
133
The transaction costs of the retailers associated with transacting with the manufacturers in the two countries were given by:
2
il
il
il
il
qjh
cOjh
; i l D 1:5 qjh
C 3qjh
;
for i D 1; 2I l D 1; 2I j D 1; 2I h D 1; 2 :
The relationship cost functions were:
b i l .i l / D 2i l ;
b . / D ;
j
j
j
for i D 1; 2;
for j D 1; 2:
The demand functions at the demand markets were:
d111 .3 / D 23111 1:53121 C 1000; d121 .3 / D 23121 1:53111 C 1000 ;
d211 .3 / D 23211 1:53221 C 1000; d221 .3 / D 23221 1:53211 C 1000 :
and the transaction costs between the retailers and the consumers at the demand
markets (see (6.12)) were given by:
j
j
cOkhl
.Q2 / D qkhl
j C 5;
for j D 1; 2I k D 1; 2I h D 1; 2I l D 1 :
We assumed for this and the subsequent examples that the transaction costs as perceived by the retailers and associated with transacting with the demand markets
j
j
were all zero, that is, ckhl
.qkhl
/ D 0, for all j , k, h, l.
The Euler method converged and yielded the following equilibrium product shipment pattern:
i l
qjh
D 15:605;
8i; l; j; h ;
j
qkhl
D 15:605 ;
8j; k; h; l :
The vector had components: 1 D 2 D 256:190, and the computed demand
D 3121
D 3211
D 3221
D 276:797.
prices at the demand markets were: 3111
Next, we analyze the importance of the network components by studying their
impact on the network efficiency through their removal. Table 6 shows the results
of this analysis.
Table 7.6 The importance of the supply chain decision-makers
Nodes
Importance Value
Ranking
Manufacturer (i l)
Retailer (j )
Demand Market (khl)
0.3204
0.4854
0.3086
2
1
3
Note that, given the cost structure and the demand price functions, since the retailer’s nodes carry the largest amount of equilibrium product flow, they are ranked
the most important. The negative importance values for demand markets are due to
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J.M. Cruz
the fact that the existence of each demand market brings extra flows on the transaction links and nodes and, therefore, increases the marginal transaction cost. The
removal of one demand market has two effects: first, the contribution to the network
performance of the removed demand market becomes zero; second, the marginal
transaction cost on links/nodes decreases, which decreases the equilibrium prices
and increases the demand at the other demand markets. If the performance drop
caused by the removal of the demand markets is overcompensated by the improvement of the demand-price ratio of the other demand markets, the removed demand
market will have a negative importance value. It simply implies that the negative
externality caused by the demand market has a larger impact than the performance
drop due to its removal.
The vulnerability score for this supply chain network is "A D 0:1657.
Example 2
The first numerical example consisted of one country, two source agents, two currencies, two intermediaries, and two financial products. Hence, L D 1, I D 2, H D 2,
J D 2, and K D 2. The network for the first example is depicted in Fig. 7.3. The
data for this example is the same as in Example 1 except that in this example we
allow the manufacturers to also transact directly with demand markets.
Fig. 7.3 Global supply chain network for Example 2
7 The Effects of Network Relationships on Global Supply Chain Vulnerability
135
The transaction costs, in turn, associated with the transactions between manufacturers and the demand markets (from the perspective of the consumers) were given
by:
O k; h :
cOi l O .q i l O / D 0:1q i l O C 1; 8i; l; l;
khl
khl
khl
The Euler method converged and yielded the following equilibrium supply chain
flow pattern:
i l
D 2:017 ;
qjh
8i; l; j; h ;
i l
qkhl
D 26:82 ;
8i; l; k; h; l ;
j
qkhl
8j; k; h; l :
D 2:017 ;
The vector had components: 1 D 2 D 268:58, and the computed demand
D 3121
D 3211
D 3221
D 269:236. The
prices at the demand markets were: 3111
importance of the nodes of this network and their ranking are reported in Table 7.7.
For this network the most important nodes are the manufacturers nodes since they
transact and have relationships with retailers and demand markets. The vulnerability
score for this supply chain network is "A D 0:019.
Table 7.7 The importance of the supply chain decision-makers
Nodes
Importance Value
Ranking
Manufacturer (i l)
Retailer (j )
Demand Market (khl)
0.486
0.03
0.19
1
2
3
Example 3
In this numerical example, the global supply chain network was as given in Fig. 7.4.
This example consisted of two countries with two manufacturers in each country; two currencies, two retailers, and two demand markets. Hence, L D 2, I D 2,
H D 2, J D 2, and K D 2.
The data for this example is the replication of the data for Example 1, from
1 country to two countries. Therefore, the demand functions at the demand markets
were:
d111 .3 / D 23111 1:53121 C 1000 ;
d211 .3 / D 23211 1:53221 C 1000 ;
d121 .3 / D 23121 1:53111 C 1000 ;
d221 .3 / D 23221 1:53211 C 1000 ;
d112 .3 / D 23112 1:53122 C 1000 ;
d212 .3 / D 23212 1:53222 C 1000 ;
d122 .3 / D 23122 1:53112 C 1000 ;
d222 .3 / D 23222 1:53212 C 1000 :
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J.M. Cruz
Fig. 7.4 Global supply chain network for Example 3
The Euler method converged (in 318 iterations) and yielded the following equilibrium product shipment pattern:
i l
qjh
D 16:305 ;
8i; l; j; h ;
j
qkhl D 16:305 ;
8j; k; h; l :
The vector had components: 1 D 2 D 266:882 and the computed demand
prices at the demand markets were: 3111
D 3121
D 3211
D 3221
D 3212
D
3222
D 277:379.
The importance of the nodes of this network and their ranking are reported in
Table 7.8. The vulnerability score for this supply chain network is "A D 0:060. This
network is less vulnerable than the one from Example 1, since the retailers can get
their products from many more manufacturers and sell them to many more demand
markets as compare to the retailers in Example 1.
Table 7.8 The importance of the supply chain decision-makers
Nodes
Importance Value
Ranking
Manufacturer (i l)
Retailer (j )
Demand Market (khl)
0.18
0.42
0.307
2
1
3
7 The Effects of Network Relationships on Global Supply Chain Vulnerability
137
We note that supply chain in Example 1 is the most vulnerable, follow by the
network in Example 3. A vulnerable supply chain would have a high vulnerability
score. Network in Example 2 is the least vulnerable since manufacturers have more
options to sell their products, to retailers and demand market. The results in this
chapter can be used to assess which nodes and links in supply chain networks are the
most vulnerable in the sense that their removal will impact the performance of the
network in the most significant way. Moreover, for each member of the supply chain
network the highest is it relationship or connectivity the lowest is its vulnerability.
Therefore, supply chain risk management should be based on clear performance
requirements and lines of communication or relationship between all members of
the chain. It is important to note that the vulnerability of the supply chain depends
on the design and structure of the network and on the type of relationship between
its members.
7.5 Managerial Implications
As managers determine the appropriate practices to manage the supply chain efficiency and vulnerability, the supply chain design and structure should take in consideration risk issues. When considering risk issues it is important to the firm to create
a portfolio of relationships. Strong supply chain relationships enable firms to react
to changes in the market, improve forecasting and create supply chain visibility,
which lead to improve profit margins [11]. The benefits are reduction of production,
transportation and administrative costs. Moreover, multiple relationships can help
companies deal with the negative consequences related to dependence on supply
chain partners. Thus, supply chain vulnerability can be minimized as an exposure to
serious disturbance is reduced. Companies will be able to deal with disturbance arising from risks within the supply chain as well as risks external to the supply chain
when there is an optimal interaction and co-operation between the entities along the
chain.
The benefits of investing in social relationship are not only economical but also
technical and social. On the technical development the greatest benefit is the possibility of sharing the resources of suppliers and shortening the lead-times. Spekman
and Davis [35] found that supply chain networks that exhibit collaborative behaviors
tend to be more responsive and that supply chain-wide costs are, hence, reduced.
These results are also supported by our economic model where we demonstrated
that a higher level of relationship lowers transaction costs and risk and uncertainty.
As a result, supply chain prices are reduced and the overall transactions increases.
Risk management in supply chain should be based on clear performance requirements, optimal level of investment in supply chain relationships, and on process
alignment and cooperation within and between the entities in the supply chain.
Therefore, the structure and design of the supply chain will determine how vulnerable it will be.
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J.M. Cruz
7.6 Conclusions
In this chapter, we develop a framework for the analysis of the optimal levels of
social relationship in a global supply chain network consisting of manufacturers,
retailers, and consumers. We propose a network performance measure for the evaluation of supply chain networks efficiency and vulnerability. The measure captures
risk, transaction cost, price, transaction flow, revenue, and demand information in
the context of the decision-makers behavior. Manufacturers and retailers are multicriteria decision-makers who decide about their production and transaction quantities as well as the amount of social relationship they want to pursue in order to
maximize net return and minimize risk.
We construct the finite-dimensional variational inequality governing the equilibrium of the competitive global supply chain network. The model allows us to
investigate the interplay of the heterogeneous decision-makers in the global supply
chain and to compute the resultant equilibrium pattern of product outputs, transactions, product prices, and levels of social relationship. A computational procedure
that exploits the network structure of the problem is applied to several numerical
examples.
Results of our numerical examples highlight the importance of considering the
impact of relationship levels in a global supply chain context. Furthermore, they
stress the importance of a network perspective, the importance of each decision
makers in the network and the overall efficiency and vulnerability of the global supply chain network . These examples, although stylized, have been presented to show
both the model and the computational procedure. Obviously, different input data and
dimensions of the problems solved will affect the equilibrium product transaction,
levels of social relationship, price patterns, and the supply chain vulnerability.
Future research will extend this framework to include other criteria and the introduction of dynamics. Future research may also focus on the study of type of
relationship investments required in each stages of the supply chain network. It is
important to know to what extent do the relationships between elements in supply chain differ depending on the stage of the alliance and on aspects of the costs
and benefits of the relationship. How do the combinations of these elements play
in each time period and stage of the supply chain? These questions await empirical
study. We feel we have only scratched the surface and look forward to future studies
that will help researchers better conceptualize and theorize specific aspect of supply
chain relationship, vulnerability and risk management.
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Chapter 8
A Stochastic Model
for Supply Chain Risk Management
Using Conditional Value at Risk
Mark Goh and Fanwen Meng
Abstract In this chapter, we establish a stochastic programming formulation for
supply chain risk management using conditional value at risk. In particular, we investigate two problems on logistics under conditions of uncertainty. The sample
average approximation method is introduced for solving the underlying stochastic
model. Preliminary numerical results are provided.
8.1 Introduction
For supply chains that comprise hundreds of companies and several tiers, there are
numerous risks to consider. Generally, these risks can be classified into two types:
risks arising from within the supply chain (operational risk) and risks external to the
chain (disruption risk). The attributes of operational risks are due to the interactions
between firms across the supply chain, such as supply risk, demand risk, and trade
credit. Disruption risks arise from the interactions between the supply chain and its
environment, such as terrorism, or natural disasters such as the severe acute respiratory syndrome (SARS). Therefore, supply chain risk management can be defined as
the identification and management of operational risks and disruption risks through
a coordinated approach amongst supply chain members to reduce supply chain vulnerability. For recent related work, see [5] and the references therein. A survey on
studies in this regard can be found in Tang [25].
In stochastic optimization, Value at Risk (VaR) is a widely used risk measure
for quantifying the downside risk. A drawback of this approach is that it often destroys the convexity of the model, which makes the resulting optimization problem hard to solve numerically. An extensive recent study on a related measure of
risk, Conditional Value at Risk (CVaR), popularized by Rockafellar and Uryasev
in [18, 19], as the tightest convex approximation of VaR, has shown that CVaR is
a coherent risk measure that enjoys convexity and subadditivity. Therefore, CVaR
T. Wu, J. Blackhurst (eds.), Managing Supply Chain Risk and Vulnerability
© Springer 2009
141
142
M. Goh, F. Meng
has advantages over VaR at least in numerical computation. Due to this, in this
chapter, we use CVaR as a risk measure in the framework of supply chain risk
management. For a detailed discussion on VaR and CVaR, the reader is referred
to [1, 2, 4, 7, 8, 9, 10, 14, 18, 19, 24, 27, 28].
Suppose f W Rn Rm ! R is a loss function which depends on the control
vector x 2 X Rn and the random vector y 2 Rm . Here X denotes the set
of decision constraints and y W ˝ ! Rm is a random vector defined on
probability space .˝; F; P /, which is independent of x. Here x is a decision vector
and y serves as a vector representing uncertainties, e. g., the risks involved in supply
chains. Then, for each x 2 X , the loss z D f (x; y) is a random variable with
a distribution in R induced by that of y. Recall that for a given confidence level
˛ 2 .0; 1/, the VaR of the loss z associated with a decision x is defined as
VaR˛ .x/ D min fujP fyjf .x; y/ ug ˛g ;
(8.1)
which is the minimum value of the loss at a point such that the probability of the loss
is less than or equals to ˛. CVaR is defined as the expectation of the loss f .x; y/
in the conditional distribution of its upper ˛-tail. A more operationally convenient
definition [18, 19] of CVaR, as the optimal value function of an unconstrained minimization problem, is as follows.
CVaR˛ .x/ D min f˛ .x; u/ju 2 Rg ;
(8.2)
where
1
E Œf .x; y/ uC ;
(8.3)
1˛
where the superscript plus sign denotes the nonnegative part of a scalar, i. e., the
plus function ŒtC WD max f0; tg. Note that VaR˛ .x/ is the lower (or left) endpoint
of the closed bounded interval arg minu ˛ .x; u/ and
˛ .x; u/WDu C
CVaR˛ D ˛ .x; VaR˛ .x// :
(8.4)
Further, Rockafellar and Uryasev [18, 19] showed that the CVaR minimization problem
min fCVaR˛ .x/jx 2 X g
(8.5)
is equivalent to
min f˛ .x; u/j.x; u/ 2 X Rg ;
(8.6)
in the sense that these two problems achieve the same minimum value.
In general, the loss function f is assumed to be linear in x. To deal with the plus
function involved in the CVaR minimization problem, some auxiliary variables are
often introduced. Then, algorithms based on linear programming can be employed
for solving the underlying CVaR minimization problem [1, 4, 14, 28]. However,
introducing additional variables can increase the size of the problem greatly as the
sample size of the random variable y increases. This might result in a big challenge
in computation. In this chapter, we assume that f is a general convex loss function.
8 A Risk Management Model
143
In other words, f can be a nonlinear function, such as a quadratic function, or
a piecewise linear/quadratic function.
In Sect. 8.2, we establish a general stochastic model for supply chain risk
management using CVaR. A sampling approach called Sample Average Approximation (SAA) is introduced to solve the stochastic model in Sect. 8.3. SAA
methods have been extensively investigated in stochastic optimization [3, 6, 23].
Recently, the SAA method was applied for supply network design problems under uncertainty [21] and stochastic mathematical programs with equilibrium constraints [12, 23, 29]. Based on the general stochastic model and the SAA method discussed in Sects. 8.2 and 8.3, we investigate an example of a supply chain consisting
of two suppliers, one contract manufacturer, and two distributors as an illustration
in Sect. 8.4. We investigate the risk management of the wine supply chain where the
uncertain demand follows a discrete distribution in Sect. 8.5. Section 8.6 concludes.
8.2 A Stochastic Model with Conditional Value at Risk
The supply chain under consideration consists of one sole decision maker, a manufacturer, and a number of tiers of finitely many players in the chain which are closely
connected to the manufacturer. For example, in the two-tier case, the players of the
upstream tier could be suppliers who ship raw materials to the manufacturer, while
the players from the downstream tier are the distributors of the manufactured products. At each pair, there are uncertainties and risks involved, ranging from supply of
raw material, production quality, and demand.
We formulate a stochastic model of supply chain risk management using the risk
measure of CVaR. We suppose that the associated risks, denoted by a random vector
y 2 Rm , of the underlying supply chain, follow a certain distribution. Let x 2 Rn
denote the decision variable, X denote the basic domain of decision variables, such
n
as, the nonnegative orthant RC
or some bounded region in Rn , and '.x; y/ the profit
function of the decision maker. Then, the corresponding loss function f .x; y/ WD
'.x; y/.
The decision maker aims to both maximize his expected profit and minimize his
expected loss, subject to some constraints. In general, the decision maker might set
a prior loss tolerance, ˇ, concerning the value of risk. We then set the following
constraint of the model:
(8.7)
CVaR˛ .x/ ˇ ;
where ˛ is the confidence level given by the decision maker.
Further, let hl .x; y/ W Rn ˝ ! R, l D 1, . . . , k, denote the constraints, representing the capacities, the product flows, and other activity constraints with uncertain demand and other risks involved in the chain. In this chapter, we are interested
in the mathematical expectations of such underlying constraints, i. e., E Œhl .x; y/,
although the decision maker might have an overly optimistic or pessimistic attitude
as facing some extreme value distributions of uncertainties y. We assume the ex-
144
M. Goh, F. Meng
pectations of such constraints are satisfied by the following requirements:
E Œhl .x; y/ D 0 ;
l D 1, 2, . . . , j ;
(8.8)
E Œhl .x; y/ 0 ;
j D l C 1, . . . , k :
(8.9)
We now formulate the objective function of the model. The motivation and analysis
is as follows. It is known that the attitude of the decision makers has a critical role
in the decision process. An optimistic or pessimistic attitude can lead to an extreme
solution of the system. However, finding such an optimal solution is costly and
might even lead to additional cost to the decision makers under certain situations
such as incomplete market information. Due to this, we ignore all analysis related
to extreme value distributions. Instead, we consider the expected objective in the
analysis. For an extensive study and application of this approach, we refer to recent
publications in stochastic programming, such as [12, 22, 29].
In general, two criteria are considered for the decision maker, that is, (i) maximizing the profit; (ii) minimizing the loss. To characterize these two criteria in the
objective function simultaneously, we introduce a simple risk averse rate 2 Œ0; 1
and define the objective as a convex combination of the two criteria, namely,
.1 /E Œf .x; y/ C CVaR˛ .x/.
Thus, the stochastic model can be formulated as:
min.1 /E Œf .x; y/ C CVaR˛ .x/
s:t: E Œhl .x; y/ D 0 ; l D 1, 2, . . . , j ;
E Œhl .x; y/ 0 ;
CVaR˛ .x/ ˇ ;
(8.10)
l D j C 1; : : : ; k ;
x2X:
Note that, by (8.2), CVaR˛ .x/ is the optimal value function of an unconstrained
minimization problem, making the resulting problem (8.10) hard or even impossible to solve directly. To overcome this obstacle in computation, we establish an
equivalent formulation of problem (8.10). Before stating Proposition 1, we need the
following lemma, which is taken from ([18], Theorem 10).
Lemma 1. Suppose that E Œjf .x; y/j < 1 for any x 2 X . Then, for x 2
X; ˛ .x; u/, as a function of u 2 R, is finite and convex.
Proposition 1. Suppose that E Œjf .x; y/j < 1 for any x 2 X . The minimization
problem (8.10) is equivalent to
1
E Œf .x; y/ uC
(8.11)
min.1 /E Œf .x; y/ C u C
1˛
s:t: E Œhl .x; y/ 0 ; l D j C 1; : : : ; k ;
1
E Œf .x; y/ uC ˇ; .x; u/ 2 X R ;
uC
1˛
8 A Risk Management Model
145
in the sense that their objectives achieve the same minimum value. Moreover, if the
CVaR constraint in (8.10) is active, .x ; u / achieves the minimum of (8.11) if and
only if x achieves the minimum of (8.10) with
C
1
:
u 2 arg min u C
E f .x ; y/ u
u2R
1˛
Proof. To ease notation, set XO D X \ fx 2 Rn jE Œhl .x; y/ D 0; l D 1, 2, . . . , j ,
E Œhl .x; y/ 0; l D j C 1, . . . , kg. In the following, we consider two cases:
(i) D 0; (ii) 0 < 1:
For case (i), it is evident that (8.10) is reduced to minimize E Œf .x; y/ over XO
subject to CVaR˛ .x/ ˇ, and (8.11) becomes minimizing E Œf .x; y/ over XO R
subject to ˛ .x; u/ ˇ. This is exactly the same situation considered in [18]. The
desired result follows directly by ([18], Theorem 16).
We now consider case (ii). If .x ; u / solves (8.11), then ˛ .x ; u / ˇ, and
.1 /E f .x ; y/ C ˛ .x ; u / D
˚
min .1 /E f .x ; y/ C ˛ .x ; u/j˛ .x ; u/ ˇ :
u2R
This implies that for any
u 2 UO WD fu 2 Rj˛ .x ; u/ ˇg ;
.1 /E f .x ; y/ C ˛ .x ; u / .1 /E f .x ; y/ C ˛ .x ; u/ :
With 0 < 1, it then nfollows that ˛ .x o ; u / ˛ .x ; u/ for any u 2 UO .
Thereby, ˛ .x ; u / D min ˛ .x ; u/ju 2 UO . In addition, by Lemma 1, ˛ .x ; u/
is finite and convex in u. Thus, u 2 UO . Then,
˛ .x ; u / D min ˛ .x ; u/ D min ˛ .x ; u/ D CVaR˛ .x / ;
u2UO
u2R
which implies u 2 arg minu2IR ˛ .x ; u/. Next, we show x solves (8.10). According to the equivalent expression (8.2) of CVaR, for any x 2 XO , CVaR˛ .x/ ˇ
if and only if there exists u.x/ such that ˛ .x; u.x// D CVaR˛ .x/ ˇ. Thereby,
.x; u.x// is a feasible point to problem (8.11). Further, note that x is feasible
to (8.10) since CVaR˛ .x / D ˛ .x ; u / ˇ. Also, .x ; u / is an optimal solution of (8.11). Then, for any x 2 XO satisfying CVaR˛ .x/ ˇ we have
.1 /E f .x ; y/ C CVaR˛ .x / D .1 /E f .x ; y/ C ˛ .x ; u /
.1 /E Œf .x; y/ C ˛ .x; x.u// D .1 /E Œf .x; y/ C CVaR˛ .x/ :
Thereby, x solves (8.10).
On the other hand, suppose that x solves (8.10). Let u 2 arg minu2R ˛ .x ; u/.
Then, CVaR˛ .x / D ˛ .x ; u / ˇ. This implies that .x ; u / is feasible
146
M. Goh, F. Meng
to (8.11). Note that, for x 2 XO , there exists u.x/ 2 R, such that CVaR˛ .x/ D
˛ .x; u.x//. Then, for any .x; u/ feasible to (8.11), i. e., .x; u/ 2 XO R satisfying
˛ .x; u/ ˇ, it follows that
CVaR˛ .x/ D ˛ .x; u.x// D min f˛ .x; u/ju 2 Rg
min f˛ .x; u/ju 2 R; ˛ .x; u/ ˇg ˇ :
Thus, x is feasible to (8.10). As x is a solution of (8.10), then for any .x; u/ 2
XO R feasible to (8.11),
.1 /E f .x ; y/ C CVaR˛ .x / D .1 /E f .x ; y/ C ˛ .x ; u /
.1 /E Œf .x; y/ C CVaR˛ .x/ D .1 /E Œf .x; y/ C ˛ .x; u.x//
D .1 /E Œf .x; y/ C min f˛ .x; u/ju 2 Rg
.1 /E Œf .x; y/ C min f˛ .x; u/ju 2 R; ˛ .x; u/ ˇg
.1 /E Œf .x; y/ C ˛ .x; u/ :
Thus, .x ; u / solves (8.11). This completes the proof.
