36106 Managerial Decision Modeling Decision Analysis in Excel Kipp Martin University of Chicago Booth School of Business January 31, 2015 1 Reading and Excel Files Reading: I Powell and Baker: Sections 13.1, 13.2, and 13.3 I Course Pack: “Decision Analysis”’ by George Wu Files used in this lecture: I wertzTree.xlsx I wertzTree key.xlsx I wertzUtility.xlsx I sarahChangData.xlsx I sarahChangKey.xlsx I sarahChangOptimal.xlsx I sarahChangSensitivity.xlsx 2 Lecture Outline Software Install Motivation Example 1: Wertz Game and Toy The Cost of Uncertainty Decision Theory Example 2: Sarah Chang Sensitivity Analysis Goal Seek Utility Learning Objectives 1. Begin to incorporate uncertainty into an Excel model 2. Learn to model sequential decision problems 3. Learn how to use Precision Tree in Excel Decision Outcome Decision 4 Outcome Software Install – DecisionTools Suite CRITICAL AND IMPORTANT: 1. Close all programs except Excel. 2. Minimize number of open files in Excel. Remember my Corollary to Murphy’s law – When it comes to computers, Murphy was an optimist. Another Corollary: Excel Add-ins increase the probability that problems arise. Software Install – DecisionTools Suite Please install http://www.palisade.com/academic/students.asp Please do the default install. We will use: I Precision Tree I @Risk I Risk Optimizer 6 Software Install – DecisionTools Suite If you do the default install, you should see desktop icons like: 7 Software Install – DecisionTools Suite Make sure Excel is closed. Open Excel by “clicking” on the PrecisionTree 6 desk icon. This should open Excel for you. Now click on the @Risk icon. Now add these to your Ribbon. Software Install – DecisionTools Suite Under File select Options 9 Software Install – DecisionTools Suite Select Add-Ins and then under Manage: Excel Add-ins, select Go.. 10 Software Install – DecisionTools Suite If you have opened Excel by clicking on both @Risk 6 and PrecisionTree 6 you should see 11 Software Install – DecisionTools Suite From now on, you can open Excel and do not need to use the desktop icons. You should see Tab items for both PrecisionTree and @Risk. 12 Software Install – DecisionTools Suite Your software download comes with lots of documentation and examples. 13 Motivation See http: //www.palisade.com/cases/bucknell.asp?caseNav=byProduct I Disaster Planning I Geothermal Power Plant Equipment Procurement I Portfolio Management I Exchange Rate Analysis I Endangered Species Protection I Pollution Cleanup Motivation Key Concept: most people do not understand I the concept of an optimal solution I variables I parameters I constraints I an objective function Thinking about your problem in the context of these ideas may be very beneficial. Motivation Key Concept: the biggest the benefit of an Excel model is that it forces a user to: I think about decision alternatives I think about potential outcomes that result from making a decision I quantify an outcome (you need numbers and formulas in Excel) I quantify uncertainty (you need numbers and formulas in Excel) Motivation We are going to study Decision Analysis. Differences from Solver models: I There are a limited number of possible decisions to make (as opposed to potentially infinite) I The outcomes of a decision are uncertain I Decisions are made sequentially over time Decision Outcome Decision 17 Outcome Motivation We are going to use PrecisionTree to model these kinds of problems. I We are going to look at the expected value of our decisions I This requires a structured approach to modeling which has great benefits I Warning: no guarantee that this approach does not lead to a bad outcome 18 Motivation It is critical to realize that when making decision under uncertainty: I a good decision may lead to a bad result I a poor decision may lead to a good result See the discussion by former Booth student Zeger Degraeve at http://www.youtube.com/watch?v=1qor-igeE0k 19 Example 1: Wertz Game and Toy Wertz Game and Toy Data (Section 13.2 of Powell and Baker) 20 Example 1: Wertz Game and Toy We look at four criteria: I maximax payoff I maximin payoff I minimax regret I maximize expected payoff 21 Example 1: Wertz Game and Toy Decision: full line 22 Example 1: Wertz Game and Toy Decision: single line 23 Example 1: Wertz Game and Toy Decision: full line 24 Example 1: Wertz Game and Toy Maximize expected payoff: Calculate the expected payoff of decision di : Pj = probability of state of nature j Vij = value of outcome given decision i and state of nature j EV (di ) = N X Pj Vij j=1 Make the decision with the maximum expected payoff. Assumption: PN j=1 Pj = 1.0 Example 1: Wertz Game and Toy Decision: Two Versions 26 The Cost of Uncertainty The basic problem: Decision Outcome Decision Outcome Must make a decision before the outcome is known. It would be nice to know the outcome before making the decision. For example, if Wertz managers knew the market response would be good, they would bring out the full line. How much should Wertz be willing to pay to know the outcome first? 