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Prepared by Lee Revere and John Large

Chapter 3 Decision Analysis. Prepared by Lee Revere and John Large. Learning Objectives. Students will be able to: List the steps of the decision-making process. Describe the types of decision-making environments. Make decisions under uncertainty.

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Prepared by Lee Revere and John Large

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  1. Chapter 3 Decision Analysis Prepared by Lee Revere and John Large 3-1

  2. Learning Objectives Students will be able to: • List the steps of the decision-making process. • Describe the types of decision-making environments. • Make decisions under uncertainty. • Use probability values to make decisions under risk. • Develop accurate and useful decision trees. • Revise probabilities using Bayesian analysis. • Use computers to solve basic decision-making problems. • Understand the importance and use of utility theory in decision theory. 3-2

  3. Chapter Outline 3.1Introduction 3.2 The Six Steps in Decision Theory 3.3 Types of Decision-Making Environments 3.4 Decision Making under Uncertainty 3.5 Decision Making under Risk 3.6 Decision Trees 3.7 How Probability Values Are Estimated by Bayesian Analysis 3.8 Utility Theory 3-3

  4. Introduction • Decision theory is an analytical and systematic way to tackle problems. • A good decision is based on logic. 3-4

  5. The Six Steps in Decision Theory • Clearly define the problem at hand. • List the possible alternatives. • Identify the possible outcomes. • List the payoff or profit of each combination of alternatives and outcomes. • Select one of the mathematical decision theory models. • Apply the model and make your decision. 3-5

  6. John Thompson’s Backyard Storage Sheds 3-6

  7. Decision Table for Thompson Lumber 3-7

  8. Types of Decision-Making Environments • Type 1: Decision making under certainty. • Decision makerknows with certaintythe consequences of every alternative or decision choice. • Type 2: Decision making under risk. • The decision makerdoes knowthe probabilities of the various outcomes. • Decision making under uncertainty. • The decision makerdoes not knowthe probabilities of the various outcomes. 3-8

  9. Decision Making under Uncertainty • Maximax • Maximin • Equally likely (Laplace) • Criterion of realism • Minimax 3-9

  10. Decision Table for Thompson Lumber • Maximax: Optimistic Approach • Find the alternative that maximizes the maximum payoff. 3-10

  11. Thompson Lumber: Maximax Solution 3-11

  12. Decision Table for Thompson Lumber • Maximin: Pessimistic Approach • Choose the alternative with maximum minimum output. 3-12

  13. Thompson Lumber: Maximin Solution 3-13

  14. Thompson Lumber: Hurwicz • Criterion of Realism (Hurwicz) • Decision maker uses a weighted average based on optimism of the future. 3-14

  15. Thompson Lumber: Hurwicz Solution CR = α*(row max)+(1- α)*(row min) 3-15

  16. Decision Making under Uncertainty • Equally likely (Laplace) • Assume all states of nature to be equally likely, choose maximum Average. 3-16

  17. Decision Making under Uncertainty 3-17

  18. Thompson Lumber;Minimax Regret • Minimax Regret: • Choose the alternative that minimizes the maximum opportunity loss . 3-18

  19. Thompson Lumber:Opportunity Loss Table 3-19

  20. Thompson Lumber:Minimax Regret Solution 3-20

  21. In-Class Example 1 • Let’s practice what we’ve learned. Use the decision table below to compute (1) Maximax (2) Maximin (3) Minimax regret 3-21

  22. In-Class Example 1:Maximax 3-22

  23. In-Class Example 1:Maximin 3-23

  24. In-Class Example 1:Minimax Regret Opportunity Loss Table 3-24

  25. Decision Making under Risk Expected Monetary Value: In other words: EMV(Alternative n) = Payoff 1 * P(S1) + Payoff 2 * P(S2) + … + Payoff n * P(Sn) 3-25

  26. Thompson Lumber:EMV 3-26

  27. Thompson Lumber: EMV Solution 3-27

  28. Expected Value of Perfect Information (EVPI) • EVPI places an upper bound on what one would pay for additional information. • EVPI is the expected value with perfect information (EV|PI) minus the maximum EMV. 3-28