In this chapter, for convenience, we assume that all the underlying expected functions in (8.11) are finite and continuous. (8.11) is the usual (one-stage) stochastic
programming problem. Hence, it might be possible to apply some well developed
optimization approaches in stochastic programming to solve this problem. However, a challenge is on how to deal with the mathematical expectations. In Sect. 8.3,
we will introduce a sampling approach method for solving (8.11). If is chosen
to be 1, the decision maker wishes to solely minimize his loss or risk. This is
viewed as a conservative strategy. In this case, the original problem (8.10) is reduced to
min CVaR˛ .x/
s:t: E Œhl .x; y/ D 0 ;
l D 1, 2, . . . , j ;
E Œhl .x; y/ 0 ;
l D j C 1, . . . , k ;
CVaR˛ .x/ ˇ ;
x2X:
(8.12)
Likewise, if D 0, the decision maker treats the expected profit more important than the potential loss. In practice, the decision maker can choose a value of
2 Œ0; 1 based on his own preference for risk.
8.3 Sample Average Approximation Program
We now discuss numerical methods for solving (8.11). We introduce a Monte Carlo
simulation method, the sample average approximation method. SAA methods have
been extensively investigated in stochastic optimization in the past few years [22].
More recently, the SAA method has been applied to supply network design prob-
8 A Risk Management Model
147
lems under uncertainty [21] and stochastic mathematical programs with equilibrium
constraints
˚ [12, 29]. Let y 1 ; y 2 , . . . ,y N be an independent identically distributed (i.i.d) sample of
y. Define
N
1 X
fNN .x/ WD
f .x; y i / ;
N
i D1
N
C
1 X
f .x; y i / u ;
fON .x; u/ WD
N
i D1
N
1 X
hN lN .x/ WD
hl .x; y i / ;
N
l D 1, . . . , k :
i D1
The SAA program of problem (8.11) is given as follows.
1 N
min.1 /fNN .x/ C u C
fN .x; u/
1˛
N
s:t: hlN .x; y/ D 0 ; l D 1, 2, . . . , j ;
hN lN .x; y/ 0 ;
1 O
uC
fN .x; u/ ˇ ;
1˛
(8.13)
l D j C 1, . . . , k ;
x 2 X; u 2 R :
Note that the above SAA program is a deterministic nonlinear programming problem. Thus, we can employ some well developed methods in nonlinear programming
to solve (8.13). According to ([22], Proposition 7), we derive the following results.
Proposition 2. Let Z be a nonempty compact subset of Rn R. Suppose that (i)
f .; y/ and hl .; y/ are continuous on Z for a.e. y 2 ˝; (ii) f .x; /; Œf .x; / uC ;
hl .x; /, are dominated by an integrable function, for any .x; u/ 2 Z and l D 1;
. . . , k. Then, fNN .x/; fON .x; u/, and hN lN .x/ converge to E Œf .x; y/ ; EŒf .x;y/ uC ,
and E Œhl .x; y/ ; l D 1, . . . , k, w.p.1 uniformly on Z, respectively.
To ease notation, we denote by v , S , vN N , and SNN the optimal value, the set
of optimal solutions of (8.11), the optimal value, and the set of optimal solutions
of (8.13), respectively. We derive the following proposition concerning the convergence of the optimal value of the SAA program.
Proposition 3. Suppose that there exists a compact set ZN of Rn R such that:
N (ii) all conditions in Proposition 2 are
(i) S is nonempty and is contained in Z;
N
satisfied on the set Z; (iii) w.p.1 for N large enough the set SNN is nonempty and
N (iv) If zN D .xN ; uN / be feasible to (8.13) and zN ! z w.p.1, then
SNN Z;
z is a feasible point of (8.11); (v) For some point z 2 S , there exists a sequence
of fzN g being feasible to (8.13) such zN ! z w.p.1. Then vNN ! v w.p.1 as
N ! 1.
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M. Goh, F. Meng
Proof. For simplicity, let g and Z denote the objective function and the feasible sets
of the original problem (8.11), gN and ZN denote the objective and the feasible set
of the SAA program (8.13). By virtue of the indicator function [17], ı.j/, where
denotes a set of any finite dimensional vector space, then the original problem
(8.11) and its SAA problem (8.13) can be rewritten as:
min fg.z/ C ı.zjZ/jz 2 Rn Rg
and
min fgN .z/ C ı.zjZN /jz 2 Rn Rg ;
respectively. Thus, we only need to investigate the convergence of the above two
unconstrained minimization problems. By Proposition 2, it is easy to see that gN .z/
N Then, the result follows directly with help
converges to g.z/ w.p.1 uniformly on Z.
of ([22], Proposition 6 and Remark 8).
Note that the conditions in (8.3) can be satisfied by imposing some appropriate
properties on the underlying functions such as convexity or continuity, together with
some constraint qualifications such as the Slater condition. But, this is beyond the
scope of this chapter. The reader is referred to [22] for a detailed discussion. In many
cases, the underlying functions f , hl , l D 1, . . . , k, are all smooth. However, the
term Œf .x; y/ uC is nonsmooth, which leads to the nonsmoothness of problem
(8.11) and its SAA counterpart (8.13) generally. To overcome the nonsmoothness,
we use some well-developed smoothing techniques. First, note that
Œf .x; y/ uC D Œ.f .x; y/ u/ D min f0; u f .x; y/g :
So, we may replace the term Œf .x; y/ uC in (8.11) by using the min function
min fa; bg. However, this function is nonsmooth as well, so we consider the following smoothed counterpart of min fa; bg:
.a; b; / D 1 p
.a b/2 C 2 .a C b/ ;
2
which is the Chen–Harker–Kanzow–Smale (CHKS) smoothing function [12, 16, 29]
with ¤ 0 as the smoothing parameter, which is driven to zero in computation. Clearly,
is continuously differentiable everywhere except at D 0 and
.a; b; 0/ D min fa; bg. The smoothing function for min f0; u f .x; y/g is then
as follows:
1 p
.u f .x; y//2 C 2 u C f .x; y/ :
.0; u f .x; y/; / D 2
˚ In practice, we choose a sequence l with positive small values of l and letting
l ! 0 as l ! 1. For any given ¤ 0, we derive the smoothing version of (8.11)
as follows.
8 A Risk Management Model
149
min.1 /E Œf .x; y/ C u C
p
1
.u f .x; y//2 C 2 uC
E
f .x; y/
2.1 ˛/
s:t: E Œhl .x; y/ D 0 ; l D 1,2, . . . , j ;
E Œhl .x; y/ 0 ; l D j C 1, . . . , k ;
hp
i
1
E
uC
.u f .x; y//2 C u2 u C f .x; y/ ˇ ;
2.1 ˛/
.x; u/ 2 X R :
(8.14)
Similarly, the corresponding smoothing SAA program is as follows.
min
N
1 X
f .x; y i /
N
i D1
!
N q
X
1
i
i
2
2
C uC
.u f .x; y // C u C f .x; y /
2N.1 ˛/
i D1
s:t:
N
1 X
hl .x; y i / D 0 ;
N
l D 1, 2, . . . , j ;
(8.15)
i D1
N
1 X
hl .x; y i / 0 ; l D j C 1, . . . , k ;
N
i D1
N q
X
1
i
i
2
2
.u f .x; y // C u C f .x; y / ˇ ;
uC
2N.1 ˛/
i D1
.x; u/ 2 X R :
Thus, to derive an approximate solution of (8.10), we can solve the SAA smoothing
problem (8.15) using some well developed optimization approaches.
8.4 An Illustration of the Stochastic Model
We now illustrate the stochastic model and the SAA method discussed above by
considering a supply chain consisting of two suppliers, one contract manufacturer,
and two distributors. The manufacturer needs to procure raw materials from the suppliers and sell the completed products to the distributors. Denote by p1 ; p2 the prices
of raw materials sold to the manufacturer and by q1 and q2 the prices of the product
sold to the distributors. Denote by c the unit shipping cost of raw materials paid by
the manufacturer and the raw material loss rate. Let ˛ denote the confidence level
and ˇ denote the loss tolerance.
150
M. Goh, F. Meng
Let x1 and x2 denote the quantities of raw materials purchased by the manufacturer, x3 and x4 the quantities of products sold to the distributors. Clearly, the total
quantity, x3 C x4 , of completed products sold to the distributors cannot exceed the
difference of the total quantity of raw materials and the total loss of raw materials,
.1 /.x1 C x2 /. So, we have the following constraint:
.1 /.x1 C x2 / x3 x4 0 :
In addition, the capacities for these two suppliers are set as follows:
0 x1 40 ;
0 x2 40 ; and x1 C x2 60 :
For simplicity, we consider two types of external risk involved in the chain. Specifically, let y1 denote the random variable concerning the risk (loss) of a supplier
defaulting and y2 the random variable concerning the risk (loss) of no demand from
the distributors. The loss function is given by
f .x; y/WDp1 x1 C p2 x2 C c.x1 C x2 / q1 x3 q2 x4 C w1 y1 C w2 y2 ;
where wi represents the risk severity factor with wi 0 and w1 C w2 D 1. In
this example, the underlying loss is irrespective of the internal factors related to the
quantities of raw materials or/and the completed products. In fact, the loss function
can be written separately as f .x; y/ D f1 .x/ C f2 .y/ where f1 .x/ represents the
normal costs of the manufacturer while f2 .y/ D w T y denotes the loss due to the
risks only. Note that in general the loss function might not be separable in the decision variable x and the random variable y. Note also that the loss function f can be
nonlinear and even nonsmooth in some situations [11, 13].
Based on the previous arguments, the corresponding SAA program and the
smoothing SAA program can then be written as follows:
!
N
N
X
1
1 X
C
f .x; y i / u
f .x; y i / C u C
min
N
N.1 ˛/
i D1
i D1
s:t: .1 /.x1 C x2 / x3 x4 0 ;
x1 C x2 60 ;
uC
1
N.1 ˛/
x2R ;
4
0 xi 40 ;
N
X
i D1
u 2 R;
i D 1; 2 ;
C
f .x; y i / u ˇ ;
x3 ; x4 0 ;
8 A Risk Management Model
151
and
min 1
N
uC
N
P
f .x; y i /C
!
N p
P
.u f .x; y i //2 C 2 u C f .x; y i /
i D1
1
2N.1˛/
i D1
s:t: .1 /.x1 C x2 / x3 x4 0 ;
x1 C x2 60 ;
uC
1
2N.1 ˛/
0 xi 40 ; i D 1; 2 ; x3 ; x4 0 ;
q
.u f .x; y i //2 C 2 u C f .x; y i / ˇ ;
N
X
i D1
x 2 R ;u 2 R:
4
In the numerical test, we set D 0:2, the values for p1 ; p2 and q1 ; q2 , c are set to be
2.1, 2.3, 5.5, 6.0, 0.75 per unit of raw materials or completed products, respectively.
Set ˇ D 0:001, D 0:05, w1 D 0:7, w2 D 0:3. For simplicity, the random vector
y D .y1 ; y2 /T is assumed to follow the uniform distribution on [10, 40].
We conduct the test using the Matlab built-in solver fmincon with different values
of the smoothing parameter and sample sizes N , M and N 0 . Let .xN N ; uN N / denote
the solution of the corresponding SAA program. Note that the numbers of samples
for deriving the lower and upper bounds are N M and N 0 , respectively. The results
are displayed in Table 8.1.
Table 8.1 Numerical results for a supply chain risk management problem
˛
N
M
N0
xN N
uN N
0.95
0.95
0.95
0.98
0.98
0.98
104
104
104
106
106
106
1500
2000
2500
1000
2000
2500
100
100
100
100
100
100
4000
5000
6000
4000
5000
6000
(40, 20, 0, 57)
(40, 20, 0, 57)
(40, 20, 0, 57)
(40, 20, 0, 57)
(40, 20, 0, 57)
(40, 20, 0, 57)
128.6837
128.5688
128.6501
128.1244
127.9133
128.0078
8.5 A Wine Supply Chain Problem
In this section, we consider a wine industry logistics problem, which is modified
from Yu and Li [26]. A wine company is formulating its production, inventory, and
transportation plan. This company owns three bottling plants located in E, F, and
G, and three distribution warehouses located in three different countries (or cities)
152
M. Goh, F. Meng
L, M, and N, respectively. Uniform-quality wine in bulk (raw material) is supplied
from four wineries located in A, B, C, and D.
For simplicity, without considering other market behaviors (e. g. novel promotion, marketing strategies of competitors, and market-share effect in different markets), each market demand merely depends on the local economic conditions. Assume that the future economy is either boom, good, fair, or poor, i. e., four situations
with associated probabilities of 0.45, 0.25, 0.17, or 0.13, respectively. The unit production costs and market demands under each situation are listed in Table 8.2.
Table 8.2 Characteristics of the problem
Future
Economic situation
Demands
L
M
N
Unit product cost
E
F
G
Likelihood of each
economic situation
Boom
Good
Fair
Poor
400
350
280
240
200
185
160
130
755
700
675
650
0.45
0.25
0.17
0.13
188
161
150
143
650
600
580
570
700
650
620
600
Let i denote the index of four wineries, j the index of the three distribution
centers, and k the index of three bottling plants. We call each possible economic
situation a “scenario”, denoted by s. For i D 1, 2, 3, 4, j D 1, 2, 3, k D 1, 2, 3, and
each scenario s, we define the following notation:
• xi k – the amount of bulk wine to be shipped from winery i to bottling plant k,
• yk – the amount of bulk wine to be bottled in bottling plant k,
• zkj – the amount of bottled wine shipped from bottling plant k to distribution
center j ,
• uk – the stock of bulk wine in bottling plant k carried from previous weeks,
• vk – the stock of bottled wine in bottling plant k carried from previous weeks,
• csj – the uncertain unit cost, depending on each scenario s, for bottling wine in
bottling plant j ,
• Dsj – the uncertain market demand, depending on each scenario s, from the distribution center j .
In the problem, the random factors involved are uncertain unit costs/prices from
bottling plants and the random demands from distributors. Let
WD .D 1 ; D 2 ; D 3 ; c 1 ; c 2 ; c 3 /
denote the underlying random vector. For convenience, we use the index set {1, 2, 3,
4} to denote the four observations/scenarios of the future economy situation {Boom,
Good, Fair, Poor}, respectively. For example, the index corresponds to “Boom”.
Then, .s/ WD .Ds1 ; Ds2 ; Ds3 ; c 1 ; c 2 ; c 3 /, s D 1, 2, 3, 4, are all possible values of ,
as per Table 8.2. We denote the decision variables by w, where w WD .x; y; z; u; v/,
x WD .x11 , . . . , x43 /, y WD .y1 ; y2 ; y3 /, z WD .z11 , . . . , z33 /, u WD .u1 ; u2 ; u3 /, and
v WD .v1 ; v2 ; v3 /.
8 A Risk Management Model
153
We assume that (65.6, 155.5, 64.7, 62, 150.5, 60.1, 84, 174.5, 88.4, 110.5, 100.5,
109.3) are the unit costs of transporting bulk wine from each winery A, B, C, and D
to each bottling plant E, F, and G, respectively. Also, we assume that (200.5, 300.5,
699.5, 693, 533, 362, 164.9, 306.4, 598.2) are the unit costs of transporting bottled
wine from each bottling plant E, F, and G to each distribution center L, M, and N,
respectively. We denote by (75, 60, 69) the unit inventory costs for bulk wine in
bottling plant E, F, and G, respectively, and by (125, 100, 108) the unit inventory
costs for bottled wine in bottling plant E, F, and G, respectively.
In addition, we denote by i , i D 1, 2, 3, 4, the maximum amount of bulk wine
that can be shipped from winery i to the bottling plants; denote by vk , k D 1,
2, 3, the maximum production capacity of bottled wine for each bottling plant k;
denote by k , k D 1, 2, 3, the maximum storage space for the bulk wine in plant k;
denote by k , k D 1, 2, 3, the maximum storage spaces for bulk wine in plant k.
Here, we set D .300; 150; 200; 150/, y D .340; 260; 300/, D .150; 100; 120/,
D .50; 50; 50/.
The total cost f consists of the transportation cost fT , production cost fp , and
inventory cost fI . For each realization .s/, the above three cost functions are given
as follows:
fT .w; .s// D 65:6x11 C 155:5x12 C 64:7x13 C 62x21 C 150:5x22 C 60:1x23
C 84x31 C 174:5x32 C 88:4x33 C 110:5x41 C 100:5x42 C 109:3x43
C 200:5z11 C 300:5z12 C 699:5z13 C 693z21 C 533z22
C 362z23 C 164:9z31 C 306:4z32 C 598:2z33 ;
fP .w; .s// D cs1 y1 C cs2 y2 C cs3 y3 ;
and
fI .w; .s// D 75.x11 C x21 C x31 C x41 y1 C u1/ C 60.x12 C x22
C x32 C x42 y2 C u2/ C 69.x13 C x23 C x33 C x43
y3 C u3/ C 125.y1 C v1 z11 z12 z13/ C 100.y2 C v2
z21 z22 z23/ C 108.y3 C v3 z31 z32 z33/ :
Consequently, for each scenario s, the total cost function is as follows.
f .w; .s// D fT .w; .s// C fP .w; .s// C fI .w; .s// :
Note that f is actually a function involved with a random factor . The stochastic
model under consideration is:
min CVaR˛ .w/
s:t:
xi 1 C xi 2 C xi 3 i ; i D 1, 2, 3, 4 ;
yk vk ; k D 1, 2, 3 ;
(8.16)
154
M. Goh, F. Meng
0 yk C vk zk1 zk2 zk3 k ;
0 z1j C z2j C z3j xi k ; yk ; zkj ; uk ; vk 0 ;
k D 1, 2, 3 ;
for each s ; j D 1, 2, 3 ;
i D 1, 2, 3, 4 , k D 1, 2, 3 ,
Dsj ;
j D 1, 2, 3 :
Based on the previous discussions, the above problem can be formulated equivalently as:
1
E Œf .w; / C
1˛
s:t: xi 1 C xi 2 C xi 3 i ;
min C
yk vk ;
i D 1, 2, 3, 4 ;
k D 1, 2, 3 ;
0 x1k C x2k C x3k C x4k C uk yk k ; k D 1, 2, 3 ;
0 yk C vk zk1 zk2 zk3 k ; k D 1, 2, 3 ;
(8.17)
0 z1j C z2j C z3j Dsj ; for each s, j D 1, 2, 3 ;
2 R;
xi k ; yk ; zkj ; uk ; vk 0 ;
i D 1, 2, 3, 4 ,
k D 1, 2, 3 ,
j D 1, 2, 3 :
Using the CHKS smoothing function as discussed in Sect. 8.3, we solve the following smoothed discretized problem of (8.16):
i
X hp
1
ps
4"2 C .f .w; .s// /2 C f .w; .s// 2.1 ˛/ sD1
4
min C
s:t:
xi 1 C xi 2 C xi 3 i ; i D 1, 2, 3, 4 ;
yk vk ; k D 1, 2, 3 ;
0 x1k C x2k C x3k C x4k C uk yk k ; k D 1, 2, 3 ;
0 yk C vk zk1 zk2 zk3 k ; k D 1, 2, 3 ;
(8.18)
0 z1j C z2j C z3j Dsj ; for each s,j D 1, 2, 3 ;
2 R ; xi k ; yk ; zkj ; uk ; vk 0 ; i D 1, 2, 3, 4 , k D 1, 2, 3 , j D 1, 2, 3;
where " > 0.
We have carried out numerical tests on the problem and report some numerical
results. Again, the tests are carried out by implementing mathematical programming
codes in MATLAB 6.5 installed in a PC with the Windows XP operating system.
We used the MATLAB built-in solver fmincon for solving the associated problems.
We report the amounts of bulk wine to be shipped and bottled x, y; the amount
of bottled wine shipped z; and the corresponding total cost, the transportation cost,
the production cost, the inventory holding cost, the minimum conditional value at
risk CVaR˛ , the value at risk of the total cost VaR˛ .
8 A Risk Management Model
155
Table 8.3 Numerical results of the smoothing method for wine supply chain problem
" D 104 ; ˛ D 0:95
Result
x
(0.0000.0.0000.25.3640.29.9288.32.5259.25.3476,
29.9288. 32.5259. 25.3476. 29.9288. 32.5259. 25.3476)
(119.7384.117.6691.123.3638)
(136.5054.64.0625.68.1631.135.9777.63.5347,
67.6353. 137.4613. 65.0183. 69.1189)
603 490
360 510
239 410
3 570
1
0.5000
y
z
Total cost
Transportation cost
Production cost
Inventory holding cost
CVaR˛
VaR˛
In Table 8.3, we set the smoothing parameter " D 104 and the confidence level
˛ D 0:95. In the numerical test, we have also chosen different values for the smoothing parameter and the confidence level, such as " D 105 , 106 , 107 , and ˛ D 0.9,
0.96. We also notice that, for the problem under consideration, the numerical results
stated in Table 8.3 do not change greatly with small changes in the values of the
confidence level and the smoothing parameter.
In this example, we have attempted to highlight that risk can and must be measured in every supply chain. In the case of the wine supply chain, we show that VaR
does not cover risks of interest (CVaR ¤ VaR). Further, having a numerical value
attached to either VaR or CVaR is helpful to mangers and decision makers on providing a simple but comprehensive statement on the exposure to the supply chain
risk on an aggregate level. This can then help mangers to further decide on what
actions are needed to mitigate such risks, for instance, changing the choice of ˛ to
get a lower quantitation risk score, which could then translate to keeping more wine
or increasing higher inventory and transportation costs.
8.6 Conclusion
In this chapter, we have established a stochastic model for supply chain risk management using a measure of risk, the conditional value at risk. For the case where the
random variable follows a continuous distribution, we introduced a sample average
approximation approach in combination with some smoothing techniques to solve
the underlying stochastic problem. This makes each iterative subproblem a smooth
and convex optimization problem. We illustrate the established model by considering a small supply chain management example. Finally, a wine supply chain under
uncertain demand with a discrete distribution is discussed.
This research, as applied to the supply chain area, is timely and useful given the
recent spate of fuel cost disruptions to the supply chain and the current economic
156
M. Goh, F. Meng
crisis, which ultimately affects production and incurs a need for better management
control of the overall supply chain of supplies, manufacturers, and distributors. Our
proposed technique is especially in dealing with problems associated with uncertainties in distributions, where the traditional objective of profit maximization is
still desired while constraining the risk of a false production or untrue demand.
Acknowledgements We would like to thank the referees for their constructive suggestions, which
helped to improve the presentation of this chapter.
References
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Chapter 9
Risk Intermediation in Supply Chains
Ying-Ju Chen and Sridhar Seshadri
Abstract In some supply chains, retailers are relatively small and averse to taking
risk. In such a situation, traditional methods of contracting, that typically assume
risk neutrality on retailers, might not suffice to maximize the seller’s/distributor’s
expected profit. We present tools for analyzing and solving such a problem from the
viewpoint of a (risk-neutral) seller/distributor. We present two types of models that
can be used to create contracts, one set in a discrete setting and the other in a continuous setting. In both settings, individual retailers are characterized with different
degrees of risk aversion.
We first explain in the discrete setting how the varying degrees of risk aversion
present hurdle for the design of a uniform contract for all retailers. We then show
how to mitigate the problem using ideas from the theory of mechanism design.
We offer a simple solution to the contract design problem and show how it can be
easily implemented. We next show that in the continuous setting in which the distribution of retailers is continuous, which could be viewed as a limiting case of the
discrete setting, the contract design problem actually simplifies. In this continuous
setting, we show that it becomes relatively easy to design contracts and establish
their optimality from the seller’s/distributor’s viewpoint. We conclude the chapter
with a summary of problems that are still open in this area.
9.1 Introduction
We consider a single period model in which multiple risk-averse retailers purchase
a single product from a common vendor. We assume that the retailers operate in
identical and independent markets. The retailers face uncertain customer demand
and accordingly make their purchase order quantity decisions in order to maximize
their expected utility. The vendor offers the same supply contract to each retailer.