27 The Cost of Uncertainty Expected Value of Perfect Information (EVPI) – the increase in the expected payoff if one knew with certainty which state of nature would occur. The expected payoff with perfect information must be at least as great as the expected payoff of the optimal solution. For example, for Wertz the EVPI must be at least 53 which is the optimal expected payoff. The Cost of Uncertainty Expected Value of Perfect Information – make the calculation as follows: Step 1: For each possible state of nature, determine the optimal decision and corresponding outcome Step 2: Weight each outcome by the probability of the state of nature associated with that outcome and calculate the expected value Step 3: Subtract the EV of the optimal decision from the number calculated in Step 2. The Cost of Uncertainty Expected Value of Perfect Information – Wertz: Step 1: For each state of nature determine the outcome for the optimal decision. I Good: best outcome is 300 (full line is the optimal decision) I Fair: best outcome is 60 (single version is the optimal decision) I Poor: best outcome is -10 (single version is the optimal decision) Step 2: Weight each optimal outcome by the probability assigned to that state of nature .2 ∗ 300 + .5 ∗ 60 + .3(−10) = 60 + 30 − 3 = 87 Step 3: Subtract the EV of the optimal decision from the number calculated in Step 2. EVPI = 87 − 53 = 34 30 Example 1 (Follow UP): Wertz Game and Toy 31 Example : Wertz Game and Toy Wertz is a very simple model. There is only one decision made at time 0 It is trivial to find the optimal decision in an Excel table. Just calculate the expected payoff for each decision. However, real life is more complicated, and often involves a sequence of decisions. More sophisticated tools are required. Decision Theory See Decision Analysis by George Wu. Four Steps in Decision Making Process Step 1: Structuring a Decision Problem (alternatives, uncertainties, and objectives) Step 2: Assessment and Information Gathering Step 3: Evaluation of Decision Problem (PrecisionTree used in this step) Step 4: Sensitivity Analysis (PrecisionTree used in this step) Decision Theory Step 1: Structuring a Decision Problem Instead of the Solver (A (adjustable cells), B (best cell), and C (constraint cells) ) we have: I What are the alternatives? I What are the critical uncertainties? I What are the objectives? Decision Theory Step 2: Assessment and Information Gathering: Collect the relevant information, I assess the values of the outcomes given decisions that were made (e.g. in Wertz the outcome of a good market response, given the decision to produce the full line is 300) I determine the likelihood of uncertain events (e.g. in Wertz the probability of a fair market response is 0.5) Discussion Point: What is meant by the probability of an event? Decision Theory What do we mean by probability? See pages 8 and 9 of the Decision Analysis case. Probabilities measure the likelihood of uncertain events. In most cases a probability is a judgement. This does not imply it is arbitrary. Sarah Chang says the probability of successfully developing the microprocessor in six months is .40. Sarah Chang is saying that she believes this event is just as likely as drawing a red ball from an urn where 40% of the balls in the urn are red. Decision Theory Step 4: Sensitivity Analysis: Determine how sensitive the optimal solution is to the probabilities and the outcome values. We use the sensitivity analysis features of Precision Tree. For example, how much can probability estimates change before we change our decisions? 37 Example 1: Wertz Game and Toy We are going to build in Excel something that looks like this: Good 100 Fair 60 Poor -10 Single Version Good Two Versions 200 Fair 50 Poor -40 Full Version 300 Good Fair 40 Poor -100 38 Example 1: Wertz Game and Toy Icon coding scheme: I a green square – a point in time where we make a decision I a red circle – a chance node, an uncertain outcome occurs I a blue triangle – indicates the end of branch Time proceeds left to right. Probabilities and monetary values are placed next to nodes Expected values are computed by the folding-back process The optimal path is indicated by TRUE nodes. Example 1: Wertz Game and Toy 40 Example 2: Sarah Chang Step 1: Structuring a Decision Problem Step 2: Assessment and Information Gathering Note the breakdown between Decisions and Outcomes. 