The terms of the contract offered to the retailers are similar to the ones found in the
classical newsvendor problem. Under this contract, each retailer purchases a certain
T. Wu, J. Blackhurst (eds.), Managing Supply Chain Risk and Vulnerability
© Springer 2009
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Y.-J. Chen, S. Seshadri
quantity at a regular purchase price. If the realized demand is greater than the quantity ordered then the retailer has the option to purchase the units that are short at
an emergency purchase price which is higher than the regular price. If the demand
is less than the order quantity then the retailer has the option to return the leftover
inventory at a salvage price that is lower than the regular price. (This contract is referred to in what follows as the original newsvendor contract (ONC).) The retailers
are price takers and sell the product at the same fixed price. The problem of deciding upon the quantity to order from the vendor is similar to the classic newsvendor
problem, except that due to risk aversion, each retailer maximizes his expected utility rather than his expected profit. The problem faced by a newsvendor is known as
the “risk-averse newsvendor problem”.
This problem has been well studied in the literature. In particular is well known
that the risk-averse retailer’s order quantity (i. e., the one that maximizes his expected utility) will be smaller than the order quantity that maximizes his expected
profit (see Horowitz, 1970; Baron, 1973; Eeckhoudt et al., 1995). Obviously, the
reduction in the order quantity of the retailer leads to a lower expected profit (for
the retailer) compared to the expected profit obtained under the profit maximizing
order quantity. Eeckhoudt et al. give examples in which risk averse retailers will
order nothing due to high demand uncertainty. Therefore, risk aversion of the retailers has been portrayed in the literature as leading to the loss of efficiency in supply
chains. (We use the term “efficiency” to refer to the combined expected profit of the
seller and the retailer. In general, this term refers to the total expected profit of all
participants in a supply chain.)
In this chapter we show not only that this loss of efficiency can be eliminated
through risk reducing pricing contracts but also that any risk neutral intermediary
will find it beneficial to offer such risk reducing contracts to the retailers. In our
model, the intermediary is referred to as the distributor1 and purchases the goods as
per the terms of the ONC from the vendor. In turn the distributor offers the goods
to the retailers on contract terms that are less risky from the retailers’ viewpoint,
namely: We propose that, as opposed to the ONC, under the risk reducing contracts
offered by the distributor to the retailers, the emergency purchase and the salvage
prices should be set equal to the regular purchase price, and that in addition a fixed
payment should be made by the distributor to the retailer. Therefore, a retailer’s
payoff consists of a fixed component (independent of the demand) and a variable
component that increases linearly with the realized demand. Consequently, as the
retailer’s payoff depends only upon the demand, the retailer is indifferent to the order
quantity decision and is content to relegate the responsibility of determining an order
quantity to the distributor. The distributor makes the order quantity decision fully
aware that he has to satisfy all the demand faced by the retailer. Thus the distributor
bears the cost if necessary of buying the product at the emergency purchase cost and
1
The distributor can be an independent firm, the vendor, or one of the retailers. For the sake
of clarity we will refer to the intermediary as the Distributor, and the risk averse players facing
uncertain demand as the Retailers. The analysis, though, is valid for any two levels in a vertical
marketing channel, where the lower level facing uncertain demand is risk averse and the upper
level is risk neutral (or less risk averse).
9 Risk Intermediation in Supply Chains
161
also if necessary of disposing any unsold product at the salvage price. We prove that
by performing this function of “(demand) risk intermediation” the distributor raises
the retailers’ order quantities such that the maximum efficiency is obtained. The
key theorem in this chapter is to establish that the contracts offered to the retailer
not only maximize the efficiency in the supply chain but are also optimal from the
distributor’s viewpoint.
Contracts similar to the ones proposed in this chapter are being adopted within
the context of vendor managed inventory (VMI) programs. In many VMI programs
the vendors make the inventory decisions on behalf of the retailers and also bear
the risks and costs associated with these decisions (Andel, 1996). In addition to
the contracts found in VMI programs, we have observed several supply contracts,
for example in the publishing, cosmetics, computers, apparel and grocery industries,
that transfer the demand risk from the buyer to the vendor. In the publishing industry
(Carvajal, 1998) the retail outlets return their unsold magazines to the distributor at
their purchase price and get additional shipments if they run out (such contracts were
first introduced in the depression era). The terms of this contract are instrumental in
persuading small retail merchants, who are averse to risk, to stock sufficient quantity
of a wide variety of magazines.
Moses and Seshadri (2000) describe the incentives used by the manufacturers in
the cosmetics industry to increase the stocking level at department stores. The incentives in the cosmetic industry comprise of liberal return policies and the sharing
of inventory holding costs between the producer and the department stores. In the
personal computer industry (Kirkpatrick, 1997), which is an industry plagued by
steep price depreciation, the standard practice of vendors is to offer price guarantees to their VAR’s (value added resellers) and hence the vendors absorb the risk of
price erosion of their products during the period that they are held in the retailers’
inventory. Similarly apparel retailers, who as an industry are facing increasing markdowns, are pressurizing their vendors to offer margin guarantees (Bird and Bounds,
1997), i. e., the vendors are expected to absorb the markdown risk faced by the retailers in case the goods have to be disposed at “sale” prices. The grocery retailers’
response to increasing inventory risk due to the proliferation of SKU’s (Lucas, 1996)
is to charge a fixed slotting fees (similar to the fixed fee proposed by us), ranging
from $ 5000 to $ 20,000 per year per SKU (stock keeping unit), from the manufacturers/distributors irrespective of the sale volume of the items. The slotting fee is
simply a rent charged for use of the shelf space. Therefore, we see a trend in the industry where simple price discounting contracts that were previously offered by the
vendors (to induce the retailers to purchase a larger quantity) are being substituted
by relatively sophisticated contracts that are designed to transfer the demand risk
from the retailers to their vendors. The economic justification for such contracts is
not complete unless as done in this chapter, the impact of risk reduction for riskaverse retailers is carefully accounted for, and the optimal form of incentives (i. e.,
contracts) is established taking into account the nature of the risk and the retailer’s
aversion to risk.
Our work shows how supply contracts can play a crucial role in the reduction
of financial risk resulting from demand uncertainty. We model the role of incen-
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Y.-J. Chen, S. Seshadri
tives (embodied in pricing contracts) in supply chains where uncertainty leads to
inefficient decision making. Instead of entirely focusing on the risk-averse retailers’
order quantity decisions (as done in the entire literature dealing with the risk averse
newsvendor problem) the focus is on optimal mechanisms that can be used to influence the decisions of the retailers. In our model, we assume that the retailers operate
in identical and independent markets and the problem setting for each retailer is the
single period newsvendor problem. This problem of designing pricing contracts under demand uncertainty and risk aversion is complicated because of the following
reasons:
(1)
(2)
(3)
Retailers might differ with regard to their aversion to risk. Therefore, different
retailers may derive different expected utility from the same contract.
The distributor does not know how risk averse any particular retailer is and
only knows the distribution of risk aversion among the retailers.
The laws against price discrimination prohibit the distributor from offering
different contracts selectively to different retailers, i. e., any contract that the
distributor decides to offer to a specific retailer, has to be offered to all the
retailers.
We begin our analysis by showing that in general it is not in the distributor’s best
interest to offer the same contract to all retailers. In other words, the distributor
does not in general maximize either his expected profit or the efficiency, by simply
performing the functions of buying and reselling the product to all retailers on the
same terms. A menu of contracts is necessary to maximize the expected profit of
the distributor, and in fact the fundamental contribution of this chapter is to exactly
characterize the menu that the distributor should offer in order to maximize his expected profit. This menu rather interestingly maximizes the efficiency as well. Every
contract in the menu has two parameters, a fixed payment that the distributor makes
to the retailer, and a unit price that the distributor charges the retailer for every unit
sold by the retailer. (The choice of this form of each contract in the menu is neither
random nor accidental. We prove that these contract terms create stochastic payoffs
for the risk-averse retailer that dominates the payoffs under the terms of the ONC in
a strong sense.)
We emphasize that the menu does not depend on the distributor’s knowledge of
the degree of risk aversion of each and every retailer, but only upon the knowledge of
the distribution of risk aversion over the ensemble of retailers. The menu of contracts
is either continuously or discretely parameterized by the fixed side payment and the
selling price depending upon whether the distribution of risk aversion is a discrete
one or a continuous one. Each retailer selects a contract from the menu, choosing
the one that provides him the highest expected utility. The menu of contracts derived
by us has the following special properties:
• In order to maximize his expected profit, the distributor should offer a menu of
contracts so tailored that every (risk averse) retailer selects a unique contract from
the menu. This fact is not readily discernible because the distributor could choose
to create a menu such that some retailer finds nothing attractive in the menu.
9 Risk Intermediation in Supply Chains
163
• Each retailer chooses a contract from the menu and by doing so obtains as
much or higher expected utility (EU), as compared to the EU from the original newsvendor contract (ONC). Therefore, all retailers are as well off or better
off with the entry of the distributor in the supply chain.
• The contracts in the menu are independent of the order quantity. The retailer is
willing to relegate the ordering decision to the distributor. Furthermore, the order quantity stipulated by the distributor is the expected value (EV) maximizing
solution to the newsvendor problem. Therefore, the mutually beneficial (beneficial to retailers and the distributor) menu of contracts is also instrumental in
maximizing efficiency.
• The menu of contracts is such that retailers who are less risk averse, prefer the
contracts with higher expected profit and utility (and consequently bear higher
risk).
• The menu always contains a risk free (fixed payment) contract. This contract is
selected by a subset of retailers, namely those that are the most risk averse. Under
fairly general conditions, the subset of retailers who select this risk free contract
is independent of the product characteristics, and dependent only upon the retailers’ attitude towards risk. This shows that the fraction of retailer population that
will face no demand risk (and in effect are owned by the distributor) does not
depend on the product but on the distribution of risk aversion.
It is common knowledge how in the last two decades the concept of risk intermediation has been used to create not only novel investment and insurance products
but also a global marketplace for such products and services. A large number of
firms now offer a menu of products with different risk-return choice to customers
worldwide. Viewed in this light, the existence of a similar market for hedging risky
payoffs resulting from uncertain demand should not be entirely surprising. The contracts observed in some of the industries studied by us further confirm the insight
provided by our analysis. It is also logical that such contracts are seen for products
that have short life cycle or are perishable such as grocery, personal computers and
apparel, as these are the industries that are the most exposed to demand uncertainty.
(The use of the single period inventory model as the decision making framework
embodied in the newsperson problem is appropriate for such products as well.)
The rest of the chapter is organized as follows. We first provide a discussion
on the relevant literature in the end of this section. In Sect. 9.2, we discuss the
assumptions of our modeling framework and present the risk reducing contract for
a single retailer (Sect. 9.2.1). In Sect. 9.3, we focus on the discrete setting in which
there are a finite number of retailers that differ in their risk aversion magnitude and
derive structural properties of the optimal menu of contracts. Section 9.4 presents
results on how the population of retailers will be segmented on the basis of risk
aversion. In Sect. 9.5, we switch to the continuous setting in which the retailers’
risk aversion magnitude is drawn from a continuous distribution. This allows us to
show that the menu proposed in Sect. 9.3 achieves the optimality in nearly all menus
of contracts. Section 9.6 concludes our work and discusses some possible directions
for future research.
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Y.-J. Chen, S. Seshadri
9.1.1 Relevant Literature
In this section we review the relevant literature, including supply chain coordination
and the pricing contracts.
9.1.1.1 Supply Chain Coordination
Recent research on contract mechanisms for achieving coordination in supply chains
includes the work of Barnes-Schuster and Bassok (1996), Bassok and Anupindi
(1997), Donohue (1996), and Moses and Seshadri (2000). Moses and Seshadri study
the problem of coordinating the review period and order quantity in a supply chain
consisting of a single manufacturer supplying many retailers from a distribution center. They show that coordination between the manufacturer and the retailers, on both
the order quantity as well as the review period, can be achieved using credit terms
alone as the policy variable. Donohue models a supply chain for fashion goods.
There are two modes of supply, and a single supplier and a single buyer in the
model. First, the buyer commits to an order quantity. Second, as more information
becomes available, the buyer is allowed to change the order quantity on payment of
a penalty for the deviation. Donohue shows that coordination can be achieved in this
situation through pricing alone. Barnes-Schuster and Bassok too consider a supply
chain with a single supplier and buyer. In their model, the buyer makes cumulative
commitments to purchase over a time horizon. The contract includes a termination option. Similar price-quantity commitment models are studied by Bassok and
Anupindi.
In contrast to these papers, the inclusion of risk aversion in supply chain coordination, and optimal design within a class of contracts are the novel features of
our work. Moreover, our research is aimed at understanding how contracts, and in
particular risk sharing plays a role in determining the distribution channel structure.
9.1.1.2 Pricing Contracts
Quantity discounts form an important pricing mechanism. A review of the marketing
and the operations management literature reveals that there are four main reasons
why quantity discounts are offered, namely: (i) to discriminate between retailers of
different sizes or retailers with different holding costs (Oren et al., 1983), (ii) to reduce the transaction costs of the seller by inducing a larger order quantity from the
buyer (Monahan, 1984; Lee and Rosenblatt, 1986; Lal and Staelin, 1984), (iii) to coordinate buyer seller transactions across single as well as multiple products, (Kohli
and Park, 1989, 1994) and (iv) to mitigate loss in efficiency due to double marginalization and principal agent effects (Dolan, 1987; Jeuland and Shugan, 1983; Lal and
Staelin, 1984; Porteus and Whang, 1991; Weng, 1995).
9 Risk Intermediation in Supply Chains
165
Traditional quantity discounts while widely used can not achieve complete coordination between the buyers and the seller for two reasons: (i) the (risk sharing) benefits as described by us can not be attained by simply varying the price as a function
of the order quantity; and (ii) franchise fees are often required in addition to quantity
discounts for achieving maximal channel profits (Oren et al., 1983; Weng, 1995).
It is now well understood that such failures in coordination can arise as a result
of using improperly constructed prices schedules. The theory of non-linear pricing
(Wilson, 1993) can be brought to bear upon the problem is such situations. Quantity
discounts and franchise fees are also examples of non-linear pricing. The menu of
contracts necessary for inducing the retailers’ participation in the distributor’s network is yet another example of using a non-linear price schedule to separate out
retailers with different attitudes towards risk.
9.2 Model, Assumptions, and Analysis
We consider the classical single period inventory problem. In this problem, the distribution of the demand as well as the retail price, p, are given. The retailer’s problem is to choose the order quantity, S . In the contract, items are supplied at an initial
unit price of c. If the demand in the period exceeds the quantity ordered, S , then the
retailer obtains emergency shipments to cover any excess demand at a unit cost of
e. On the other hand, if the demand is less than S , then the retailer sends the unsold
items back to the seller, and obtains a credit of s per unit returned. The framework
has been extended by us in Agrawal and Seshadri (2000) to incorporate risk aversion
as well as to model multiple retailers as follows.
Model Assumptions
1. The retailers are alike in terms of demand distribution and cost parameters, and
differ only with regard to their aversion to risk.
2. The retailer demands are independent and identically distributed random variables. The retail price (p) and the distribution of demand are unaffected by the
contracts offered to the retailers.
3. Every contract has to be offered to every retailer. The retailer in turn selects
a contract from the menu offered. This condition prevents direct (illegal) price
discrimination by the distributor.
4. The retailers are not resellers, but purchase only to satisfy their own demand.
5. The distributor is risk-neutral (the distributor can be the manufacturer itself or
the least risk averse retailer).
6. We use utility functions for money. Until Sect. 9.3 we make no additional assumption about the utility functions of retailers, except that the utility functions
are concave and non-decreasing in the amount of wealth. From Sect. 9.3 onwards, the small gambles framework is adopted in our analysis (Pratt, 1964). In
this framework the coefficient of risk aversion is assumed to be unaffected by
the outcomes.
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Y.-J. Chen, S. Seshadri
7. Retailers are expected utility (EU) maximizers, where, EU D expected value
(EV) – the risk premium.
8. We assume that the general form of contracts that are made available to the retailers are given by C.F; c; s; e/, where,
F D Fixed side payment to the retailer ,
c D Regular purchase price/unit ,
s D Salvage value/unit of the unsold retailer stock ,
e D Emergency purchase price/unit ,
and, p e c s.
9. If two contracts provide the same EU to a retailer, the retailer will choose the
contract that has the larger fixed payment. If the distributor offers a contract that
provides the same EU as the ONC to the retailer, then the retailer will choose
the contract offered by the distributor.
These modeling assumptions hold if (i) the product by itself contributes a small
portion to the retailer’s wealth (for Assumption 6), and (ii) retailers serve their local
markets, and these markets have little or no overlap (for Assumption 2). Assumption 9 is standard in the analysis of such problems, for example see the discussion
on p. 588, Kreps (1990). The assumption allows us to work with weak inequalities
in Sect. 9.3.
9.2.1 A Single Retailer
In this section we consider the case of a single risk-averse retailer, and show that
a risk neutral intermediary has an incentive to offer a risk sharing contract to the
retailer. This has the effect of raising the ordering quantity to the EV maximizing
value. The single period demand will be denoted as D, its distribution, mean and
standard deviation as FD ./, , and . The retailer’s utility function for payoffs is
U./, a concave non-decreasing function. Let EΠstand for the expected value, and
ŒAC for the positive part of A. The random pay-off given the ordering quantity S ,
can be written as
Y
.S; F; c; s; e/ D F C pD cS C sŒS DC eŒD S C :
U
EV
The EU and EV maximizing order quantities, denoted as Sopt
and Sopt
, are given by
U
Sopt
.F; c; s; e/ D arg max EU.pD cS C sŒS DC eŒD S C /
S
EV
Sopt .F; c; s; e/ D arg max E pD cS C sŒS DC eŒD S C
S
1 e c
D FD
:
es
9 Risk Intermediation in Supply Chains
167
Q U
U
EV
It is well known that (i) Sopt
.0; c; s; e/ Sopt
.0; c; s; e/, and (ii) EΠ.Sopt
;
Q EV
0; c; s; e/ EΠ.Sopt
; 0; c; s; e/. The latter fact can be exploited by a risk neutral
intermediary to act as a distributor as follows. Assume that the distributor takes the
ONC, and in turn offers the contract C.F; c 0 ; c 0 ; c 0 /, where, p c 0 e. In this contract the distributor offers to pay a fixed fee F to the retailer, and in addition charges
a unit price c 0 for every unit sold. Under this arrangement the distributor decides the
order quantity, S , and bears the costs of emergency shipment and of salvage.
Lemma 1 gives the conditions under which a class of contracts of the form
C.F; c 0 ; c 0 ; c 0 / will be accepted by the retailer, and Lemma 3 shows that the distributor will use the EV maximizing value for the order quantity S .
Lemma 1. Contract C.F; c 0 ; c 0 ; c 0 / is preferred by the retailer to the contract
C.0; c; s; e/ if
i
hQ
i
hQ
EV
U
; F; c 0 ; c 0 ; c 0 / E
.Sopt
; 0; c; s; e/ , and
(i) E
.Sopt
(ii)
p c 0 e s.
This result can be strengthened as follows. Define “v to be more risk averse than u”
when v./ D k.u.//, where k./ is an increasing concave function, see for example
Arrow (1974).
Theorem 1. Given ˇ and a retailer “x” who has an increasing utility function, u(),
such that this retailer is indifferent between the contracts C.F ˇ; c 0 ; c 0 ; c 0 / and the
ONC, then every retailer with an increasing utility function v(), who is more risk
averse than retailer “x” will prefer C.F ˇ; c 0 ; c 0 ; c 0 / to the ONC.
Given that the distributor can induce the retailer to take a “risk sharing” contract,
the order quantity has to be decided upon by the distributor. We now prove that
the optimal order quantity that the distributor will stipulate to the retailer is the EV
maximizing solution to the original newsvendor problem.
EV
.0; c; s; e/:
Lemma 2. The optimal ordering quantity for the distributor is Sopt
9.2.1.1 Multiple Retailers
In this section we consider the case when there are multiple retailers. Assume that
the distributor offers the same contract C.F; c 0 ; c 0 ; c 0 / to all the retailers. We restrict
attention to practical contracts in which c 0 p. This class of contracts will be called
Ceq . The contract C.F; p; p; p/ will be called a “risk free” contract because the retailer is paid a fixed fee F regardless of the quantity sold.
Theorem 2. If the distributor offers a single contract to the whole population of
retailers, and there are no diseconomies of scale in distribution, then the contract
offered will be a risk free contract of the form C.F; p; p; p/. Moreover the contract
that maximizes the distributor’s expected profit need not be selected by the entire
population of retailers.
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Remark: Risk pooling in supply chains has been studied by several researchers, see
for example Eppen and Schrage (1981), Federgruen and Zipkin (1984), Jackson and
Muckstadt (1989), Schwartz et al. (1985), and Schwartz (1989). As shown by their
work, risk pooling leads to economies of scale in distribution under fairly general
conditions. Therefore, from the viewpoint of minimizing the total cost of holding
inventory, cost of emergency shipment and salvage cost, the distributor prefers to
add more retailers to the distribution network. On the other hand, in order to attract
more retailers, the distributor has to make increasingly attractive offers to all the
retailers. Thus after attracting several of the most risk averse retailers to take a contract, the marginal profit to the distributor from inducing an extra retailer to accept
the contract can become negative. The risk pooling and risk sharing effects therefore
work in opposite directions.
We have carried out numerical investigations to understand just how the risk
pooling and risk sharing effects interact when the distributor is constrained to offer
a single contract of the form C.F; c 0 ; c 0 ; c 0 / to all the retailers. In these investigations, the demand is assumed to be normally distributed. To illustrate our point we
consider complete risk pooling, i. e., the distributor can instantaneously and costlessly (other than the original costs of s, c, e), pool the inventory of all the retailers.
The retailers are assumed to have CARA (constant absolute risk aversion) risk preferences and posses different degrees of risk aversion. The (retailers’) coefficient of
risk aversion is assumed to be uniformly distributed over a compact interval. The
base case has p D 11, e D 10, c D 9, s D 1. The demand is normally distributed
with mean D 100 and standard deviation D 5.
We summarize the results below and the details are shown in the attached figures.
We find that as the demand becomes more volatile (i. e., = increases), Figs. 9.1
and 9.2, the distributor covers more retailers whereas risk-averse retailers order less
when only the ONC is available. (The distributor’s profit is shown if she covers only
the retailers that are more risk-averse than the value on the x-axis.) These two (profit
and order quantity under the ONC) are connected. The distributor’s role becomes
more important when there is greater loss of efficiency. The distributor is able to
offer a better “deal” at a lower price, thus the marginal benefit of adding a less
risk-averse retailer to the ones that are already covered by the risk-free contract is
higher.
A similar effect is observed as the emergency cost e increases in Figs. 9.3 and 9.4.
However, as the retailers’ margin p c increases two effects work in opposite directions (see Figs. 9.5 and 9.6). As the profitability is higher, risk-averse retailers order
less when price increases to obtain a “sure thing”. That is, if the price is sufficiently
high they will order nothing and wait to see the demand. Then, they order the exact quantity using the emergency shipment mode. Thus, initially as price increases
more are covered by the distributor. But, once many retailers start ordering nothing
the distributor prefers to cover only those and not the ones that order something due
to the sharp difference in the compensation required to entice the additional ones to
switch to the distributor.
9 Risk Intermediation in Supply Chains
169
Effect of Demand Variance on the Distributors market
2000
Distributor's Expected Profit $/period
1800
1600
1400
1200
3.5
4
1000
4.5
5
800
600
400
200
47
49
45
41
43
37
39
33
35
31
27
29
23
25
19
21
17
13
15
9
11
7
5
3
1
0
No of retailers
Fig. 9.1 Effect of volatility of demand on distributor’s share of the market when a single contract
is offered to all retailers
Effect of Demand Variance on the Ordering Quantity
(Without distributor)
160
140
Order Quantity
120
100
3.5
4
80
4.5
5
60
40
20
49
47
45
41
43
39
37
35
31
33
29
27
23
25
21
19
17
15
13
11
9
7
5
1
3
0
No of retailers
Fig. 9.2 Effect of volatility of demand on the order quantity in the absence of a distributor
170
Y.-J. Chen, S. Seshadri
Effect of Emergency cost on Distributors market
7000
Distributor's Expected Profit $/period
6000
5000
9
4000
10
11
3000
12
2000
1000
47
49
45
41
43
37
39
35
31
33
29
27
23
25
21
19
15
17
13
9
11
5
7
1
3
0
No of retailers
Fig. 9.3 Effect of emergency cost on distributor’s share of the market when a single contract is
offered to all retailers
Effect of Emergency cost on the Ordering Quantity
(Without distributor)
160
140
Order Quantity
120
100
9
10
80
11
12
60
40
20
No of retailers
Fig. 9.4 Effect of emergency cost on the order quantity in the absence of a distributor
49
45
47
41
43
39
37
35
33
31
29
27
25
23
19
21
17
15
13
11
9
7
5
3
1
0
9 Risk Intermediation in Supply Chains
171
Effect of Retailer's price on the Distributors market
3000
Distributor Profit per Period
2500
2000
11
12
13
1500
14
1000
500
47
49
45
41
43
37
39
35
33
31
29
27
25
23
19
21
17
15
13
9
11
7
3
5
1
0
No. of Retailers
Fig. 9.5 Effect of selling price on distributor’s share of the market when a single contract is offered
to all retailers
Effect of Retailer's price on the Ordering Quantity
(Without distributor)
160
140
Order Quantity
120
11
100
12
13
80
14
60
40
20
No. of Retailers
Fig. 9.6 Effect of selling price on the order quantity in the absence of a distributor
47
49
43
45
41
39
37
35
33
31
29
25
27
23
21
19
17
15
13
11
9
7
5
3
1
0
172
Y.-J. Chen, S. Seshadri
9.3 Multiple Contracts
The question that naturally follows Sect. 9.2 is whether there is an incentive (at
all) for the distributor to offer contracts to all the retailers. In order to answer this
question, we adopt the small gambles framework. We first consider the case in which
there are a finite number of retailers that differ in their risk aversion magnitude.
Later, in Sect. 9.5, we switch to the continuous case.
Consider a set of n retailers, denoted by N . The retailers are indexed by i and
ordered in the decreasing order of risk aversion. Let
i :
ri :
co-efficient of risk aversion; where i i C1 .
reservation utility for retailer i , which is defined as the expected utility derived
by retailer i under the ONC, C.0; c; s; e/.
We assume that every retailer in N has a strictly positive order quantity under the
ONC, and therefore has a strictly positive reservation utility. We shall consider contracts from the class Ceq . To simplify the notation, we denote a contract from this
class as C.F; c 0 /. The expected utility to retailer i from the contract C.F; c 0 / is
given by
Y
0
0
0
0
EŒU. .S; F; c ; c ; c // D F C .p c / i .p c 0 /2 2 =2 :
The distributor offers the same menu of contracts to all the retailers in N . The menu
will be written as Q D f.Fi ; ci /g. The set of retailers who accept a contract from this
set, Q, will be denoted as M.Q/. To keep the notation simple, we also denote the
contract accepted by retailer i from the set Q as .Fi ; ci /. To focus on the risk sharing
role played by the distributor, we have chosen not to model any scale economies
obtained from risk pooling or from transportation. Therefore we assume that the
distributor does not carry any inventory and trans-shipments between retailers are
not allowed. There is no loss of generality in making this assumption as long as
there are no scale diseconomies in distribution. The distributor’s profit maximization
problem is shown below.
i
X hY EV
; 0; c; s; e .Fi C .p ci //
E
Sopt
P W max
Q
s:t:
i 2 M.Q/
If i 2 M.Q/ ) Fi C .p ci / i .p ci /2 2 =2 ri
Fi C .p ci / i .p ci /2 2 =2 Fj C .p cj / i .p cj /2 2 =2
8i 2 M.Q/ ;
j 2 Q:
The distributor’s objective is to offer a menu that will maximize her expected profit.
The first set of constraints, defines the set M.Q/ – a retailer will accept some contract from the menu of the contracts, only if his expected utility from the contract is
at least as great as his reservation utility. The second set of constraints requires that
the retailer will pick that contract from the menu which gives him the highest EU.
We assume that Q consists of undominated contracts, that is, there is no contract in
9 Risk Intermediation in Supply Chains
173
the menu which is strictly preferred to another by all retailers. We need the following properties of the retailers’ reservation utilities for characterizing the set Q.
Lemma 3. The reservation utilities, ri ’s, are non-decreasing in i , and if i > i C1
then ri < ri C1 :
Lemma 4. (i) r is a convex function of , i. e., for i 1 > i > i C1 ;
ri C1 ri
ri ri 1
:
i i C1
i 1 i
(ii) If e > c > s; > 0, and the demand distribution is continuous, then r is
a strictly convex function of :
We now state that every retailer will select a contract from the menu in the optimal solution to the distributor’s problem. After showing this result, the precise
characterization of the optimal menu of contracts will be given later.
Theorem 3. Every retailer will be included in the set M.Q/ in the optimal solution
to problem P.
So far we have argued that it is in the distributor’s interest to offer a menu such
that every retailer selects a contract from it. Now we shall investigate the structure
of the optimal menu of contracts.
Lemma 5. In the optimal (and undominated) menu of contracts, there will be (exactly) one risk free contract.
It should be noted that the risk free contract is a less expensive contract for the
distributor to offer because the distributor does not have to pay any risk premium.
However, the distributor has to offer all retailers the same menu of contracts. To
entice all retailers and maximize profits simultaneously she may perforce have to
the offer “riskier” contracts, with (ci < p). On the other hand, the distributor always
has the option of designing the risk free contract to attract more than just the most
risk averse retailer. Let k be the number of retailers that take the risk free contract
in the optimal menu.
In the next section we will discuss the question of determining the value of k
to maximize the distributor’s profit. Before we get to that question, we develop the
optimal structure of the menu of contracts offered to retailers, k C 1; k C 2; . . . ; n.
To obtain this characterization we make an additional assumption, namely that the
reservation utility, ri is an increasing and strictly convex function of i . This assumption holds good when e > c > s, > 0; Si > 0, and the demand distribution
is continuous.
Theorem 4. For a given value of k (i. e., retailers 1; 2; :::; k accept the risk free
contract, Fk D rk ; ck D p), the distributor’s profit is maximized by offering the
174
Y.-J. Chen, S. Seshadri
contract .Fi ; ci /; i k C 1 given by,
ci D p 2.ri ri 1 /
.i 1 i / 2
0:5
;
Fi C .p ci / i .p ci /2 2 =2 D ri :
We summarize the properties of the optimal menu of contracts.
1. The distributor makes a profit from all contracts.
2. The prices charged to the retailers are decreasing in i , i. e., ci > ci C1 ; i .k C 1/.
3. The fixed side payments made to the retailers are decreasing in i , i. e., Fi >
Fi C1 ; i .k C 1/.
4. From the fact that retailer i obtains the same EU from contracts .Fi ; ci / and
.Fi C1 ; ci C1 /, the EV’s of the contracts .Fi ; ci / are increasing in i k.
5. Retailers 1; 2; :::; k1 obtain EU’s greater than their reservation utility. All other
retailers get exactly their reservation utility.
9.4 Risk Aversion and Channel Structure
In this section we will discuss how many retailers should get the fixed contract, i. e.,
the decision variable is now k. The distributor’s profit maximization problem is (see
problem P):
0 hQ 1
i
EV
E
Sopt
; 0; c; s; e rk k
B
i C
max @ P hQ EV
A;
C
E
Sopt ; 0; c; s; e ri C i .p ci /2 2 =2
k
i >k
where Fi and ci are as defined in Sect. 9.3. This problem can be solved numerically
using a search technique. However, further insight can be obtained by assuming that
the coefficient of risk aversion can take values on the interval Œ0; 1, and has the density function fr ./. In this model, the fraction of retailers in the population whose
coefficient of risk aversion lies in the interval, Œ; C d./ is given by fr ./d./.
The distribution function of risk aversion and its complement are denoted by Fr
and Frc . Assume that the reservation utility is a continuously differentiable (convex) function of . Passing to the limit, the cost c.x/ charged to the retailer with
a coefficient of risk aversion equal to x will be given by,
2dr.x/ 1 0:5
:
c.x/ D p dx 2
9 Risk Intermediation in Supply Chains
175
The profit function can then be restated as,
EV
.x/ D.EV Sopt
; c; s; e r.x//Frc .x/
Z0
C
x
dr.y/
EV
/fr .y/dy :
EV Sopt
; c; s; e r.y/ C y
dy
d
.x/
dr.x/ c
D
Fr .x/ xfr .x/ :
dx
dx
> 0, the maxima of the profit function .x/ are indeFrom the fact that dr.x/
dx
pendent of the reservation utility. Moreover, if the function xFrc .x/ is uni-modal
and has a unique maximum in the interior of Œ0; 1, then the optimal value of x is
independent of the reservation utility.
Remark. The above assumption implies that the function Frc .x/ xfr .x/ is initially
positive and then becomes and stays negative. Note that if we interpret x as the
price and the complementary cdf as the effective demand, xFrc .x/ represents the
revenue as a function of price. Its unimodality is commonly assumed in many papers on revenue management, and a sufficient condition for unimodality is when
the distribution has the increasing generalized failure rate property (IGFR), namely,
xfr .x/=.1 Fr .x// is increasing in x. Ziya et al. (2004) compare three conditions
that induce revenue unimodality, and mention some common distributions that satisfy these conditions such as normal, uniform, and gamma. The reader is referred to
these papers and references therein for more details.
Remark. Note that this assumption is scale invariant, i. e., if x is scaled to bx then
xFrc .x=b/ remains unimodal. Moreover, the ‘point’ that achieves the maximum is
also scale invariant.
In particular, the above condition holds when has a beta distribution with parameters (p; q). We therefore see that for a wide variety of unimodal and bi-modal
distributions the optimal fraction of retailer population that select the risk free contract is independent of the product characteristics such as selling price or purchase
costs. The optimal fraction for a few distributions is given below in Table 9.1.
Table 9.1 Optimal fraction of retailers who are given the risk free contract
Distribution of fr .x/
Optimal Value of x
Uniform (U[0,1])
2
q
1
Triangular with fr .0/ D 0, fr .1/ D 2
Triangular with fr .0/ D 2, fr .1/ D 0
Triangular and symmetric fr .0/ D fr .1/ D 0; fr .0:5/ D 2
Truncated Normal with mean D 150, D 5
1
3
q
1
3
D 0:577
1
6
D 0:408
0.5
176
Y.-J. Chen, S. Seshadri
We illustrate the results using the same example considered earlier, with p D 11,
e D 10, c D 9, s D 1 and demand normally distributed with mean of 150 and standard deviation of 5 and also for p D 14 with the rest of the parameters remaining
the same. In Figs. 9.7 and 9.8 we show the reservation price and the optimal fixed
side payment to entice a retailer to source from the distributor. In Figs. 9.9 and 9.10
we show the optimal variable cost to charge a retailer that has a given coefficient of
risk-aversion. The distributor’s profits are also shown assuming that the all retailer’s
with coefficient of risk-aversion higher than the value on the x-axis are given the
risk free contract. As predicted by our analytical results, the optimal fraction of retailers that are given the risk free contract is independent of the retail price (in this
case the fraction is always a half)!
Reservation Price and Side Payment (p = 11)
350
300
250
200
04
1
0.
0.
16
22
0.
0.
34
4
28
0.
0.
0.
52
46
0.
0.
64
7
58
0.
0.
0.
76
0.
88
82
0.
0.
1
-100
0.
50
0
-50
94
150
100
Coefficient of Risk-Aversion (rho)
Reservation Price (r_i)
Fixed Side Payment
Fig. 9.7 Reservation price under the ONC and optimal side payment (p D 11)
Reservation Price and Side Payment (p = 14)
Coefficient of Risk-Aversion (rho)
Reservation Price (r_i)
Fixed Side Payment
Fig. 9.8 Reservation price under the ONC and optimal side payment (p D 14)
04
1
0.
0.
0.
16
22
0.
34
28
0.
4
0.
0.
46
0.
52
0.
58
0.
7
64
0.
0.
82
76
0.
0.
88
0.
1
0.
94
800
700
600
500
400
300
200
100
0
9 Risk Intermediation in Supply Chains
177
Variable cost (c_i) and Distributor's Expected Profit (p = 11)
12
10
8
6
4
2
1
04
0.
0.
22
16
0.
0.
34
28
0.
4
0.
0.
52
58
46
0.
0.
0.
7
64
0.
0.
76
0.
82
94
88
0.
0.
0.
1
0
Coefficient of Risk-Aversion (rho)
Variable Cost (c_i)
Distributor's Expected Profit
Fig. 9.9 Optimal ci and distributor’s expected profit as a function of fraction of retailers that obtain
the risk-free contract (p D 11)
Variable cost (c_i) and Distributor's Expected Profit (p = 14)
70
60
50
40
30
20
10
04
0.
1
0.
16
0.
22
0.
34
28
0.
4
0.
0.
52
46
0.
0.
58
0.
64
0.
7
0.
76
0.
88
94
82
0.
0.
0.
1
0
Coefficient of Risk-Aversion (rho)
Variable Cost (c_i)
Distributor's Expected Profit
Fig. 9.10 Optimal ci and distributor’s expected profit as a function of fraction of retailers that
obtain the risk-free contract (p D 14)
9.5 Continuous Formulation and the Optimality of the Menu
So far we have showed that under the proposed menu, less risky (from the demand
risk perspective) contracts are given to more risk-averse retailers. Such a menu of
contracts increases the distributor’s expected profit because the retailers order more
products. The intuitive content of this result is that the distributor can trade-off the
expected value obtained by risk averse retailers against the gain in utility from risk
reduction.
178
Y.-J. Chen, S. Seshadri
A natural question that arises is whether the menu of contracts is optimal. To this
end, we consider an alternative setting in which the number of retailers is infinite and
their coefficient of risk aversion is drawn from a continuous distribution. We label
this scenario as the continuous formulation. Through this continuous formulation,
we are able to apply optimal control theory to solve the contract design problem.
In this section, we demonstrate that the optimal menu not only has the same structure as given above but is also optimal among nearly all contracts. We also show
that the distribution of the risk aversion coefficient uniquely determines the channel
structure. Thus, distribution systems for products with long supply lead times and
short lifecycles should bear marked similarities reflecting the attitude towards risk
of channel participants.
9.5.1 Continuous Type Space
In this section, we assume that the coefficient of risk aversion can take values in
the interval Œ0; 1. We assume that it has the density function fr ./. In this representation, the fraction of retailers in the population whose coefficient of risk aversion
lies in the interval Œ; C d is given by fr ./d. The distribution function of
risk aversion and its complement are denoted by Fr and Frc . We also assume that
the reservation utility is a differentiable and convex function of . This continuous
setting is adopted from Chen and Seshadri (2006).
9.5.2 Optimal Contract Menu in the Continuous Case
First, assume that all retailers are offered a contract and focus on the design of
the optimal menu of contracts. We formulate the optimal contract design problem
in two stages. In the first stage, we assume that there exists a constant 2 Œ0; 1
such that retailers with 2 Œ; 1 will choose the risk-free contract .r./; p; p; p/
from the menu, where r./ is the reservation utility of retailer with risk aversion
coefficient . Note that .r./; p; p; p/ is the cheapest risk-free contract that satisfies
the participation constraints for all retailers 2 Œ; 1 for two reasons: It is risk-free,
so has the lowest expected value of all contracts that provide a utility of r./. We
show below that it provides utility greater than or equal to r./ for all retailers with
in Œ; 1. We first develop optimal incentive compatible contracts to every retailer
2 Œ0; under such assumptions. In the second stage, we optimize over the choice
of . Notice that we do not exclude the possibility of D 1, i. e., only the most
risk-averse retailer is offered the risk-free contract, and hence this is without loss of
generality.
Consider any menu such that g.x/ and h.x/ are respectively the mean and variance of the payoff to a retailer if menu item x is chosen, where x can take values in
the interval Œ0; and 2 Œ0; 1. We therefore consider the most general form of the
9 Risk Intermediation in Supply Chains
179
contracts. This is the most general form because retailers are concerned only about
the mean and the variance of the payoff. With some abuse of notation, let a retailer
with coefficient of risk aversion equal to x choose menu item x. Given a fixed
, the distributor’s problem is to choose f.g./; h.//; 2 Œ0; /g that solves the
following maximization problem:
(
h i
EV
; c; s; e r./ Frc ./
max EV Sopt
Z
C
0
)
EV
EV Sopt ; c; s; e g./ fr ./d ;
s.t. .IC-1/ 2 argmaxz2Œ0;/ g.z/ h.z/ ;
.IC-2/r./ max g.z/ h.z/ ;
z2Œ0;/
8 2 Œ0; ;
8 2 Œ; 1 ;
.IR-1/g./ h./ r./ 0 ; 8 2 Œ0; ;
.IR-2/r./ r./ ; 8 2 Œ; 1 ;
EV
where Sopt
FD . ec
es / (FD ./ denotes the demand distribution) is the expected
EV
value maximizing order quantity. EV.Sopt
; c; s; e/ is the expected cost that the distributor has to pay for buying the vendors’ ONC.
In the above equation, the first two inequalities are incentive compatibility (IC)
conditions for respectively the retailers that receive a specific contract designed for
her and the retailers that accept the risk-free contract. In (IC-1), we say that the
contract menu is incentive compatible since the utility of retailer is maximized if
she chooses the contract with mean g./ and variance h./. On the other hand, r./
is the utility of retailer when she receives the risk-free contract, and (IC-2)
guarantees that she prefers this to any other contracts g.z/; h.z/ with z 2 Œ0; .
The last two inequalities represent individual rationality (IR) conditions, i. e.,
each retailer shall get at least her reservation utility. Note that the reservation utility
r./ can be explicitly expressed as
n hY
o
i
Q
;
.S; 0; c; s; e/ VarΠ.S;0;c;s;e/
r./ D max E
2
S
Q
where .S; 0; c; s; e/ is the profit if the ONC is accepted and the order quantity is
S . It can be verified that r./ is strictly decreasing in , and hence the last inequality
(IR-2) is automatically satisfied.
The following theorem summarizes our results thus far.
Theorem 5. Retailers with 2 Œ; 1 choose contract .r./; p; p; p/, where constant 2 Œ0; 1, and the distributor has to serve all retailers. Then the necessary
conditions for the optimal contract menu are (i) (LO) , and (ii) retailers 2 Œ0; receive their reservation utilities.
180
Y.-J. Chen, S. Seshadri
9.5.2.1 Candidate Menu
Now we will propose a candidate menu of contracts. The inspiration is due to the
optimal menu in the discrete version, i. e., the one proposed in Theorem 4.1.2. We
will focus on the class of contracts with a fixed franchise fee and common cost
fF ./; c./g, and prove that this class is broad enough to achieve the optimality.
The cost c./ charged to the retailer with a coefficient of risk aversion equal to and the corresponding fixed side payment F ./ are given by the solution to
2dr./ 1 0:5
;
c./ D p d 2
.p c.//2 2
D r./ :
F ./ C .p c.// 2
(9.1)
2 2
The corresponding g./ and h./ are F ./ C .p c.// and .pc.//
; 8 2
2
Œ0; /:
It can then be verified that the proposed contract menu satisfies the necessary
and sufficient conditions. Note that the continuous formulation allows us to apply
the optimal control theory and consequently the verification is greatly simplified as
opposed to the discrete formulation.
9.5.2.2 Optimal Choice of Now we turn to the second stage: optimizing over the choice of . Let ./ denote
the profit function of the distributor when retailers that have a coefficient of risk
aversion greater than are offered the risk-free contract. Recall that ./ can be
restated as
EV
; c; s; e r./ Frc ./
./ D EV Sopt
Z 0
EV
EV Sopt
fr ./d :
; c; s; e r./ C r dr./
C
d
Using the rule for differentiating under the integral we obtain
dr./ c
d
./
D
Fr ./ fr ./ :
d
d
From the unimodality of Frc ./, the maxima of the profit function are independent of the reservation utility. In other words, the fraction of retailers who select
the risk free contract is independent of product characteristics if the distribution is
unimodal.
Recall that k 2 .0; 1/ is the value of at which the function Frc ./ attains its
maximum. Thus,
Frc ./ fr ./ 0 ; 2 Œ0; k ;
9 Risk Intermediation in Supply Chains
181
and the necessary condition for optimality is
D k:
We use C D fF ./; c ./g to denote the contract menu. Notice that in the continuous case the menu C we propose again gives a risk-free contract to all retailers
with coefficient higher than k. This completes the characterization of the optimal
menu of contracts, and therefore we have
Theorem 6. Let k D argmax2Œ0;1
Frc ./ and C D f.F ./; c .//; 2 Œ0; kg.
Then the proposed C is optimal among the class of menus that serve all retailers.
Moreover, under the optimal menu of contracts, all retailers 2 Œ0; k receive their
reservation utilities, and retailers 2 .k; 1 are offered the same risk-free contract.
Note that the class of menus we consider include all menus since retailers’ utility
functions are of the mean-variance format. Hence, if all retailers ought to be served,
C is indeed the optimal menu.
9.5.2.3 Verification of Optimality
We have shown that if all retailers are served, our proposed contract menu C yields
the highest expected payoff to the distributor. The purpose of this section is to show
that our proposed menu of contracts is indeed optimal even when we allow the distributor to exclude some retailers (for example, offer contracts only to those whose
coefficient of risk aversion falls in Œ0; 0:25/ [ Œ0:7; 0:993//. We do this through three
lemmas and a theorem as stated below.
Let S.C / be the set of retailers that receive and accept contracts from the menu
C . For each x 2 S.C /, the menu C specifies a bundle .F .x/; c.x//. Needless to say,
the sets S.C / of interest should be measurable with respect to the probability space
.Œ0; 1; B; Fr .//. Due to the special structure of our proposed contract, we show that
if the distributor wants to serve merely the retailers on an interval I Œ0; 1 and
ignore all other retailers, the optimal one-segment contract menu coincides with the
proposed contract C restricted to the interval I (denoted as C jI /:
Lemma 6. (D ECOMPOSITION ) Suppose C D .F .x/; c .x// is the optimal contract menu for S.C / D Œ0; 1. Then for any interval I Œ0; 1; C jI is also
optimal.
This lemma says for any given contract C with arbitrary number of segments, the
distributor will be better off if she replaces C by menu C in every segment. Next
we will study two properties of the proposed contract menu C , namely the no-skip
property and push-to-the-end property.
Lemma 7. (N O - SKIP PROPERTY ) Suppose the distributor adopts menu C and
S.C / is composed of two disjoint intervals I1 and I2 , then the distributor will be
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Y.-J. Chen, S. Seshadri
better off by offering contracts to all retailers in I1 ; I2 , and also those between I1
and I2 :
Applying this lemma inductively, we obtain that if the distributor offers the menu
C , then the optimal S.C / will be an interval. The following lemma says that while
offering family of contracts C , the distributor should not leave any uncovered intervals of retailers from both ends.
Lemma 8. (P USH - TO - THE - END PROPERTY ) Suppose the distributor adopts menu
C and S.C / is nonempty. Let sN supfx W x 2 S.C /g Then it is in the distributor’s interest to set sN D 1. On the other hand, if s inffx W x 2 S.C /g, the
distributor will set s D 0:
Combining the above three lemmas, if the distributor offers C D fF .x/;
c .x/g; she will offer contracts to the entire interval Œ0; 1 to maximize her profit.
Bearing in mind the structure of C , we can then claim that the proposed contracts
.F .x/; c .x// are optimal among all contracts that offer a menu to a measurable
set of retailers.