41 Example 2: Sarah Chang I Open the file sarahChangData.xlsx Workbook. I see the spreadsheet data for the result of the addressing and information gathering step. I open the spreadsheet model – it is currently empty. I select an arbitrary cell, say C35 I Go to the PrecisionTree tab and select Decision Tree 42 Example 2: Sarah Chang Click OK Name the model Sarah Chang Decision Model 43 Example 2: Sarah Chang Click on the end blue triangle node. Select a Decision node and name it Decision to Invest. 44 Example 2: Sarah Chang Next click on the Branches tab and do the following: I Name the branches Continue and Abandon I Give the Continue branch a value of =data!E5 I Give the Abandon branch a value of =data!E6 45 Example 2: Sarah Chang At this point, your decision tree should look like: 46 Example 2: Sarah Chang Click on the end blue triangle node for the Continue branch. Click on Chance button and give the node the name Outcome of R & D. 47 Example 2: Sarah Chang I Name the branches Succeed and Fail I Give the Succeed branch a probability of =data!F7 I Give the Fail branch a probability of =(1-data!F7) 48 Example 2: Sarah Chang Your tree should now look like this: 49 Example 2: Sarah Chang Now click on the blue triangle at the end of the Succeed outcome. Create a Decision node named Decision To Propose 50 Example 2: Sarah Chang Click on the Branches tab: I I I Name the branches Make a Proposal and No Proposal Give the Make a Proposal branch a value of -50000 or data!E9 Give the No Proposal branch a value of 0 or data!E10 51 Example 2: Sarah Chang Your tree should look like this 52 Example 2: Sarah Chang Now click on the blue triangle at the end of the Make a Proposal outcome. Create a Chance node named Bid Outcome 53 Example 2: Sarah Chang Click on Branches tab: I Name the branches Win and Lose I Give the Win branch probability of 90% or data!F11 I Give the Lose branch a probability of 10% or (1 - data!F11) I Give the Win branch a value of 850000 or data!E11 I Give the Lose branch a value of 0 or data!E13 54 Example 2: Sarah Chang Your Decision Tree should look like this: 55 Example 2: Sarah Chang Wow that was a lot of work! Sarah may wish to submit a Proposal even if the R&D failed. Consider the blue triangle termination node at the end of the fail branch of the Outcome of R&D chance node. The structure of the decision and outcome nodes at the end of the fail branch are identical to those at the end of the succeed node. However, the probabilities and values differ. Do a copy and paste! 56 Example 2: Sarah Chang Right click on the Decision to Propose node and select Copy Subtree. Right click on the blue triangle termination node at the end of the fail branch of the Outcome of R&D chance node. Select Paste Subtree Adjust values accordingly: the Win probability is changed from 90% to 5% and the Lose probability is changed from 10% to 95%. 57 Example 2: Sarah Chang Your Decision Tree should look like this. See sarahChangKey.xlsx. 58 Example 2: Sarah Chang The optimal solution: Trace the green TRUE values through the tree. The optimal strategy for Sarah is to I First, proceed with the project and continue R&D on the microprocessor I If the outcome of R&D is success then make the proposal to the Olympic committee I If the outcome of R&D is failure then do not make the proposal to the Olympic committee PrecisionTree will generate the above information for you. PrecisionTree will fold-back the tree for you. Example 2: Sarah Chang Click on Decision Analyis button to generate a Policy Suggestion. 60 Example 2: Sarah Chang The optimal policy for Sarah Chang. Notice the coloring scheme. 61 Example 2: Sarah Chang You may wish to place reports in the open workbook instead of creating a new workbook. Under Utilities select Application Settings ... 