In our model, the reservation utility of a retailer comes from her alternative “accepting the ONC”. Therefore, the reservation utility varies from type to type in
nature, and is decreasing in . The optimal contract menu C enables the distributor to extract all the information rent of retailers who are less risk averse, while
leaving the retailers with higher risk aversion the full information rent. This result is
in strict contrast to the standard case in the nonlinear pricing literature where players are endowed with the same reservation utilities. If the reservation utility is the
same, the theory predicts that the most risk-averse retailer receives just the reservation utility, and everybody else with < 1 enjoys the information rent. Since the
reservation utility is decreasing in , the optimal contract has to match the participation constraint for retailers with lower to induce their participation, and distort the
contract terms for retailers with higher . By doing so the distributor incurs a lower
cost and maximizes her profit.
The fact that a continuum of retailers receive a risk-free contract is also worth
noting. It is known as the “bunching” phenomenon, which may occur in the standard case when the monotone hazard rate property of types fails. Here the bunching
occurs in retailers with high risk aversion and the contract offers them the efficient
level, i. e., it fully covers the demand risk for those risk averse retailers.
Finally, it can be shown that the proposed menu C is unique up to a measurezero modification, which means all menus properly different from C are suboptimal.
9.6 Future Research and Conclusion
This chapter demonstrates that an important role of an intermediary in distribution
channels is to reduce the risk faced by retailers. The sharing of risk can be achieved
by offering mutually beneficial risk sharing contracts which also raise the retailers’
9 Risk Intermediation in Supply Chains
183
order quantity to the expected value maximizing quantity. Thus inefficiency created
due to risk aversion on part of the retailers can be avoided. Through our continuous
framework, we show that the contract menu is optimal among all possible menus,
provided that the distribution of risk aversion is continuous and satisfies some mild
condition commonly adopted in the revenue management literature.
We have shown that it is to the benefit of the distributor to offer a completely
risk free contract to (one or more) of the most risk averse retailers. In practice this
can be interpreted as an integrated channel in which the distributor owns the retail
channel. For a variety of unimodal and bimodal distributions, the fraction of the
retailer population who are offered the risk free contract is dependent only on the
distribution of the coefficient of risk aversion of the retailers; and not dependent on
the product parameters such as costs or revenue. This implies that in these cases, the
retailer population can be segmented on the basis of the retailers’ risk profile.
We have also demonstrated an important decentralization result. The distributor
is responsible for the ordering decision in our model, and the retailer is shown to
be content with this arrangement. Therefore, even if there are economies of scale
in distribution, the distributor will offer the menu of contracts, and independently
optimize with respect to her distribution costs.
There are still many open questions in this area. Of particular interest is the case
when there is competition between the distributors. When multiple distributors compete for the position of risk intermediation, offering the menu of contracts proposed
in this chapter is no longer the best strategy for each distributor. This is because
some retailers earn just their reservation utilities and therefore a distributor may be
willing to offer a better contract that not only leaves some surplus for the retailers but also gives rise to a positive expected payoff for the distributor. In doing so,
the retailers will accept this new contract instead and the distributor benefits from
capturing the business. The above argument shows that the competition shall significantly alter the equilibrium contract offers. More importantly, as discussed in
Rothschild and Stiglitz (1976) there may not even be an equilibrium in this market.
Another case of interest is when the price is a decision variable (i. e., the retailers
are price setters). This is a very practical scenario since in many industries, retailers
have certain local monopoly power and therefore are able to set the retail prices at
their own discretion. In this case, the presence of the distributor should affect the
retailers’ pricing decisions. In particular, when the distributor attempts to capture
certain portion of the system profit, the profit margin seen by the retailers becomes
smaller compared to the case without the distributor. In this case, we expect that the
presence of the distributor may result in higher retail prices and lower consumption.
A related issue is what if the retailers are able to exert costly effort to enhance the
demand. How to induce appropriate efforts by designing contract menus is a critical
issue for the distributor is such a scenario.
Finally, in our framework, the retailers are homogeneous and independent except that they have different risk aversion magnitude. This is definitely a simplified assumption that allows us to derive the analytical results. In reality, the supply
chain may consist of retailers that face different sizes of markets, and the demands
across different markets may even be correlated. These factors may also affect the
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supply chain structure and the optimal contracts between the distributor and the
retailers.
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Chapter 10
Forecasting and Risk Analysis
in Supply Chain Management:
GARCH Proof of Concept
Shoumen Datta, Don P. Graham, Nikhil Sagar, Pat Doody, Reuben Slone,
and Olli-Pekka Hilmola
This chapter is dedicated to Sir Clive W.J. Granger
(September 4, 1934–May 27, 2009).
Abstract Forecasting is an underestimated field of research in supply chain management. Recently advanced methods are coming into use. Initial results presented in
this chapter are encouraging, but may require changes in policies for collaboration
and transparency. In this chapter we explore advanced forecasting tools for decision
support in supply chain scenarios and provide preliminary simulation results from
their impact on demand amplification. Preliminary results presented in this chapter,
suggests that advanced methods may be useful to predict oscillated demand but their
performance may be constrained by current structural and operating policies as well
as limited availability of data. Improvements to reduce demand amplification, for
example, may decrease the risk of out of stock but increase operating cost or risk of
excess inventory.
Key words: Forecasting; SCM; demand amplification; risk management; intelligent decision systems; auto-id data; GARCH; RFID; operations management
10.1 Introduction
Uncertainty fuels the need for risk management although risk, if adequately measured, may be less than uncertainty, if measurable. Forecasting may be viewed as
a bridge between uncertainty and risk, if a forecast peels away some degrees of
uncertainty but on the other hand, for example, may increase the risk of inventory. Therefore, forecasting continues to present significant challenges. Boyle et al.
(2008) presented findings from electronics industry, where original equipment manufacturers (OEM) could not predict demand beyond a 4 week horizon. Moon et al.
(2000) presented demand forecasting from Lucent (Alcatel-Lucent), demonstrating improvement in forecasting accuracy (60 % to 80–85 %). Related observations
(Datta, 2008a) resulted in inventory markdowns.
T. Wu, J. Blackhurst (eds.), Managing Supply Chain Risk and Vulnerability
© Springer 2009
187
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Availability of increasing volumes of data (Reyes et al., 2007; Reyes and Frazier
2008) demands tools that can extract value from data. Recent research has shown
that advanced forecasting tools enable improvements in supply chain performance
(Zhao et al., 2001; Zhao et al., 2002; Bayraktar et al., 2008; Wright and Yuan, 2008),
if certain pre-requisites are optimized (ordering policies, inventory collaboration).
Autoregressive models have been effective in macroeconomic inventory forecasts
(Albertson and Aylen, 2003). Zhao et al. (2002) and Bayraktar et al. (2008) emphasize that the role of forecasting in supply chain is to indicate the right direction for
the actors rather than being exactly right, at every moment. Choosing the correct
forecasting method is often a complex issue (Chatfield and Yar, 1988).
The purpose of this work is to explore how advanced forecasting methods
could be applied in global supply chain management and their requirements. We
present real world results and use simulation of a 4-stage supply chain model, beergame (Vensim simulation). We have also used SPSS statistical analysis software
to construct autoregressive forecasting models. The problems may be described
as: (1) how to construct autoregressive forecasting models for a supply chain environment and (2) what changes may be needed in supply chain design to apply
these advanced forecasting models? In the next section, we introduce a few challenges and Sect. 10.3 discusses demand amplification in supply chain management.
In Sect. 10.4 we discuss features of autoregressive models and generalized autoregressive conditional heteroskedasticity (GARCH). Data and analysis from a supply
chain inventory model using GARCH is presented and although the results are preliminary, they are encouraging. Concluding thoughts and further research issues are
proposed in Sect. 10.5.
10.2 Supply Chain Management and Demand Amplification
Despite rapid advances in SCM and logistics, inefficiencies still persist and are reflected in related costs (Datta et al., 2004). In developing nations the actual amounts
are lower, but proportional share is higher (Barros and Hilmola, 2007). One of the
logistically unfriendly country groups are oil producers (Arvis et al., 2007).
The high cost for operations offer prosperity for the service providers. In 2006,
AP Moller-Maersk raked in US$ 46.8 billion in revenues (Hilmola and Szekely
2008). Deutsche Post reported revenues of A
C 63.5 billion in 2007 (Annual Report,
2007). Profitability and growth of these services are increasing, fueled by globalization. Global transportation growth exceeds global GDP growth (United Nations,
2005, 2007), since trade grows twice as fast as GDP. For decades companies emphasized lower inventories and streamlined supply chains but it has resulted in a situation (Chen et al., 2005; Kros et al., 2006) where material handling in distribution centers has increased (transportation growth combined with lower lot sizes).
Management science and practice continues to explore ways to decrease transaction costs (Coase 1937, 1960, 1972, 1992) through real-time information arbitrage.
Cooper and Tracey (2005) reported that in the 1990’s Wal-Mart had an informa-
10 GARCH Proof of Concept
189
tion exchange capacity of 24 terabytes. While massive investments in information
technology (IT) may be prudent, the sheer volume of data begs to ask the question
whether we have the tools to separate data from noise and if we have systems that
can transform data into decisionable information.
In supply chain management, the issue of demand amplification or Bullwhip effect has been in the forefront for some time (Forrester, 1958; Lee et al., 1997) but
it took decades before its importance was recognized. The development of supply
chain management (Oliver and Webber, 1982; Houlihan, 1985) catalysed by globalization, highlighted the strategic importance of logistics and pivotal role of information technology. Small demand changes in the consumer phase resulted in situations,
where factories and other value chain partners faced sudden peaks and down turns
in demand, inventory holdings and a corresponding impact on production and delivery (delivery structure phenomenon due to Bullwhip effect is referred to as “reverse
amplification” by Holweg and Bicheno (2000) and Hines et al. (2000) referred to
it as “splash back”). Human intervention to tame the Bullwhip effect, compared to
simple heuristics, leads to higher demand amplification (Sterman 1989).
It follows that demand amplification may have serious consequences due to
increased uncertainty and increases the significance of risk management. During
a down turn, Towill (2005) showed that amplification causes possible shortages on
product volume (products are not ordered, even if demand is undiminished) and variety as well as on idle capacity in operations and involves potential layoff costs.
In the case of positive demand, Towill (2005) identifies that stock deterioration and
sales cannibalization produces lost income.
Consumers purchase products lured by discounts and that diminishes sales in
the following time periods or seasons (Warburton and Stratton, 2002). During upswings, operations cost a premium for manufacturing and distribution (orders increase rapidly), but also decreases productivity development and increases waste
levels. Recent emphasis on outsourcing and large-scale utilization of low cost sourcing has worsened demand amplification (Lowson, 2001; Warburton and Stratton,
2002; Stratton and Warburton, 2003; Hilletofth and Hilmola, 2008). Risks associated with production and transportation delays are considerably higher. To mitigate
such risks, some corporations are using responsiveness as a strategic differentiator
and have built their supply chains to react on market changes through more localized supply networks, for example, Benetton (Dapiran, 1992), Zara (Fraiman and
Singh, 2002), Griffin (Warburton and Stratton, 2002; Stratton and Warburton, 2003),
Obermeyer (Fisher et al., 1994) and NEXT (Towill, 2005). The carbon footprint of
sourcing strategies will become increasingly relevant in view of future legislation.
Logistics may ultimately benefit from a disruptive innovation (Datta, 2008b) in energy sourcing and management using wireless sensors networks (Datta, 2008e).
In recent decades, even macroeconomists are including inventory as a key indicator of economic decline of national economies (Ramey, 1989; Albertson and Aylen,
2003). Ramey (1989) argued that manufacturing input inventories, raw materials
and work in process (WIP), fluctuated most in recession, while end-item or finished
goods inventories fluctuate less (Table 10.1). However, the labour market volatility is also an issue in changing economic environments (Ramey, 1989). Although,
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Table 10.1 All numbers billions of US-dollars (1972), annual rates of change
Recessions
Retail
Wholesale
Manufact.
Finished
Inventories
Manufact.
Input
Inventories
1960: 1–1960: 4
1969: 3–1970: 4
1973: 4–1975: 1
1980: 1–1980: 2
1981: 3–1982: 4
6.3
8.2
16.0
3.6
7.6
1.7
1.2
5.8
1.9
2.3
3.1
0.4
2.4
0.3
7.8
6.3
5.2
13.2
4.1
11.1
10
8
6
4
2
0
-2
6
8
9
1
7
8
9
1
8
8
9
1
9
8
9
1
0
9
9
1
1
9
9
1
2
9
9
1
3
9
9
1
4
9
9
1
5
9
9
1
6
9
9
1
Computers
7
9
9
1
8
9
9
1
9
9
9
1
0
0
0
2
1
0
0
2
2
0
0
2
3
0
0
2
4
0
0
2
5
0
0
2
6
0
0
2
7
0
0
2
8
0
0
2
Semiconductors
Fig. 10.1 Capacity addition change in US computer and semiconductor 1986–2008 (Federal Reserve 2008)
inventory positions seem to fluctuate, Albertson and Aylen (2003) argue that autoregressive forecasting models are able to forecast next period situation with a 50 %
accuracy. While autoregressive techniques have been widely used in finance (and
economics) in the past few decades, they may not have been applied or explored
as decision support tools by supply chain planners or analysts in the area of supply
chain management (Datta et al., 2007) or in other verticals (healthcare, energy).
Logic of demand amplification is evident in economic cycles (Forrester, 1976;
Sterman, 1985). Order backlog, existing inventory holdings, amount of production,
amount of employment and capacity additions were used in simulation trials to
forecast different levels of economic cycles. In long-term changes, both Forrester
(1976) and Sterman (1985) have emphasized the importance of capacity additions.
A similar methodology has been used in maritime economics to estimate price level
changes (Dikos et al., 2006) and investment cycle lengths in capital intensive industries (Berends and Romme, 2001). Hilmola (2007) has shown that capacity additions
in US in semiconductors and computers industries may explain the behavior of stock
market indices.
10 GARCH Proof of Concept
191
10.3 Beer Game and Role of Advanced Forecasting Methods
Forrester (1958) introduced a classical 4-stage beer-game simulation and revealed
that demand information amplifies within the supply chain as we move further upstream. Figure 10.2 shows, customer demand is flat at 8 units per time period (it
increased from 4 to 8 during time period of 100), but over-under reaction appears
when supply chain is moved further with respect to time. Production orders spike
to over 40 units per period, while waiting collapses to 0 units only 15 time units
later. This occurs mostly due to time-delayed supply process in each stage, which
is following make-to-stock (MTS) inventory principles (each phase has “target” for
end-item inventory levels, which they try to reach with order algorithms).
60
54
48
42
36
30
24
18
12
6
0
100
105
110
115
Customer demand : original
Retailordes : original
Distributionorders : original
Wholesalerorders : original
Production orders : original
120
125
130
135
140
145
150 155
Time (Month)
160
165
170
175
180
185
190
195 200
bottles per hour
bottles per hour
bottles per hour
bottles per hour
bottles per hour
Fig. 10.2 Forrester effect (delay D 4, step-wise demand change from 4 to 8 units during time
unit 100)
It may be observed from previous research that conventional forecasting methods
do not reduce negative impact from demand amplification. As shown in Fig. 10.3,
classical forecasting techniques such as exponential smoothed moving average
(EWMA) only heightens demand amplification (highest value reaches above 50
units per time period) due to the assumption that all previous values should be used
to predict demand. Although, use of EWMA may be justified under certain circumstances, the non-discriminatory or mandatory use of past data to predict future
demand may often generate an undesirable over-reaction.
Figure 10.4 reveals implementation problems for sharing of demand information. Often different supply chain phases use different competing suppliers to gain
cost efficiency and true demand is often confidential. Lam and Pestle (2006) describe 60 % of respondents in a survey (in China) indicating that their customers
are not willing to exchange information. Sharing data about high demand periods
could result in inflated purchase price if suppliers decide to form cartels. However, it
has been shown in a signaling game theoretic approach that sharing of information
increases total supply chain profit (Datta, 2004).
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60
54
48
42
36
30
24
18
12
6
0
100
105
110
115
120
125
130
135
140
Customer demand : ewma
Retailordes : ewma
Distributionorders : ewma
Wholesalerorders : ewma
Production orders : ewma
145 150 155
Time (Month)
160
165
170
175
180
185
190
195 200
bottles
bottles
bottles
bottles
bottles
per
per
per
per
per
hour
hour
hour
hour
hour
Fig. 10.3 Forrester effect in a supply chain as it tries to use EWMA at local level (0.5 weight)
within original setting (delay D 4, step-wise demand change from 4 to 8 units during time unit
100)1
40
36
32
28
24
20
16
12
8
4
0
100
105
110
115
120
125
Customer demand : transparency
Retailordes : transparency
Distributionorders : transparency
Wholesalerorders : transparency
Production orders : transparency
130
135
140
145 150 155 160
Time (Month)
165
170
175
180
185
190
bottles
bottles
bottles
bottles
bottles
195 200
per
per
per
per
per
hour
hour
hour
hour
hour
Fig. 10.4 Forrester effect in four stage supply chain, where we have transparency for the next stage
(delay D 4, step-wise demand change from 4 to 8 units during time unit 100)
In previous and current work, we suggest that improving forecasting accuracy
could be profitable by using advanced forecasting methods, such as autoregressive
moving average (ARMA) models. Figure 10.5 shows that demand forecasting in
an amplified environment may be completed by assigning a positive value for last
observed demand and a negative co-efficient for older observations (for simplicity
we have used lag of one and two).
Table 10.2 shows co-efficient of two lagging parameters are within the neighborhood of ARMA models built with a larger amount of data. However, the differences
among different models are rather minimal.
Applying advanced forecasting models to tame the Bullwhip effect is challenging
because it calls for process transformation (Zhao et al., 2002; Bayraktar et al., 2008).
In Figure 10.6 the manufacturing unit reserves forecasted amount of inventory one
1
Juha Saranen, Lappeenranta University of Technology, Finland
10 GARCH Proof of Concept
193
Fig. 10.5 Partial autocorrelation of four stage supply chain data from production phase (2401
observations from 300 time units)
Table 10.2 ARMA models built with 0.125 interval data from original beer-game setting for production phase (number of observations in integer time units given in parenthesis)
Number of
observations
Co-efficient
t 1
t 2
Goodness of fit
R2 (%)
100 (12.5)
200 (25)
300 (37.5)
2401 (300.1)
1.936
1.937
1.937
1.918
0.938
0.939
0.939
0.919
99.8
99.9
99.9
100.0
R2 (%)
whole sample
99.97
99.97
99.97
–
40
36
32
28
24
20
16
12
8
4
0
100
105
110
115
120
125
130
135
140
145
150
155
160
165
170
175
180
185
190
195
200
Ti me ( Mont h)
P r o d o r d e r s T O T A L : o r ig in a l
Fig. 10.6 Production orders as ARMA model of wholesaler demand is used in production orders
with modifications on operating structure
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period before-hand (in order to distribute knowledge from future demand into operative decisions). However, this is not enough. We have used another manufacturing
unit, which serves as an emergency inventory, dedicated for sudden upswings of demand. This emergency inventory is served with local short response manufacturing,
which continuously replenishes emergency inventory with low lot size (in this case
lot size is 7 units, lead time to emergency inventory is 1 time unit, instead of 4). During simulation trials we explored how ARMA model may be built within dynamic
environments with respect to time.
10.4 Advanced Statistical Models
Forecasting demand is a key tool in managing uncertainty. Forecast accuracy depends on the understanding and coverage of parameters as well as the accuracy of
historic data available for each variable that may have an impact on the forecast or
predictive analytics. The broad spectrum applicability of forecasting includes such
diverse verticals as healthcare and energy 2 utilization (Datta 2008e, 2008f).
One of the assumptions in the Classical Linear Regression Models relates to homoskedasticity (homo equal, skedasticity variance or mean squared deviation
( 2 ), a measure of volatility) or constant variance for different observations of the
error term. Forecast errors are heteroskedastic (unequal or non-constant variance).
For example, in multi-stage supply chains, the error associated with manufacturer’s
forecast of sales of finished goods may have a much larger variance than the error
associated with retailer’s projections (the assumption being that the proximity of
the retailer to the end consumer makes the retailer offer a better or more informed
forecast of future sales through improved understanding of end-consumer preferences). The upstream variability reflected in the Bullwhip Effect violates the basic
premise of CLRM, the assumption of homoskedasticity. CLRM ignores the realworld heteroskedastic behavior of the error term "t and generates forecasts, which
may provide a false sense of precision by underestimating the volatility of the error
terms.
Fig. 10.7 Illustrations pf homoskedasticity, heteroskedasticity and the Bullwhip Effect
2
See www.cids.ie/Research/DCSES.html and www.dcsenergysavings.com
10 GARCH Proof of Concept
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In a homoskedastic distribution, observations of the error term can be thought of
as being drawn from the same distribution with mean D 0 and variance D 2 for all
time periods (t).
A distribution is described as heteroskedastic when observations of the error term
originate from different distributions with differing widths (measure of variance). In
supply chains, the variance of orders is usually larger than that of sales and the distortion increases as one moves upstream from retailer to manufacturer to supplier. Therefore, the assumption of heteroskedasticity, over time, seems appropriate as a characteristic that may be associated with demand amplification or the Bullwhip effect.
While variance of error term may change across cross sectional units at any point
in time, it may also change over time. This notion of time varying volatility is frequently observed in financial markets and has been the driving force behind recent
advancements in time series techniques. Instead of considering heteroskedasticity
as a problem to be corrected (approach taken by CLRM practitioners in assuming
homoskedasticity of error term), Robert Engle modelled non-constant time dependent variance (heteroskedasticity) using an autoregressive moving average (ARMA)
technique.
ARMA consists of two components, an autoregressive (AR) compnent and
a moving average (MA) component. AR is a technique by which a variable can be
regressed on its own lagged values and thus link the present observation of a variable
to its past history. For example, today’s sales may depend on sales from yesterday
and the day before: MA expresses observations of a variable in terms of current and
lagged values of squared random error terms using a moving average.
Robert Engle used the MA approach to propose AutoRegressive Conditional Heteroskedasticity or ARCH to model the time varying volatility in a series. The ‘conditional’ nature of non-constant variance (heteroskedasticity) refers to forecasting
of variance conditional upon the information set available. This MA representation
was later generalized to an ARMA representation referred to as Generalized AutoRegressive Conditional Heteroskedasticity model or GARCH. The GARCH technique represents a parsimonious model than ARCH, while allowing for an infinite
number of past error terms to influence current conditional variance.
These advances from econometrics may be developed into tools for forecasting
and risks analytics with a broad spectrum of applications in business, energy, industry, security and healthcare (Datta, 2008d), as well as decision support systems
and operations management, for example, supply chain management (Datta et al.,
2007).
Impact of Real-Time High-Volume Data
from Automatic Identification Technologies (AIT)
Tracking technologies evolved from the discovery of the RADAR at MIT in the
1940’s. AIT is slowly beginning to impact information flow in the modern value
chain network. Tracking products from manufacturers to retailers may have its ori-
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gins in the 1970’s with the introduction of the bar code to identify stock-keeping
units (SKU). Now it is embracing AIT or auto id, for example, use of radio frequency identification (RFID). AIT makes it possible to electronically log product
movement in the “digital” supply chain. This information may be available in realtime. However, the standards, such as the electronic product code (EPC), to capture unique identification of physical objects and processes (Datta, 2007a) calls for
a paradigm shift (Datta, 2008c).
Since RFID updates reports every time an individual item or SKU moves from
one stage to another stage in the supply chain, or when the item is sold, it is possible
to determine the demand for an item in real-time rather than wait for batch updates
or weekly or monthly buckets to generate a forecast. The granularity of the data
from auto id systems may result in very high volume data which may reveal peaks
and troughs of demand for the product, hourly or daily. This volatility is lost when
data is aggregated in buckets or batch.
Extracting the value from this high volume near real-time data and deciphering
the meaning of the implicit volatility may be a boon to business intelligence and
predictive analytics, including forecasting.
Indeed many warehouses adopt an inventory policy of ordering products when
stock levels fall below a certain minimum amount s and order up to a maximum
amount S [the (s, S ) policy]. With auto id it is possible to ascertain this at the
instant the threshold is attained, thereby, eliminating the likelihood of out of stock
(OOS). Hence, it follows that capitalizing on the increased volume of near real-time
demand data from auto id may have profound impact on supply chain forecasting.
However, current software with its CLRM engines and clustering approach, does
not improve forecasts even with high volume data. The assumption of error terms
implicit in CLRM limits the gains in forecast accuracy from high volume data and
fails to show return on investment (ROI) from adoption of (new) auto id tools.
It is our objective to justify why deployment of new tools, for example, auto
id, calls for adoption of new techniques for data analytics, for example, advanced
techniques from financial econometrics. It is safe to state that new streams of data
emerging from a multitude of sources, for example, auto id and sensors, cannot
yield value or ROI if used in conjunction with archaic software systems running
ancient forms of analytical engines that are typically CLRM based, at least, in the
forecasting domain.
To extract decisionable information from high volume near real-time auto id and
sensor data, the use of techniques like GARCH deserves intense exploration. The
fact that GARCH may be a clue to generating ROI from auto id and RFID data is
no accident because GARCH requires high volume data to be effectively utilized
and generate results with higher accuracy levels. Hence, this convergence of auto
id data with tools from econometrics may be an innovative confluence that may be
useful in any vertical in any operation including security and healthcare, as well as
obvious and immediate use in supply chain management. Datta et al. (2007) and
this chapter, has attempted to highlight how to extract the advances in econometrics
from the world of finance and generalize their valuable use in decision systems, with
a broad spectrum of general applications.
10 GARCH Proof of Concept
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Evolution of such a tool may help analysts and planning managers since a key
concern of any manager is the accuracy of the predictions on which their budget is
based. The proper allocation of resources for acquisition of personnel and equipment
has long been plagued by errors in traditional forecasting. A part of the answer to
this problem may be latent in the potential for the combined use of VAR (vector autoregression) with other forecasting techniques. The primary VAR model best suited
for the planning function in resource allocation is the standard GARCH model. It
is well suited for pragmatic studies involving supply chain, army personnel requirements and defense equipment requirements. Any system that may be modeled using
time-series data, may explore how to include GARCH based on the error correction
innovation that may improve forecasts. Forecast accuracy of GARCH model may
be quantified in a number of different ways. Traditional methods are:
1. Mean Square Error.
2. Mean Average Percentage Error.
3. Aikiki Information.
Once the forecast is developed, the accuracy can be measured by comparing the
actual observed values with the predicted values. If the collected data falls within
the confidence interval of the forecast model, then the model provides a good fit for
the system. Although GARCH is useful in forecasting it is important to realize that
it was designed to model volatility and can be applied to positive series but not to
economic series.
GARCH Proof of Concept Demonstrated Using an Example
from Spare Parts Inventory Management
Although GARCH models have been almost exclusively used for financial forecasting in the past, we propose (Datta et al. 2007b) that with appropriate modifications,
it may be applicable to other areas. An operation exhibiting volatility may benefit
from VAR-GARCH in addition to other techniques, either in isolation or in combination. It is known that in times of conflict military supply chains experience spikes
in demand. These spikes and troughs occur over a short period of time and result in
losses due to OOS (out of stock) or surplus. GARCH may minimize forecast errors
and fiscal losses in some of the following domains:
1.
2.
3.
4.
Cost of personnel, supplies, support;
Planning, programming and budgeting;
Defense program and fiscal guidance development;
Force planning and financial program development.
In one preliminary study (supported by the US DoD, Institute for Defense Analysis,
Washington DC and also mentioned in Datta et al., 2007) the spare parts supply
chain of a military base was examined for inefficiencies. The data for a 9 month
period was collected for a spare part for a military vehicle (HumV). Because the
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US Department of Defense affixes RFID tags on some spare parts from some of its
suppliers, the hourly auto id demand data was available for analysis. The historical
data was used to develop CLRM and GARCH (1,1) model. In this case, the linear regression model was found to have Mean Square Error (MSE) of 0.20 (20 %).
By comparison, the GARCH (1,1) model produced a MSE of 0.06 (6.7 %). These
results are encouraging and the US DoD case lends credibility for exploration of
GARCH in forecasting analytics. Although this finding is promising, it needs to be
repeated with other forms of data and subjected to rigorous mathematical analysis.
Financial Profit from Application of GARCH Technique
in Retail Inventory Management
A pilot implementation using GARCH in a commercial supply chain has been undertaken with real-world retail data from a major US retailer. Preliminary results
reveal that using GARCH as a forecasting technique offers some advantages (even
with limited data volume) compared to CLRM and ARMA. The retail data are
from office supply products for business and home customers. Thousands of product lines are sourced from different suppliers, globally. In this study, nine different SKU’s from three different product classes were chosen for analysis. It is not
known whether some of the products may suffer from seasonality effects. For each
of the 9 products the historical demand data is available for 70 continuous weeks.
52 weeks of history was used to develop projections of demand variability for the
subsequent 18 weeks. This projection was compared to the actual observations of
demand variability over the 18 week test horizon. Three different techniques were
used to forecast the standard deviation. The methods used were CLRM, ARMA and
GARCH.
Figure 10.8 shows the performance of each of the three forecasting techniques
based on retail data on the 9 products. The error of the forecasted standard deviation is calculated as an average over the final 16 weeks of forecast data. CLRM is
outperformed by ARMA and GARCH models for almost all SKU’s.
The results suggest that GARCH may be better (or as good as) across different
SKU’s. GARCH outperforms ARMA for a number of products. For the eight favorable tests, an average improvement of 800 basis points was observed. That translates
to 1.1 % in-stock improvement from a preliminary application of GARCH. In this
real-world case, that amounts to about $ 13 million in additional revenue in terms
of recovered lost sales. The product-dependent variability of GARCH performance
may be linked to seasonality or other factors (accuracy of input data). Further testing
with granular data (hourly or daily) and higher volume data per SKU may increase
the accuracy and benefits from using the GARCH technique in forecasting. It may
be apparent that systemic use of GARCH type techniques in forecasting, therefore,
may substantially improve corporate profit.
10 GARCH Proof of Concept
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600%
Forecasting Error
500%
400%
300%
200%
100%
0%
1
Traditional Model
2
3
ARMA
GARCH
4
5
6
7
8
9
Product Line
Fig. 10.8 Classic Linear Regression Model (CLRM) is almost always outperformed by ARMA
and GARCH
140%
120%
Forecasting Error
100%
80%
60%
40%
20%
0%
1
ARMA
2
GARCH
3
4
5
6
7
8
9
Product Line
Fig. 10.9 Comparing autoregressive techniques: ARMA vs. GARCH (same data set but excluding
CLRM)
It is not difficult to extrapolate that high volume item level retail sales or inventory data (per minute or by the hour) may be available with the diffusion of item
level tagging using RFID or radio frequency identification tags. The volume of the
data may increase exponentially if embedded sensors are deployed to enhance security and/or detect movement of any physical object from any location. Businesses
dealing with short life cycle products (electronics, semi-conductors industries) may
explore how these advanced techniques may help to reduce the volatility of supply-
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demand since the ability to re-address sales or marketing issues are often limited
if the shelf-life of the product is merely a few months (laptops, MP3 players, cell
phones).
10.5 Temporary Conclusion
Making sense of data may benefit from high volume data acquisition and analysis using GARCH and VAR-MGARCH (Datta et al., 2007) techniques in addition
to and in combination with other tools for forecasting and risk analysis in diverse
verticals that may span from healthcare to energy (Datta, 2008e). In this work, we
explored the possibility of using advanced forecasting methods in context of supply
chains and demonstrated financial profitability from use of the GARCH technique.
It remains unexplored if concomitant business process transformation may be necessary to obtain even better results. The proposed advanced forecasting models, by
their very construction require high volume data. Availability of high volume data
may not be the limiting factor in view of the renewed interest in automatic identification technologies (AIT) that may facilitate acquisition of real-time data from
products or objects with RFID tags or embedded sensors. It is no longer a speculation but based on proof that use of advanced forecasting methods may enhance
profitability and ICT investments required to acquire real-time data may generate
significant return on investment (ROI). However, understanding the “meaning” of
the information from data is an area still steeped in quagmire but may soon begin to
experience some clarity if the operational processes take advantage of the increasing
diffusion of the semantic web and organic growth of ontological frameworks to support ambient intelligence in decision systems coupled to intelligent agent networks
(Datta, 2006). To move ahead, we propose to bolster the GARCH proof of concepts
through pilot implementations of analytical engines in diverse verticals and explore
advanced forecasting models as an integrated part and parcel of real-world business
processes and systems including the emerging field of carbonomics (Datta, 2008f).
Acknowledgements The corresponding author (SD) is deeply indebted to Prof. Clive Granger
(UCSD) for his guidance, critical reading and review of the manuscript. The author (SD) is grateful to Professor Robert Engle (NYU) for his advice. The detailed editing of this document was
accomplished by Brigid Crowley at the School of Science and Computing at ITT, Ireland. Comments from General Paul Kern of The Cohen Group (Washington DC) and Dr. Stan Horowitz of
the Institute for Defense Analysis (Washington DC) were very helpful to the corresponding author (SD). The encouragement from Mr Kazunori Miyabayashi, Senior Vice President of Hitachi
(Tokyo, Japan) and Professor Joseph Sussman, MIT is acknowledged. This work was partially
supported by the members and sponsors of the MIT Forum for Supply Chain Innovation, Massachusetts Institute of Technology (Cambridge, Massachusetts) and the Centre for Innovation in
Distributed Systems.
10 GARCH Proof of Concept
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344
Chapter 11
Supply Chain Risk Management:
Annotation of Knowledge Using
a Semi-Structured Knowledge Model
Chun-Che Huang and Tzu-Liang (Bill) Tseng
Abstract In order to increase the effectiveness and performance of supply chain
networks, firms are working towards improving Supply Chain Risk Management
(SCRM) knowledge. Appropriately managing SCRM knowledge can result in lower
costs, fewer operational disruptions and better customer satisfaction due to supplier
uncertainty has been eliminated. The lack of flexible- and well-structured knowledge representation has made the integration of SCRM knowledge activities difficult because these knowledge activities are heterogeneous in nature. Semantic heterogeneity is the main problem of SCRM knowledge representation. Annotation is
one of the approaches to solve this problem. Annotation adds semantic metadata
on web documents and proposes machine-understandable metadata for integration
of heterogeneous format documents. This book chapter proposes a semi-structured
knowledge (SSK) model to represent SCRM knowledge and uses Resource Description Framework (RDF) and Resource Description Framework System (RDFS) as
metadata languages to annotate semantic metadata. This proposed annotation process integrates heterogeneous and un-structured SCRM documents. This solution
approach shows great promise for knowledge representation/sharing in the heterogeneous SCM environment.
Key words: Semi-structured knowledge model; Semantic heterogeneity; Ontology; Annotation process; Supply chain risk management
11.1 Introduction
Managing supply chains in today’s competitive world is increasingly challenging.
Greater the uncertainties in supply and demand, globalization of the market, shorter
and shorter product and technology life cycles, and the increased use of manufacturing, distribution and logistics partners have resulted in complex international supply network relationships, have led to higher exposure to risks in the supply chain
T. Wu, J. Blackhurst (eds.), Managing Supply Chain Risk and Vulnerability
© Springer 2009
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C.-C. Huang, T.-L. Tseng
(Christopher et al., 2002). The complexity and uncertainty within a supply chain
can also increase the “chaos” risks within the supply chain. These chaos effects
result from over reactions, unnecessary interventions, mistrust, and distorted information throughout a supply chain (Childerhouse et al., 2003). Consequently, global
competition and technological change have motivated improved risk management
in supply chains. Risk management in supply chains consists of risk sharing, control and prevention, and financial instruments to negate the effects of the supply
chain risks and their capital consequences (Lee, 2004; Hallikas et al., 2004; Tang,
2006). With the increasing emphasis on supply chain vulnerability, effective tools
for analyzing and understanding appropriate supply chain risk management are now
attracting much attention.
To survive in a very competitive market today, firms are required to efficiently operate the core knowledge domain (Badaracco, 1990; Dieng et al., 1999) and focus
on high-value and applicable knowledge. The lack of flexible and well-structured
knowledge representation has made the integration of Supply Chain Risk Management (SCRM) knowledge activities difficult because these knowledge activities are heterogeneous in nature. (Nonaka and Takeuchi, 1995). Therefore, how to
make representation of SCRM knowledge consistent and flexible is critical (Cui
et al., 2001). A representation model is required to present knowledge with a flexible and well-structured format in order to store and reuse them (Malone, 2002;
Woodworth and Kojima, 2002; Nabuco et al., 2001). Furthermore, access to relevant and accurate information/knowledge is becoming increasingly complex due to
the databases and knowledge bases that are distributed, diverse, and dynamic. Resolving the heterogeneity of SCRM knowledge documents from the various heteropurpose knowledge-based systems has become a crucial problem. How to efficiently
access and retrieve these hetero-format knowledge documents, specifically solving
the semantic heterogeneity, is an imperative issue (Decker et al., 1999). A process
by annotation to transform these heterogeneous SCRM knowledge documents into
a flexible and well-structured SCRM knowledge is required.
SCRM related documents exist in various formats according to different sources,
such as documents in text, paper, and audio formats. Some documents are archived
as images. Based on the literature review, two issues are focused in SCRM knowledge representation. One issue is improving the document representations while the
other issue is refining user queries. Note that this paper focuses on the first issue.
SCRM documents include the combination of qualitative and quantitative parts, for
example, tier I and tier II suppliers documents, documentation related to natural
hazards, terrorism, pandemics, data security, demand variability and supply fluctuations, etc. Current research on SCRM document representation is not sufficient
to improve efficiencies in the knowledge representation. For example, documents
are indexed by relatively few terms compared to using the whole index space and
the SCRM document classification rules are not considered in this indexing task.
A classification rule that is related to the SCRM document representation approach
is required to effectively index the documents. Annotation is a process that makes
knowledge sources, including Web pages, un-structured text documents etc., on
the basis of a formal description of their contents (Decker, 2002; Li et al., 2001).
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That is to make the knowledge sources understandable for computer devices. These
sources should be annotated with meta-data markups in an annotation process. In
other words, annotating the contents of knowledge sources with meta-data markups
is one promising method to make them understandable for machines in the semantic web environment. In the annotation domain, metadata (i. e., data about data) is
one kind of semantically information allows the web to describe semantic properties
about some given knowledge contents of knowledge documents (Kashyap and Shet,
1996; Decker, 2002; Fensel et al., 2000). According to definition of annotation, annotation can help with improving the document representations.
Annotation research attempts to add semantic metadata in web documents and
propose machine-understandable metadata (Kashyap and Shet, 1996) for integration
of a heterogeneous format document from web knowledge sources in a structured
model. However, little research focuses on annotating metadata from a knowledge
content perspective, such as annotation for knowledgeable workers rather than computer, and modeling SCRM knowledge documents through different dimensions in
order to make the knowledge learner recognize the usefulness of designated knowledge. To operate the annotated metadata, currently three major knowledge-based
systems extensively used in semantic web: Simple HTML Ontology Extensions
(SHOE) (Heflin and Hendler, 2000), Ontobroker (Decker et al., 1999), and WebKB (Martin and Eklund, 1999). All of these studies rely on knowledge in HTML
language. They all started with providing manual mark-up by editors. However,
experiences of Erdmann et al. (2000) have shown that mark-up knowledge in these
three systems yields extremely poor results that contain syntactic mistakes, improper
references, and all of the problems illustrated in the scenario section:To avoid redundancy of the use of meta-datum, an approach to coordinate and manage meta-datum
in the metadata repository and benchmark ontology is definitely required.
This book chapter is based on a semi-structured knowledge (SSK) model (Huang
and Kuo, 2003) to presents SCRM knowledge. It also presents tools and techniques
for decision making related to supply chain risk and vulnerability and uses Resource Description Framework (RDF) and Resource Description Framework System (RDFS) as metadata languages to annotate SCRM knowledge documents which
are in unstructured heterogeneous format semantically. Moreover, it proposes an
annotation process to synthesize heterogeneous un-structured documents form heterogeneous SCRM knowledge sources and presents interaction between SSK and
benchmark ontology. Note that the benchmark ontology in this chapter refers to the
specific ontology in use. The remainder of this book chapter is organized as follows:
Sect. 11.2 describes the generation and contents of semi-structured knowledge and
the SCRM semi-structured knowledge represented with RDF and RDFS. Sect. 11.3
proposes the annotation process to transform the original heterogeneous documents
into RDF and RDFS documents using the SSK model. Sect. 11.4 presents interaction of annotated SCRM knowledge documents with the benchmark ontology and
Sect. 11.5 concludes this book chapter. The main contribution of this book chapter
is that the proposed approach develops a standard way to exchange knowledge and
it can be applied in any general SC domain through development of a SSK model
and annotation framework. Moreover, in order to manage SC risk effectively, web
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based SCRM and its documentation transitions and representations play an important role. Particularly the heterogeneity problem among documentations is required
to be solved. The heterogeneity issue is resolved by the annotation approach in
perspective of SCRM knowledge content is understandable by both machines and
knowledgeable workers. The solution approach demonstrates great promise for effective knowledge sharing in SCRM.
11.2 The Generation and Representation
of Semi-Structured Knowledge
11.2.1 The Generation of Semi-Structured Knowledge
Semi-structured knowledge (SSK) is defined as collection of knowledge resulting
from Knowledge Management (KM) activities in organizations and constructed by
the six dimensions of Zachman framework (5W1H: who, what, when, why, where
and how) (Huang and Kuo, 2003). The Zachman framework represents the perspectives and dimensions of knowledge contents in the form of a matrix, with the
perspective representing the rows, e.g. goals, and the dimensions representing the
columns, including: Entities (What? Things of interest); Activities (How? In what
manner or way; by what means); Locations (Where? Places of interest); Individual
(Who? Individuals and organizations of interest); Times (When? Things occur) and
Motivations (Why? Reasons and rules).
Notations
DA : annotation description,
DB : basic description,
DR : relationship description,
IG :
general information,
solution approach information,
IS :
KA : annotated semi-structured knowledge,
KO : organizational semi-structured knowledge,
KP : knowledgeable workers or problem solver,
KT : understandable knowledge.
SSK contains large amounts of solution approach information, domain knowledge,
and know-how and the environment impact on organizations closely. It is generated through a series of transformation processes (Fig. 11.1), which are triggered
by problematic events (e. g., inventory is too high). Every step of this process involves technical and managerial issues. At the beginning, when a problematic event
occurs, the event initiates an operation to identify requirements of users and starts
a problem-solving process.
(1)
If the problem can be solved in an organization internally, related knowledge
elements (concepts, properties, and instances) are retrieved from the bench-
11 Supply Chain Risk Management
Fig. 11.1 Flow diagram of SSK generation
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210
(2)
C.-C. Huang, T.-L. Tseng
mark ontology as follows: (i) general information (IG ) of the problematic
event is illustrated, (ii) knowledgeable workers propose the solution approach
information (IS ) after inferring to the benchmark ontology, (iii) feedback of
knowledgeable workers or problem solver (KP ) is in fusion and transformed
into understandable knowledge (KT ), (iv) combining IG , KP , IS , and other
existing SSK, which knowledgeable worker may refer to, generate the organizational semi-structured knowledge (KO ).The SSK is produced within the
organization without considering heterogeneous knowledge sources. That is,
all knowledge documents have been represented using the SSK model (see
Fig. 11.1).
If the problematic event with its IG needs be resolved with aid of other heterogeneous knowledge documents, then heterogeneous knowledge solutionrelated subject (also in Fig. 11.1) is identified, where these heterogeneous/
unstructured knowledge documents are transformed into SSK model by the annotation process. The resulted knowledge with annotation is called annotated
semi-structured knowledge (KA ). In this process, three annotation descriptions
are used. There are basic description (DB ), annotation description (DA ), and
relationship description (DR ), which are generated and added onto annotated
semi-structured knowledge (KA ). KA is primarily focused on the subject corresponding to event’s reason (why) and resolution (how). With the annotation,
the heterogeneous knowledge in the organization is represented with the six dimensions (what, who, why, when, where, and how) of solution-related knowledge. The final SSK is generated after combining the annotated semi-structured
knowledge (KA ), the analysis reasons (why) and resolutions (how) from KA ,
as well as the general information IG from KO . In some cases, the annotated
knowledge is not combined into the final documents in SSK model directly but
is referenced in the process (see Fig. 11.1). It aims at generating the solution approach information (IS ). In such a case (e. g., adding annotation), the elements
in the annotated SSK is extracted and mapped to the benchmark ontology, and
annotated document is stored in metadata repository.
In this generation process, all knowledge is represented using the SSK model
is formulated in the “semi-structured knowledge documents design” block
(Fig. 11.1). The generated documents are called “knowledge documents in
SSK model”. Notations in Fig. 11.1 are illustrated as follows:
1.
2.
3.
4.
A dashed line represents the source of data, which means “event” and
“requirement”.
A block represents the entities in the process. There are requirements
assessment, events classification, identifications of subjects, and knowledgeable workers’ involvement. The contents in parenthesis represent the
information or knowledge generated from each step, for example, Is , Kp ,
DR , etc.
An oval block represents data storage and processes.
Three different types of lines are used in the diagram. The solid line illustrates the direction of the process, while the long dash line points out
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211
the requirements of semi-structured knowledge. The dot dash line shows
the steps to construct semi-structured knowledge. As shown above, semistructured knowledge includes general information, solution approach information, and feedback from knowledgeable workers (called feedback
knowledge) and annotated semi-structured knowledge (KA ). Fig. 11.1
represents the conceptual framework of SSK generation. The detailed
models related to this framework can be referred in Huang and Kuo
(2003).
11.2.2 Semi-Structured Knowledge Representation
A better presentation of SSK is proposed by using RDF and RDFS in this paper.
Since the RDF language is developed based on XML and relies on the support of
XML (URL RDF), the features of the XML are also inherited by RDF, such as
principles of structure, extensibility, self-description, and separation between data
and model. RDF contains, not only outstanding efficiency in data management and
exchange, but also effectively presents every kind of knowledge in network, and provides a new frame for knowledge management (URL RDF). Even more important,
the global goal of RDF is to define a mechanism for describing resources that makes
no assumptions about a particular application domain, but defines (a priority) the semantics of any application domain (Fensel et al., 2000). The characteristic of RDF
allows semi-structured knowledge to appear more domain-natural and acceptable in
the future Web-based inter-organization.
Figure 11.2 shows the contents of the SSK in XML format, rather than RDF
and RDFS format. The left side in Fig. 11.2 presents SCRM SSK, which includes
general information, subject/solution approach information, and feedback knowledge, where the association rule is applies as a solution approach. The right side
in the figure shows the semi-structured knowledge with annotated knowledge. In
Fig. 11.2, the notation KA is semi-structured annotation knowledge which is composed of the following information terms: DB : basic description information; DA :
annotation description information of solution-related subject; and DR : relation description information. WhereKA represents the formal semi-structured knowledge
after the annotation process and KO represents the manufacturing semi-structured
knowledge, which is the fusion of (i) general information, (ii) solution approach information, (iii) the knowledge coming from knowledgeable workers, and (iv) feedback knowledge.