62 Optimal Value How is the 86000 calculated at the outcome node? 63 Optimal Value What is the meaning of the 86000 in the decision tree? 64 Optimal Value You should understand: I How the numbers at each decision node are calculated (and what they mean) I How the numbers at the outcome nodes are calculated I How the numbers at the terminal nodes are calculated 65 Optimal Value Example Calculations: The Outcome of R&D node has a value of $86,000. This comes from: 86000 = .4 ∗ 515000 + .6 ∗ −200000 The terminal node at the top of the tree has a probability value of 36.0%. We reach this point in the tree given successful R&D and winning the bid. These are independent events so the probability is .36 = .4 ∗ .9 66 Optimal Value Example Calculations: This terminal node also has a value of $600,000. At this terminal node, we won the bid with a return of $850,000 but paid $50,000 to prepare the bid and $200,000 to continue the R&D. This gives $600, 000 = $850, 000 − $50, 000 − $200, 000. Now, how do you interpret the $86,000 at the root decision node? Some Tips I Separate the model from the data I Separate the model from the data – you get the idea I Make use of copy and paste – but be careful of cell references I Make sure probabilities sum to 1.0 I Do not play with the formulas generated by PrecsionTree (blue, red, green) I You should only edit through the user interface 68 Some Tips If you get a Value error at nodes instead of True or False make sure: I The probabilities sum to one at each chance node. This is the number one cause of getting a Value error. You should see an error message about probabilities not summing to 1.0 in small print at the bottom of the Excel spreadsheet. I Do a File save. The Value error may go away. I Recalculate the spreadsheet. Even better, make sure under Workbook Calculations, that Automatic is checked. I Always enter probabilities and values through Precision Tree. Do not enter them directly into the cells. Have these tips at your side for the exam. Sensitivity Analysis Sensitivity Analysis: See pages 12-13 of the Decision Analysis case. How sensitive is the model to the probability estimate of winning the bid? Select the Sensitivity Analysis menu item from the Analysis group. We are going to do sensitivity analysis on cell data!F11 70 Sensitivity Analysis Add the cell data!F11 we use for sensitivity analysis. 71 Sensitivity Analysis Vary the probability of win the bid (assuming successful R&D) from .4 to .9 in increments of .05 (11 steps). 72 Sensitivity Analysis At approximately what probability should we make the Continue decision? 73 Sensitivity Analysis 74 Goal Seek Using Excel GoalSeek we can calculate exactly the probability of the bid being accepted at which we are indifferent to the decision to abandon the R&D of the chip. 75 Goal Seek The tradeoff probability is approximately 64.71% 76 Goal Seek Oil Drilling Example (practice midterm) – the optimal decision is to not hire the geologist. How much would the report have to cost in order to be indifferent between a hire and no hire decision? Redford Example (midterm part c) – how much would the value of selling the partnership have to be in order to be indifferent between building and selling the rights? Utility Motivation: Assume the probability of making one million dollars is 10% and the probability of losing one million dollars is 10%. The contribution to the expected value of winning one million is 100, 000 = .1 ∗ 1, 000, 000 The contribution to the expected value of losing one million is −100, 000 = .1 ∗ (−1, 000, 000) These two events are of equal magnitude in the expected value calculation. Problem: in real life people care about their tail! Clarification: By tail, I mean tail of their expected payoff distribution. Utility Key Concept: If you maximize expected value (payoff) there may be a nontrivial probability of losing money. Key Concept: If you maximize expected value (payoff) bad things may happen. I In Wertz, if you make the decision to produce two versions, there is a 30 percent chance you will lose 40 thousand dollars I If Sarah Chang follows the optimal policy recommended by Precision Tree there is a 60 percent chance she will lose 200,000 dollars. If you are risk averse you may wish to use a utility function. Utility In PrecisionTree the default behavior is to use expected value or payoff. You can change that by going to Settings and then Model Settings. 80 Utility If you are risk averse (concave function), select an exponential utility function. In this case we have the utility function f (x) = 1 − exp(−x/10). 81 Utility The utility function U(x) = 1 − e(−x/10). 82 Utility Wertz (tt wertzUtility.xlsx) with maximizing expected utility. 83 Utility Now the optimal decision is to go with the single version. This is a safer strategy. We lose at most 10,000 dollars. The expected utility of this decision is: .2∗(1−e(−100/10))+.5∗(1−e(−60/10))+.3∗(1−e(10/10)) = 0.183266995 84 Utility When applying this material in the public sector it may be difficult to measure the value of outcomes even when probabilities are reasonably estimated. Consider “black swan” events. Blizzards are good examples. 85

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