General Information (IG )
General information is described as fundamental information corresponding to
a problematic event, for example, a description, observer, location and time etc. The
contents are presented as follows (Fig. 11.3). The problematic event (E) is derived
from event transformation function (fE ) which comprises two parameters: o: busi-
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Fig. 11.2 An example of XML-based SSK documentation
<General_Information>
<Event>
<Event_Name> </Event_Name>
<Event_Observer></Event_Observer>
<Event_Description> </Event_Description>
<Event_When> </Event_When>
<Event_Where> </Event_Where>
</Event>
</General_Information>
E = f E (o, p )
Fig. 11.3 Format of XML for general information
ness entity (organization); and p: business process. Semi-structured knowledge is
initiated from problematic events. The purpose of event classification is to support
the distinction of semi-structured knowledge.
The problematic event is clarified and the types of structure and processes required to solve the problem are also specified. The General Information is translated
to RDF and RDFS format. IG example in RDFS format is presented in Fig. 11.4.
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213
<?xml version='1.0' encoding='ISO-8859-1'?>
<!DOCTYPE rdf:RDF [
<!ENTITY rdf 'http://www.w3.org/1999/02/22-rdf-syntax-ns#'>
<!ENTITY a 'http://protege.stanford.edu/system#'>
<!ENTITY event 'http://www.ncnu.edu.tw/iskmlab/event#'>
<!ENTITY rdfs 'http://www.w3.org/TR/1999/PR-rdf-schema-19990303#'>
]>
<rdf:RDF xmlns:rdf="&rdf;" xmlns:a="&a;" xmlns:event="&event;" xmlns:rdfs="&rdfs;">
<rdfs:Class rdf:about="&event;Country" >; <rdfs:subClassOf rdf:resource="&event;Where"/>
</rdfs:Class>
<rdf:Property rdf:about="&event;ShipmentEvent" a:maxCardinality="1">
<rdfs:domain rdf:resource="&event;Event_description"/>
<rdfs:range rdf:resource="&rdfs;Literal"/>
The property of class
</rdf:Property>
<rdfs:Class rdf:about="&event;ShipmentEventLocation">
<rdfs:subClassOf rdf:resource="&event;Region"/>
</rdfs:Class>
<rdf:Property rdf:about="&event;ShipmentPartnerRoleRouteNumber" a:maxCardinality="1">
<rdfs:domain rdf:resource="&event;ShipmentEventLocation"/>
<rdfs:range rdf:resource="&rdfs;Literal"/>
</rdf:Property>
<rdf:Property rdf:about="&event;ShipmentPartnerRoteRoute" a:maxCardinality="1">
<rdfs:domain rdf:resource="&event;ShipmentEventLocation"/>
<rdfs:range rdf:resource="&rdfs;Literal"/>
</rdf:Property>
<rdf:Property rdf:about="&event;endDate" a:maxCardinality="1">
<rdfs:domain rdf:resource="&event;Event_description"/>
The properties describe the
<rdfs:range rdf:resource="&rdfs;Literal"/>
general information of event.
</rdf:Property>
This description classes is came
<rdf:Property rdf:about="&event;event_Name" a:maxCardinality="1">
from function ƒE.
<rdfs:domain rdf:resource="&event;Event"/>
<rdfs:range rdf:resource="&rdfs;Literal"/>
</rdf:Property>
<rdf:Property rdf:about="&event;event_Observer" a:maxCardinality="1">
E = ƒE (o, p)
<rdfs:domain rdf:resource="&event;Event"/>
<rdfs:range rdf:resource="&event;Observer_info"/>
</rdf:Property>
<rdf:Property rdf:about="&event;event_description" a:maxCardinality="1">
<rdfs:domain rdf:resource="&event;Event"/>
<rdfs:range rdf:resource="&event;Event_description"/>
</rdf:Property>
<rdf:Property rdf:about="&event;event_when" a:maxCardinality="1">
<rdfs:domain rdf:resource="&event;Event"/>
<rdfs:range rdf:resource="&event;when"/>
</rdf:Property>
<rdf:Property rdf:about="&event;event_where" a:maxCardinality="1">
<rdfs:domain rdf:resource="&event;Event"/>
<rdfs:range rdf:resource="&event;Where"/>
</rdf:Property>
<rdf:Property rdf:about="&event;rigionCode" a:maxCardinality="1">
<rdfs:domain rdf:resource="&event;Region"/>
The classes represent the
<rdfs:range rdf:resource="&rdfs;Literal"/>
general information of event.
</rdf:Property>
This description classes is came
<rdf:Property rdf:about="&event;rigionName" a:maxCardinality="1">
from function ƒE.
<rdfs:domain rdf:resource="&event;Region"/>
<rdfs:range rdf:resource="&rdfs;Literal"/>
</rdf:Property>
<rdfs:Class rdf:about="&event;what">
<rdfs:subClassOf rdf:resource="&rdfs;Resource"/>
</rdfs:Class>
<event:MODIFY-CLASS rdf:about="&event;ShipmentTransportationEvent">
<rdfs:subClassOf rdf:resource="&event;Event"/>
</event:MODIFY-CLASS>
<rdfs:Class rdf:about="&event;Where" a:role="abstract">
<rdfs:subClassOf rdf:resource="&rdfs;Resource"/>
</rdfs:Class>
</rdf:RDF>
Fig. 11.4 Format of RDFS for partial general information
Solution approach Information (IS )
The Solution approach information includes important parameters used in problemsolving methods and results. This information allows users to understand messages
of solution-related subject, for example, how the solution method is to be applied.
The problem-solving processes and results may not be the same due to the differ-
214
<Process_Information>
<Subject>
<Subject_What></Subject_What>
<Subject_Who> </Subject_Who>
<Subject_When></Subject_When>
<Subject_Where></Subject_Where>
<Subject_Why></Subject_Why>
<Subject_How>
<Tech_info/>
<Specific_Info/>
</Subject_How>
</Subject>
</Process_Information>
C.-C. Huang, T.-L. Tseng
S = f s ( w 1 , w 2 , w 3 , w 4 , w 5 , h1 )
Fig. 11.5 Format of XML for solution approach information
ent methods that are used. The contents of Fig. 11.5 show important components
of solution approach information, 5W1H (What, Where, Who, When, Why, and
How). Where S is the subject of problematic event and fS is the subject transformation function. The subject S should be clear, concise, and able to represent the
characteristics of semi-structured knowledge. The structure of the subject should be
dynamic, for example, sensitive to dimension and level changes. The entity of the
subject is “what”, !1 . This parameter is most critical and dominates the rest of parameters (where, who, when, why, and how, i. e., place (!2 /, people of individual
(!3 ), timing (!4 ), motivation (!5 /, and solution process (h1 )). Note that different
solution approaches contain different data. The 5W1H (What, Where, Who, When,
Why and How) is used to specify “Subject.” The following example of RDF and
RDFS format of IS illustrates association analysis (Fig. 11.6).
Knowledge (KP , KT )
Knowledge (KP , KT ), where KP represents knowledge from the knowledgeable
worker or analyzer and KT represents feedback knowledge from the domain knowledgeable worker or administrator that includes (i) the explanation from the problem
solvers for the results of solution approach information, and (ii) the feedback from
other knowledgeable workers (including problem solver) to this information and
knowledge.
KP corresponds to the knowledge resulted from a knowledgeable worker or
analyzer using a particular solution approach, e. g., the Apriori association rules
(Agrawal and Srikant 1994). This knowledge is more focused on solution-related
expertise; i. e., the knowledge is generated based on a subject S corresponding to
a problematic event. KP is derived from knowledge process function fp which is
composed of three parts: E: problematic event; S : subject, and P : knowledgeable
worker (problem solver).
KT corresponds to the feedback knowledge that provides different professional
knowledge from different standpoints and perspectives of knowledgeable workers.
KT is derived from knowledge transformation function fT which is composed of the
11 Supply Chain Risk Management
<?xml version='1.0' encoding='ISO-8859-1'?>
DTD declaration
<rdf:RDF xmlns:rdf="&rdf;" xmlns:a="&a;" xmlns:subject="&subject;" xmlns:rdfs="&rdfs;">
……….
<rdf:Property rdf:about="&subject;regionName" a:maxCardinality="1">
<rdfs:domain rdf:resource="&subject;Region"/>
<rdfs:range rdf:resource="&rdfs;Literal"/>
</rdf:Property>
<rdfs:Class rdf:about="&subject;when">
<rdfs:subClassOf rdf:resource="&rdfs;Resource"/>
The 5W1H classes
</rdfs:Class>
which represents the gen<rdfs:Class rdf:about="&subject;who">
eral information of solu<rdfs:subClassOf rdf:resource="&rdfs;Resource"/>
tion information IS.
</rdfs:Class>
<rdfs:Class rdf:about="&subject;Where">
<rdfs:subClassOf rdf:resource="&rdfs;Resource"/>
</rdfs:Class>
<rdfs:Class rdf:about="&subject;what">
<rdfs:subClassOf rdf:resource="&rdfs;Resource"/>
</rdfs:Class>
<rdfs:Class rdf:about="&subject;Employee_Info">
<rdfs:subClassOf rdf:resource="&subject;Human resource_Info"/>
</rdfs:Class>
<rdfs:Class rdf:about="&subject;Expert_Info">
<rdfs:subClassOf rdf:resource="&subject;Employee_Info"/> S = ƒS (˶ 1 , ˶ 2 , ˶ 3 , ˶ 4,
</rdfs:Class>
<rdfs:Class rdf:about="&subject;Why">
<rdfs:subClassOf rdf:resource="&rdfs;Resource"/>
</rdfs:Class>
<rdfs:Class rdf:about="&subject;How">
<rdfs:subClassOf rdf:resource="&rdfs;Resource"/>
</rdfs:Class>
….…
…..
<rdfs:Class rdf:about="&subject;Subject">
These description
<rdfs:subClassOf rdf:resource="&subject;Process Information"/>
properties came from
</rdfs:Class>
<rdf:Property rdf:about="&subject;Subject_How" a:maxCardinality="1"> function ƒS which help
defines the 5W1H to
<rdfs:range rdf:resource="&subject;How"/>
descript solution ap<rdfs:domain rdf:resource="&subject;Subject"/>
proach subject.
</rdf:Property>
<rdf:Property rdf:about="&subject;Subject_What" a:maxCardinality="1">
<rdfs:domain rdf:resource="&subject;Subject"/>
<rdfs:range rdf:resource="&subject;what"/>
</rdf:Property>
<rdf:Property rdf:about="&subject;Subject_When" a:maxCardinality="1">
<rdfs:domain rdf:resource="&subject;Subject"/>
<rdfs:range rdf:resource="&subject;when"/>
</rdf:Property>
<rdf:Property rdf:about="&subject;Subject_Where" a:maxCardinality="1">
<rdfs:domain rdf:resource="&subject;Subject"/>
<rdfs:range rdf:resource="&subject;Where"/>
</rdf:Property>
<rdf:Property rdf:about="&subject;Subject_Who" a:maxCardinality="1">
<rdfs:domain rdf:resource="&subject;Subject"/>
<rdfs:range rdf:resource="&subject;who"/>
</rdf:Property>
……….
</rdf:RDF>
215
˶ 5, h1 )
Fig. 11.6 Format of RDFS for partial solution approach information
following: KP : knowledge from the knowledgeable worker; P 0 : people in general
(not limited to knowledgeable worker); and Ci : the i th content category.
The format of XML, which includes illustration of association analysis, is shown
in Fig. 11.7.
There are two types of knowledge: knowledgeable workers’ explanation for the
results of solution approach information and the feedback of other knowledgeable
workers for the information and knowledge. The RDFS format of basic format of
216
C.-C. Huang, T.-L. Tseng
<Feedback_Knowledge>
<Knowledge>
<Knowledge_Who>
<Id/>
<depart/>
<Name/>
<Position/>
</Knowledge_Who>
<Knowledge_When></Knowledge_When>
<Knowledge_Where></Knowledge_Where>
<Reference_Id></Reference_Id>
<Knowledge_Why></Knowledge_Why>
<Suggest/>
</Knowledge>
</Feedback_Knowledge>
K P = f P ( E, S , P)
K T = f T ( K P , P ' , Ci )
Fig. 11.7 Format of XML of feedback knowledge
KP C KT are generated. The generating of semi-structured knowledge represented
within the Zachman Framework clarifies the processes and activities of knowledge generation in the organization. This semi-structured knowledge formulated as
RDF and RDFS documents are helpful in capturing, storing, managing, and sharing
knowledge in organizations over the semantic web.
11.3 Annotation Framework for Supply Chain Risk
Management Knowledge
The annotation processes is shown in Fig. 11.8. The SCRM knowledge documents
in heterogeneous format are solved and stored in the following three steps: (Heflin
and Hendler 2000):
Step 1:
Step 2:
Each SCRM knowledge contents are captured from un-structured or heterogeneous SCRM knowledge documents. Attach XML-description tags
on SCRM knowledge contents. Then the XML-based metadata for this
SCRM knowledge content is generation.
Meta-datum of knowledge contents are classified into basic description
information (DB ), annotation description information (DA ), relation description information (DR ) and transformed into the documents in RDF
and RDFS format. The annotated SCRM knowledge (KA ) in SSK model
is generated. Conceptual schemas are also created in this step. The conceptual schema is a RDFS file which is used to describe structure of the
concepts and properties in the annotated SCRM knowledge. This schema
is used in querying required information of concept by mapping onto the
benchmark ontology. Here, it is presumed that the benchmark ontology
can offer sufficient information (e. g. instances, constraints, and relationships) for these concepts (Theobald and Weikum, 2002).
11 Supply Chain Risk Management
217
Fig. 11.8 Annotation processes
Step 3:
(1)
(2)
(3)
Store annotated SCRM knowledge document with conceptual
schema into the metadata repository.
Store the mapping results (e. g., metadata) between the benchmark
ontology and the annotated SCRM document into the metadata
repository.
Register the link to the original SCRM document in the register.
The metadata repository is capable to validate the availability of metadata and the
consistence between the elements in the benchmark ontology and the metadata of
the original sources SCRM documents. The register validates the link consistence
between the annotated SCRM knowledge document and original SCRM knowledge
source.
In practice, industries should recognize the changes in the SCRM environment.
Particularly, each change in the SCRM conceptualization, for example, changes in
the strategy of the company, in the production planning, and in the inventory segmentation, that requires an update of ontology. The requirement of the ontology
218
C.-C. Huang, T.-L. Tseng
update is often discovered in extracting and mapping the metadata into the benchmark ontology. The annotation agent should update the benchmark ontology when
the requirement is fulfilled.
The SCRM annotation consists of three parts of description, namely basic description (DB ), annotation description (DA ), and relationship description (DR ).
• Basic description (DB ) illustrates the general statements of the SCRM knowledge
document and its source.
• Annotation description (DA ) is based on the 5W1H Zachman framework (What,
Where, Who, When, Why, and How) to represent annotated SCRM knowledge
in the SSK model.
• Relationship description (DR ) illustrates two types of relationship: (i) the relationship between the annotated SCRM knowledge document and other heterogeneous/unstructured SCRM documents and (ii) the relationship between the
benchmark ontology and heterogeneous ontology. For example, while SCRM
documents are clustered into several groups, the meta-data in each SCRM document in the same group records both its own document id and id(s) of other
documents in the same group.
Figure 11.9 illustrates the annotation format using XML tag instead of RDF and
RDFS. The notation B, in Fig. 11.9, represents the basic description of annotated
subject, used as fundamental information, corresponding to a subject that needs to be
annotated. For example, name, identifier, registry, version and language SCRM. B
is derived from the basic description function fB which is composed of the following: ID : solution-related subject document identification; and OD : SCRM ontology
identification. B corresponds to the relationship among (i) SCRM knowledge document identification, (ii) ontology information that the SCRM knowledge responds
to, and (iii) a basic description of annotated SCRM knowledge.
The notation R (relation description of annotated subject) in Fig. 11.9 describes
the relation information between annotated SCRM knowledge documents and their
related knowledge sources (e. g. other organization’s ontology). R is derived from
relation indication function fR which is composed of the following: IR : relationship
information; and t: the relation type. R is a group of source tags to describe (i) the
relationship between the annotated SCRM knowledge document, other heterogeneous SCRM documents, (ii) the relationship between the benchmarking ontology,
and heterogeneous ontology. Note that SCRM annotation description does not just
include one level 5W1H (What, Where, Who, When, Why, and How) structure.
Additional levels of 5W1H description tag are dynamically structured and used for
more detailed description.
Illustrative example: A company posts a problem to search for the solution in
SCRM: The defective rate of the Printed Circuit Board (PCB) installed in the electronic device is relatively high in this month. After thoroughly investigating the
case, it appears the issue is about faulty chip insertion during the assembly stage.
To reduce the defective PCB and the risk of supply chain shutting down and avoid
the delay of producing the final product, it is suggested that launching an advanced
Radio Frequency ID (RFID) system to improve the chip ID recognition. The solu-
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219
<Basic description>
<Name/> - The label assigned to the SCRM metadata subject
<Identifier/> - The unique identifier assigned to the SCRM metadata subject
<Version/> - The version of the SCRM metadata subject
B = ƒB (ID, OD)
<Language/> - The language in which the SCRM metadata subject is specified
<Ontology/> - A statement that clearly represents the concept and essential nature
of the SCRM metadata
<Obligation/> - Indicates if the SCRM metadata subject is required to always or
sometimes be present
<Comment/> - A remark concerning the application of the SCRM metadata subject
<…….>
</Basic description>
B
<Annotation description>
<what/>- contents of the subject to activity
<who/>- something involved in subject and activity
<where/>- Locations of the subject
<when/>- Time of the subject
<why/>- motivations of subjects and reasons of activity
<how/>- Solution approaches of the subject
</Annotation description>
<Relation description>
<Identifier> - The related unique identifier to the source
<Type>-The relation type
<Art_info>articulation info (if articulation process trigger)
<……..>
</Relation description>
A = ƒA (w1, w2, w3, w4, w5, h1)
R = ƒR (IR, ti)
Fig. 11.9 SCRM annotation format presented in XML tag
tion is responded in HTML format and the entire interaction process is presented
in a knowledge representation enhancement system (KRES). In general, this type of
support system is suitable to use in computer industry to augment inventory/logistics
control. The details of system operations are as follows:
First, the solution-related document is received and browsed with Internet Explorer (IE) (Fig. 11.10).
Through the annotation process, the SCRM document is transformed into semistructured format. In this step, the subject information is obtained from the source
document and classified into three description categories of description, (DB , DA ,
DR ), through the semi-automatic analysis and validation operated by human annotation expert or annotation agents. An annotation agent or annotation expert (i) parses
the source HTML document, and knowledge contents required to be annotated are
captured; (ii) analyzes the semantic hiding in each knowledge content, and searches
the related meta-datum in the metadata repository as well as the suitable elements
in the benchmark ontology; (iii) bases on the meta-datum and the elements to generate XML-based description tags to annotate the SCRM knowledge content; (iv) if
the search reaches nothing, the annotation agent and expert infers and identifies the
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C.-C. Huang, T.-L. Tseng
Fig. 11.10 The original HTML document before annotated browsed in IE
semantic hiding in the knowledge contents, then creates a new XML-based description tag to annotated the SCRM knowledge content; (v) classifies SCRM knowledge
content with description tag into the adequate categories, (DB , DA , DR ). The annotated SCRM knowledge of the original document in XML-based Semi-Structured
format is generated. For example, DB , basic description (Name, Identifier, Ontology, Obligation, and Comment) is captured and annotated on top rows of the source
document (Document_Id, Note, and primary question). Moreover, the message on
the row “Note” indicates that the knowledge belongs to the defective Printed Circuit
Board (PCB) and the risk of supply chain ontology. Therefore, the information “the
defective PCB” and “risk of supply chain” are attached to the tag “ontology,” which
also allows other knowledge user realize these SCRM knowledge document is related to the defective Printed Circuit Board (PCB) and the risk of supply chain ontology. The knowledge contents represented in text format in rows “Primary Question” and “Suggested resolution” of Fig. 11.10, are also captured and annotated into
5W1H (Zachman framework), where knowledge content in “Primary Question” corresponds to the “What”, “When”, “Where”, “Who”, and “Why” dimensions, respectively, and knowledge content in “Suggested resolution” corresponds to the “How”
dimension and annotated with “Sales Promotion” tag. The generated XML in SSK
model is presented as follows (Fig. 11.11).
Next, based on the XML-based SSK model, the annotated semi-structured knowledge (KA ) and the conceptual schemas are generated and stored in RDF and RDFS,
respectively. In this step, the annotation agent who is responsible to (i) transforms
the XML-based description tags into concepts and properties; and SCRM knowledge contents into instances and values (ii) constructs the conception schema in
RDFS for the structure of annotated SCRM knowledge (e. g. concepts hierarchy,
11 Supply Chain Risk Management
221
<Basic description>
<Name> SCRM_q1.html</Name>
<Identifier>\\IASERVER\SCRM\MA000001025</Identifier>
<Version> 1.0</Version>
<Language> English</Language>
<Ontology> the defective PCB ; Risk of supply chain </Ontology>
<Obligation>department vision</Obligation>
<Comment>The source was created in HTML</Comment>
……...
</Basic description>
<Annotation description>
<who><entry> RFID tag</entry><entry >The upper stream supplier s </entry></who>
<where><country>Taiwan</country></where>
<when><Yesr>2008</Year><Quarter>Q2</Quarter></when>
<what>< formula> To attach the RFID tag</formula></what>
<why><Reason> Faulty chip insertion during the assembly stage.</Reason></why>
<how>< formula> To attach the RFID tag in the chip between the supplier and the manufacturer </formula></how>
</Annotation description>
<Relation description>
<Identifier>\\IASERVER\SCRM\MA000000852</Identifier>
<Type>Cluster</Type>
……
</Relation description>
Fig. 11.11 (DB , DA , DR ) represented with XML
and concepts class and its corresponding properties); (iii) annotates these concepts
and their instances based on the RDF syntax. Last, a RDF and RDFS document
describes the annotated SCRM knowledge in SSK is completed. The exemplified
annotated SCRM knowledge content in RDF is presented in Fig. 11.12.
The conception schema of the exemplified annotated SCRM knowledge document is partially described in Fig. 11.13. Through the annotation process, the formal and consistent meta-datum from the annotated SCRM knowledge document
in SSK model is generated. By viewing the annotated SCRM knowledge in SSK
model, knowledgeable worker can easily realize the purpose, contents of the heterogeneous and unstructured SCRM knowledge document. Furthermore, the annotations are based on RDF standard; therefore, metadata is machine understandable on
the Semantic Web. In this annotated SCRM knowledge document, every resource in
RDF and RDFS is annotated an URI (Uniform Resource Identifiers), which makes
the annotated SCRM knowledge sources reusable and machine processable on the
web (Decker, 2002).
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C.-C. Huang, T.-L. Tseng
<?xml version='1.0' encoding='ISO-8859-1'?>
<!DOCTYPE rdf:RDF [
<!ENTITY rdf 'http://www.w3.org/1999/02/22-rdf-syntax-ns#'>
<!ENTITY AnnotatedSSK_mo 'http://www.ncnu.edu.tw/im/iskmlab/AnnotatedSSK_model#'>
<!ENTITY rdfs 'http://www.w3.org/TR/1999/PR-rdf-schema-19990303#'>
]>
<rdf:RDF xmlns:rdf="&rdf;" xmlns:AnnotatedSSK_mo="&AnnotatedSSK_mo;" xmlns:rdfs="&rdfs;">
<AnnotatedSSK_mo:quarter rdf:about="&AnnotatedSSK_mo;AnnotatedSSK_00079"
AnnotatedSSK_mo:Quarter="Q2"
AnnotatedSSK_mo:Year="2008"/>
<AnnotatedSSK_mo:Country rdf:about="&AnnotatedSSK_mo;AnnotatedSSK_00080"
AnnotatedSSK_mo:Countryname="Taiwan"/>
<AnnotatedSSK_mo:What rdf:about="&AnnotatedSSK_mo;AnnotatedSSK_00068"
AnnotatedSSK_mo:formual=" To attach the RFID tag "/>
<AnnotatedSSK_mo:Who rdf:about="&AnnotatedSSK_mo;AnnotatedSSK_00071"
AnnotatedSSK_mo:entry="RFID tag "/>
<AnnotatedSSK_mo:Who rdf:about="&AnnotatedSSK_mo;AnnotatedSSK_00072" “5W1H” Annotation
AnnotatedSSK_mo:entry=" The supplier and the manufacturer "/>
of Knowledge Subject
<rdf:Description rdf:about="&AnnotatedSSK_mo;AnnotatedSSK_00046"
Event
AnnotatedSSK_mo:ADid="AD1">
<AnnotatedSSK_mo:when rdf:resource="&AnnotatedSSK_mo;AnnotatedSSK_00079"/>
<AnnotatedSSK_mo:where rdf:resource="&AnnotatedSSK_mo;AnnotatedSSK_00080"/>
<rdf:type rdf:resource="&AnnotatedSSK_mo;Annotation description"/>
<AnnotatedSSK_mo:what rdf:resource="&AnnotatedSSK_mo;AnnotatedSSK_00068"/>
<AnnotatedSSK_mo:who rdf:resource="&AnnotatedSSK_mo;AnnotatedSSK_00072"/>
<AnnotatedSSK_mo:why rdf:resource="&AnnotatedSSK_mo;AnnotatedSSK_00057"/>
<AnnotatedSSK_mo:how rdf:resource="&AnnotatedSSK_mo;AnnotatedSSK_00058"/>
</rdf:Description>
<AnnotatedSSK_mo:Why rdf:about="&AnnotatedSSK_mo;AnnotatedSSK_00057"
AnnotatedSSK_mo: Reason =" Faulty chip insertion during the assembly stage "/>
……..
</AnnotatedSSK_mo:How>
<rdf:Description rdf:about="&AnnotatedSSK_mo;AnnotatedSSK_00060"
“Basic Annotation” of
AnnotatedSSK_mo:Comment="SCRM_q2.html"
Knowledge Subject Event,
AnnotatedSSK_mo:Identifier="1.0"
where basic identifier and
AnnotatedSSK_mo:Language=" English "
related ontology
AnnotatedSSK_mo:Name="The source was created in HTML"
AnnotatedSSK_mo:Obligation="\\IASERVER\Marketing\MA000001025"
AnnotatedSSK_mo:Version="department vision">
<rdf:type rdf:resource="&AnnotatedSSK_mo;Basic description"/>
<AnnotatedSSK_mo:Ontology> the defective PCB </AnnotatedSSK_mo:Ontology>
<AnnotatedSSK_mo:Ontology>Risk of supply chain</AnnotatedSSK_mo:Ontology>
</rdf:Description>
<rdf:Description rdf:about="&AnnotatedSSK_mo;AnnotatedSSK_00061"
……..
</rdf:RDF>
Fig. 11.12 Exemplified annotated SCRM knowledge document stored in RDF format
11 Supply Chain Risk Management
223
<rdf:Property rdf:about="&AnnotatedSSK_mo;ADid" a:maxCardinality="1" >
<rdfs:domain rdf:resource="&AnnotatedSSK_mo;Annotation description"/>
<rdfs:range rdf:resource="&rdfs;Literal"/>
</rdf:Property>
<rdfs:Class rdf:about="&AnnotatedSSK_mo;Annotation description">
The concepts,
<rdfs:subClassOf rdf:resource="&rdfs;Resource"/>
properties and
</rdfs:Class>
their hierarchy re<rdfs:Class rdf:about="&AnnotatedSSK_mo;Basic description">
lationships is iden<rdfs:subClassOf rdf:resource="&rdfs;Resource"/>
tified in RDFS of
</rdfs:Class>
the annotated doc<rdf:Property rdf:about="&AnnotatedSSK_mo;Comment"
ument
a:maxCardinality="1">
<rdfs:domain rdf:resource="&AnnotatedSSK_mo;Basic description"/>
<rdfs:range rdf:resource="&rdfs;Literal"/>
</rdf:Property>
<rdfs:Class rdf:about="&AnnotatedSSK_mo;Country">
<rdfs:subClassOf rdf:resource="&AnnotatedSSK_mo;Where"/>
</rdfs:Class>
<rdf:Property
rdf:about="&AnnotatedSSK_mo;Countryname"
:maxCardinality="1">
<rdfs:domain rdf:resource="&AnnotatedSSK_mo;Country"/>
<rdfs:range rdf:resource="&rdfs;Literal"/>
</rdf:Property>
……….
Fig. 11.13 Partial conceptual schema of the exemplified annotated SCRM knowledge document
11.4 Interaction of Annotated SCRM Knowledge Documents
with the Benchmark Ontology
The knowledge shared in a SC has been presented in a flexible and well-format
knowledge representation structure. In general, industries generate different documents in SSK model for different purposes. In order to avoid the redundancy of the
use of meta-datum, an approach to coordinate and manage meta-datum in the metadata repository and benchmark ontology is required. After organizations receiving
these annotated SCRM documents, the important step, extracting and mapping the
meta-datum of annotated SCRM knowledge document into benchmark ontology is
processed.
11.4.1 Extracting and Mapping
In addition to annotating SCRM knowledge documents into SSK model, the annotation agent further performs the role of extractor (Schenk, 1999) that retrieves the
string-values of all elements in the annotated semi-structured SCRM knowledge and
performs pertinent functions on them in the following methods: (i) decomposing the
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C.-C. Huang, T.-L. Tseng
meta-datum (annotated knowledge elements) of annotated SCRM documents into
basic elements; (ii) extracting these basic elements and their corresponding URI.
Finally, the meta-datum are extracted and used to map them to the corresponding
elements of the benchmark ontology.
Figure 11.14 presents the architecture of extraction. The basis for the development of the application program is the Document Object Model (DOM) application interface (API) (URL DOM), a recommendation of the W3C for accessing
and modifying HTML and XML-based documents. A streaming API for accessing
the SCRM documents is not suitable, since the annotation agent at extracting step
may contain forward and backward reference to find elements in SCRM documents.
These references are required to be resolved in real time such that the complete
SCRM document in SSK model can be accessed in time. (Huck et al., 1999)
Mapping is a process that bridges, transforms, and unifies knowledge elements
of semi-structured knowledge into the target equivalence or relative elements of the
benchmark ontology.
Mapping is an operator (Frasincar et al., 2002) defined as follows:
[.S.e1 /; S.e2 /; : : : ; S.en // ;
where [ corresponding to a collection, S to a set, and e1 , : : : , en to elements.
The elements are concepts, classes, or properties as well as instances of these
concepts classes in both SCRM knowledge document and the benchmark ontology.
Fig. 11.14 Architecture of the Extraction
11 Supply Chain Risk Management
225
The mapping operator combines (set union) elements in the SCRM documents in
SSK model and the benchmark ontology to obtain the final mapping result. In the
annotation process, by storing the mapping results and together with the annotated
SCRM document into the metadata repository, a degree of local autonomy of annotated SCRM knowledge document to coexist with content consistency (Fensel et al.,
2000) of partial interoperability of the benchmark ontology could be achieved.
Furthermore, by using extracting and mapping, the knowledge elements could
not only be retrieved from annotated SCRM knowledge documents and mapped to
the benchmark ontology, but also be composed “from” the benchmark ontology vice
versa. Figure 11.16 illustrates the two-way interaction between the benchmark ontology and SSK. That is, organizations can generate SCRM knowledge documents
in SSK model by constructing from the benchmark ontology concepts, properties
and its values of instances. Note that the benchmark ontology of supply chain illustrated in Fig. 11.15 is referenced to Chen (2003).
7RS/HYHO
2QWRORJ\
[Geographic location]
Where
(Supply chain)
[Corporation]
When
Semi-Structured
Knowledge
{Time}
Why
April
May
June
3th quarter
July
August
September
4th quarter
(Member of Supply chain)
[Product]
[Business subject]
To order
January
February
March
2nd quarter
Year
[Employee]
Who
1st quarter
Domain Ontology
Project
6FKHGXOLQJ
Extracting & Mapping
Composing
October
November
December
UGI5')[POQVUGI UGI
[POQVSURGXFW SURGXFW
[POQVUGIV UGIV!
SURGXFW3URGXFW
UGIDERXW SURGXFW.%BB
UGIVODEHO 6!
SURGXFW3URGXFWB,'
UGIUHVRXUFH VXEMHFWVXEMHFWWHVWB
!ಹ
SURIXFW3URGXFW!
Enterprise
Ontology
(Business
Data
Entities
ontology)
Organization
To stock
To promotion
To analyze
How
[Method]
)RUHFDVW
$QDO\WLFDO
SURFHVVPRGHO
Business
Process
Application Ontology
Product
Design
Information
Resource
U(SSK (e1), SCON (e1' ))
UGI5')[POQVUGI UGI
[POQV2UGHU 2UGHU
[POQVUGIV UGIV!
RUGHU2UGHUUGIDERXW 2UGHU
.%BB
UGIVODEHO 6!
RUGHU2UGHUB,'
UGIUHVRXUFH VXEMHFWVXEMHFWWHVWB
!ಹ
RUGHU2UGHU!
3ODQQLQJ
0HWKRGV
Material
Flow
Process
What
Task and Methods
Ontology
Operation
Product
Order
Supply
Chain
Unit
U(SSK (e2), SCON (e2'))
Shipping
Inventory
Service
Quality
Fig. 11.15 The interaction between SSK and the benchmark ontology
Facility
Resource
Machine
226
C.-C. Huang, T.-L. Tseng
11.4.2 Interaction Between SSK and the Benchmark Ontology
The main purpose of the interaction is to extract concepts, properties, instances from
the SCRM documents in SSK model, compare them with the elements of benchmark
ontology, and induce the extracted elements in desired taxonomies to support the
elements of benchmark ontology. Two types of interaction are:
(1)
(2)
Structural interaction: extracting concepts and properties of semi-structured
SCRM knowledge documents in order to map them into the benchmark ontology.
Instance-based interaction: extracting instances of semi-structured SCRM
knowledge documents in order to for map them into benchmark ontology.
Structural interaction: Extracting concepts and properties from the conceptual
schema of annotated SCRM knowledge document, and map these concepts and
properties into the corresponding concepts and properties in the benchmark ontology.
In this semi-structured knowledge, concepts have its hierarchical relationship
corresponding to the knowledge application domain. For example, grey area in
Fig. 11.12, the hierarchical structure of concepts represented with the “where” dimension is corresponding to the “location” concepts in the benchmark ontology,
where the manufacturing process holds. Furthermore, the contents of location are
represented by “country” and “country name” respectively. In Fig. 11.12, “Taiwan”
is used as a country name.
The annotation agent analyzes and extracts (i) concepts and (ii) properties from
RDFS of annotated SCRM knowledge documents (conceptual schema). Then the
agent searches and compares them with all concepts and properties in the benchmark
ontology. If the concept (or property) is equivalent or related to extracted concepts
(or properties), the mapping between the two concepts (or properties) is bridged
from the conceptual RDFS file to benchmark ontology.
Following the mapping example of Fig. 11.12, the sub-concept and properties of
the concept corresponding in the “where” dimension are presented in the left side
paragraph of Fig. 11.16. In the paragraph, concept “where” has one sub-concept
“Supply Chain Risk Management”. Within the “Supply Chain Risk Management”
concept, there is one property “Suppliername” describes the “Supply Chain Risk
Management” concept. The annotation agent analyzes these concepts and properties
in a three-level hierarchy relationship, searches and compares related concepts in the
benchmark ontology to verify the mapping. Finally, the agent finds a concept “the
defective PCB Planning” which is subclass of “Supply Chain Risk Management” is
matched to concepts of SSK document. Then the annotation agent maps the concept
“Supply Chain Risk Management” to the concept “the defective PCB Control” in
the benchmark ontology (on the right side of Fig. 11.16).
The map on the concepts is described as follows:
[ (AnnotatedSSK(where. Supply Chain Risk Management, COntology.Enterprise
(the defective PCB Control)) . . . (Mapping 1) ,
11 Supply Chain Risk Management
Concepts of SSK Document in RDFS
<rdfs:Class
rdf:about="&AnnotatedSSK_mo;Where">
<rdfs:subClassOf
rdf:resource="&rdfs;Resource"/>
Mapping 1
</rdfs:Class>
<rdfs:Class
rdf:about="&AnnotatedSSK_mo;Country">
<rdfs:subClassOf
rdf:resource="&AnnotatedSSK_mo;Where"/>
</rdfs:Class>
<rdf:Property
rdf:about="&AnnotatedSSK_mo;Countryname">
<rdfs:domain
rdf:resource="&AnnotatedSSK_mo;Country"/>
<rdfs:range rdf:resource="&rdfs;Literal"/>
</rdf:Property>
Super class of
Property
where
Factory
Country
Region
Countryname
Regionname
Region
of
Destination
Mapping 2
Regioncode
Region
of
Origin
227
Corresponds Concepts of benchmark Ontology in RDFS
…..
<Enterprise:MODIFY-CLASS
rdf:about="&Enterprise;Factory">
<rdfs:comment>The collection of business
properties that reflects multiple factories of choice or a
specified region.</rdfs:comment>
<rdfs:subClassOf
rdf:resource="&Enterprise;Place"/>
</Enterprise:MODIFY-CLASS>
Refererence
…….
<Enterprise:MODIFY-CLASS
rdf:about="&Enterprise;Region">
<rdfs:subClassOf
rdf:resource="&Enterprise;Factory"/>
</Enterprise:MODIFY-CLASS>
…….
<rdf:Property rdf:about="&Enterprise;RegionName"
a:maxCardinality="1">
<rdfs:domain
rdf:resource="&Enterprise;Region"/>
<rdfs:range rdf:resource="&rdfs;Literal"/>
</rdf:Property>
Reference
<Enterprise:ADD-SYNONYM-SLOT
rdf:about="&Enterprise;RegionOfDestination"
a:maxCardinality="1"
rdfs:comment="Region where product be
done in the next operation." >
<rdfs:range rdf:resource="&rdfs;Literal"/>
</Enterprise:ADD-SYNONYM-SLOT>
<Enterprise:ADD-SYNONYM-SLOT
rdf:about="&Enterprise;RegionOfOrigin"
a:maxCardinality="1"
rdfs:comment="Region where product came
from." >
<rdfs:range rdf:resource="&rdfs;Literal"/>
</Enterprise:ADD-SYNONYM-SLOT>
<rdf:Property rdf:about="&Enterprise;RegionCode"
a:maxCardinality="1">
<rdfs:domain
rdf:resource="&Enterprise;Region"/>
<rdfs:range rdf:resource="&rdfs;Literal"/>
</rdf:Property>
Fig. 11.16 The mapping between the benchmark ontology and the conceptual schema
Mapping 1 is indicated with the two-way solid arrowhead line in Fig. 11.16.
[ (AnnotatedSSK(what. Supply Chain Risk Management, (Suppliername)),
SCOntology.Enterprise(Tool : : : the defective PCB Control)):(ToolName))) : : :
(Mapping 2) .
Mapping 2 indicates that the property “Suppliername” in the annotated document
is mapped into the property “ToolName” in benchmark ontology (a double heads
arrow with solid line in Fig. 11.16). Replace country name with type of supply
chain risk management.
These mapping relationships are stored together with the annotated SSK document in the metadata repository. By utilizing the mapping, other application agents
and knowledgeable workers, besides the annotation agent, can easily recognize the
228
C.-C. Huang, T.-L. Tseng
meaning of concepts between the annotated SCRM documents and the benchmark
ontology. The agents and workers can track concepts in the SCRM documents,
through the mapping backward to corresponding concepts in benchmark ontology
and obtain more information about their parents, brothers, or children. For example, the concept “SCRM” in Fig. 11.16 has been mapped. Therefore, the properties
of the inventory control such as “ToolName”(the name of operation activities; i. e.,
replenishment etc), “the defective PCB control code”(the code of the operation activities), “PSBOfOrign”, and “PCBOfDestination” can be extended to retrieve more
SCRM information, which is presented in dot line block.
Instance-based interactions: Extract instances of annotated SCRM documents
in SSK model then generate the corresponding instances in the benchmark ontology.
In the structural interaction, concepts and properties are extracted from the conceptual schema of annotated SCRM knowledge document, and these concepts and
properties are mapped into the corresponding concepts and properties in the benchmark ontology. In the same way, instances of these concepts and properties are
also extracted and mapped in the instance-based interaction. The main purpose of
instance-based interaction allows the knowledgeable workers to obtain more instances by mapping the extracted instance onto the corresponding instance (e. g.,
belong to property A) in benchmark ontology, and the other instances (belong to
property A) are extracted and presented to the knowledgeable workers. All of instances from a document in the SSK map themselves into the ones in the benchmark
ontology and obtains more instances for knowledgeable workers. The mapping of
instances just likes “recording” the instances into benchmark ontology.
The example in Fig. 11.17 illustrates the instance mapping between the annotated SCRM knowledge document in Fig. 11.12 (left-side in Fig. 11.17) and the
benchmark ontology (right-side in Fig. 11.17). In the left-side of the figure, the
concepts in the “when” dimension is assigned to the instance which has the URI:
“mo;AnnotatedSSK_00079.” That is, the instance has the URI: http://www.ncnu.
edu.tw/im/iskmlab/AnnotatedSSK_model#AnnotatedSSK_00079, which indicates
the concept “quarter” has one instance that has property Quarter="Q2" and Year=
"2008". The concept class of “Date Period” in the right-side of Fig. 11.16 generates
the corresponding instance which has the URI: “&Enterprise;SCDomainOntology_
00567”, where the property Year="2008" , beginDate="2008/04", endDate="2008/
06", quarter="Q2".
The instance mapping corresponding to the solid two-way arrowhead line in
Fig. 11.17 is formatted as follows:
[ instance(AnnotatedSSK(when(quater):AnnotatedSSK_00079),
SContology.Enterprise(Time_info.(DatePeriod):
SCDomainOntology_000567)) : : : (Mapping 3) .
Mapping 3 shows that the instance “annotatedSSK_00079” in the annotated
SCRM document corresponds to the instance “Enterprise;SCDomainOntology_
00567” in the benchmark ontology.
The same as above, the other annotating instances of the concept in the annotation
document are mapped to their corresponding instances in the benchmark ontology.
11 Supply Chain Risk Management
229
<rdf:Description
rdf:about="&AnnotatedSSK_mo;Test_0004
6"
AnnottedSSK_mo:ADid="AD1">
<AnnotatedSSK_mo:when
rdf:resource="&AnnotatedSSK_mo;
AnnotatedSSK_00079"/>
<AnnotatedSSK_mo:where
rdf:resource="&AnnotatedSSK_mo
;AnnotatedSSK_00080"/>
<rdf:type
rdf:resource="&AnnotatedSSK_mo;Annotati
on description"/>
<AnnotatedSSK_mo:what
rdf:resource="&AnnotatedSSK_mo;Test2_0
0068"/>
<….. >
Mapping 3
<…. >
<…. >
</rdf:Description>
<AnnotatedSSK_mo:quarter
rdf:about="&AnnotatedSSK_mo;Annotated
SSK_00079"
AnnotatedSSK_mo:Quarter="Q2"
AnnotatedSSK_mo:Year="2003">
<AnnotatedSSK_mo:Country
rdf:about="&AnnotatedSSK_mo;Annotat
edSSK_00080"
AnnottedSSK mo:Countryname=
"Taiwan">
<AnnotatedSSK_mo:What
rdf:about="&AnnotatedSSK_mo;Test2_000
68"
AnnottedSSK mo:SalesPromotion
="Topromotion the A1C Digital Camera">
<Enterprise:eventDetail
rdf:about="&Enterprise;SCDomainOntology_0055
5"
Enterprise:eventCodeValue=
"MA000001025"
Enterprise:eventCodeValueDescription=
"Marketing ontology serial number"
Enterprise:eventRepairCodeValue=
"@IASERVER-Manufacturing">
</Enterprise:eventDetail>
<Enterprise:DatePeriod
rdf:about="&Enterprise;SCDomainOntology_0056
7"
Enterprise:Year="2003"
Enterprise:beginDate="2003/04"
Enterprise:endDate="2003/06"
Enterprise:quarter="Q2">
<Enterprise:Region
rdf:about="&Enterprise;SCDomainOntology_0
0557"
Enterprise:SYNONYM="Formosa"
Enterprise:RegionName="Milling"
Enterprise:RegionCode="#000128">
<Enterprise:Status
rdf:about="&Enterprise;SCDomainOntology_0
0564"
Enterprise:StatusProgram="To mill the product"
Enterprise:StatusProgramIdentifier
="#PO000564">
<Enterprise:Status
rdf:about="&Enterprise;SCDomainOntology_0
0565"
Enterprise:StatusProgram="Quality of milling
is level 2"
Enterprise:StatusProgramIdentifier
="#PO000565">
<Enterprise:StatusProgram>To mill the product
with the quality of level 2
</Enterprise:StatusProgram>
</Enterprise:Status>
Mapping 4
Other Instances value of property
which is generated and mapped from
annotated SSK document.
Fig. 11.17 The instance mapping between the example (Figure 12) and benchmark ontology
For example,
[ instance(AnnotatedSSK(where SCRM(countryname):AnnotatedSSK)_00080,
SCOntology.Enterprise(Place.Factory.Region.
(RegionName,RegionCode):SCDomainOntology_00557)
: : : (Mapping 4) .
The Mapping 4 belongs to instances mapping from the concepts in the “where”
dimensions of SSK document onto the instance of “Region” concept in the benchmark ontology. The property value of the “RegionName” of the mapped instances
230
C.-C. Huang, T.-L. Tseng
is “replenishing”, which have additional information about the mapped instances,
such as SYNONYM = “Re-stock” OperationName= “replenishing”, and OperationCode= “#000128” in the benchmark ontology.
Other dimensions, e. g., “what” are also mapped and is illustrated in the block
with a dash line and mapped by a double heads arrow with dash line in Fig. 11.16,
where it obviously indicates that the instance of property “StatusProgram” D "To
replenish the product."
The annotated documents in SSK model and the related conceptual schema (RDF
Schema) are stored to the metadata repository and the links (index and location) of
original source documents are registered in the register. The elements of annotated
SCRM knowledge document in SSK model is extracted and mapped into the corresponding elements in the benchmark ontology. The information of heterogeneous
SCRM knowledge document is captured and reused.
11.5 Conclusions
The SSK model was proposed to (i) make representation of SCRM knowledge consistent and flexible (ii) share industry SCRM knowledge with not only in meaningful, but also an explicit sharable manner over the web in organization. The SCRM
knowledge documents in the SSK model, which is based on Zachman Framework (Inmon and Zachman, 1997), and the technique of knowledge representationResource Description Framework (RDF), were very effective to share on the semantic web.
The annotation process resolves heterogeneity of SCRM knowledge document
from the various hetero-purpose information systems. The process allows organizations efficiently access and retrieve the hetero-format or unstructured SCRM knowledge documents. Moreover, it also supports the original HTML documents to be
converted to the XML documents. Finally, the exemplified annotated MP knowledge documents are stored in RDF format
For different purposes, industries may generate different SCRM documents in
SSK model. In order to avoid the redundancy of meta-datum, an approach was proposed to coordinate and manage meta-datum and benchmark ontology, which is
called interaction of annotated MP knowledge documents with the benchmark ontology. Through the proposed approach, the organization is able to generate unified
documents, which significantly improve degree of knowledge share.
The future research should emphasize (i) semantic logic inference engine for
peer application agents, and (ii) the management of mapping results of annotated
SCRM knowledge document. When increase amount of annotated SSK document
are stored in the metadata repository the mapping results are also increased. How
to manage this mapping, extract necessary information, and to aid the accuracy of
annotation process deserves further research.
11 Supply Chain Risk Management
231
Acknowledgements This work was partially supported by funding from the Nation Science
Council of the Republic of China. (NSC 96-2416-H-260-005-MY2; NSC-97-3114-P-260-001-Y).
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