  29. Expected Value with Perfect Information (EV|PI) In other words EV׀PI = Best Payoff of S1 * P(S1) + Best Payoff of S2 * P(S2) +… + Best Payoff of Sn * P(Sn) 3-29

  30. Expected Value with Perfect Information (EV|PI) 3-30

  31. Expected Value of Perfect Information Expected value with no additional information Expected value with perfect information EVPI = EV|PI - maximum EMV 3-31

  32. Thompson Lumber:EVPI Solution EVPI = expected value with perfect information - max(EMV) = $100,000 - $40,000 = $60,000 3-32

  33. In-Class Example 2 Let’s practice what we’ve learned. Using the table below compute EMV, EV׀PI, and EVPI. 3-33

  34. In-Class Example 2: EMV and EV׀PI Solution 3-34

  35. In-Class Example 2:EVPI Solution EVPI = expected value with perfect information - max(EMV) = $100,000*0.25 + 35,000*0.50 +0*0.25 = $ 42,500 - 27,500 = $ 15,000 3-35

  36. Expected Opportunity Loss (EOL) • EOL is the cost of not picking the best solution.EOL = Expected Regret 3-36

  37. Thompson Lumber: Payoff Table 3-37

  38. Thompson Lumber: EOLThe Opportunity Loss Table 3-38

  39. Thompson Lumber: Opportunity Loss Table 3-39

  40. Thompson Lumber: EOL Solution 3-40

  41. Thompson Lumber:Sensitivity Analysis Let P = probability of favorable market EMV(Large Plant): = $200,000P + (-$180,000)(1-P) EMV(Small Plant): = $100,000P + (-$20,000)(1-P) EMV(Do Nothing): = $0P + 0(1-P) 3-41

  42. Thompson Lumber:Sensitivity Analysis(continued) 250000 200000 Point 1 Point 2 150000 Small Plant 100000 50000 EMV Values 0 -50000 0.2 0.4 0.6 0.8 1 0 -100000 Large Plant EMV -150000 -200000 Values of P 3-42

  43. Decision Making with Uncertainty: Using the Decision Trees • Decision trees are most beneficial when a sequence of decisions must be made. • All information included in a payoff table is also included in a decision tree. 3-43

  44. Five Steps toDecision Tree Analysis • Define the problem. • Structure or draw the decision tree. • Assign probabilities to the states of nature. • Estimate payoffs for each possible combination of alternatives and states of nature. • Solve the problem by computing expected monetary values (EMVs) at each state of nature node. 3-44

  45. Structure of Decision Trees A graphical representation where: A decision node (indicated by a square ) from which one of several alternatives may be chosen. A state-of-nature node (indicated by a circle ) out of which one state of nature will occur. 3-45

  46. Thompson’s Decision Tree Favorable Market A State of Nature Node 1 Unfavorable Market Construct Large Plant A Decision Node Favorable Market Construct Small Plant 2 Unfavorable Market Do Nothing Step 1: Define the problem Lets re-look at John Thompson’s decision regarding storage sheds. This simple problem can be depicted using a decision tree. Step 2: Draw the tree 3-46

  47. Thompson’s Decision Tree Step 3: Assign probabilities to the states of nature. Step 4: Estimate payoffs. A State of Nature Node $200,000 Favorable (0.5) Market 1 Construct Large Plant -$180,000 Unfavorable (0.5) Market A Decision Node $100,000 Favorable (0.5) Market Construct Small Plant 2 -$20,000 Unfavorable (0.5) Market Do Nothing 0 3-47

  48. Thompson’s Decision Tree Step 5: Compute EMVs and make decision. A State of Nature Node $200,000 Favorable (0.5) Market 1 EMV =$10,000 Construct Large Plant Unfavorable (0.5) Market -$180,000 A Decision Node Favorable (0.5) Market $100,000 Construct Small Plant 2 EMV =$40,000 Unfavorable (0.5) Market -$20,000 Do Nothing 0 3-48

  49. Thompson’s Decision:A More Complex Problem • John Thompson has the opportunity of obtaining a market survey that will give additional information on the probable state of nature. Results of the market survey will likely indicate there is a percent change of a favorable market. Historical data show market surveys accurately predict favorable markets 78 % of the time. Thus P(Fav. Mkt | Fav. Survey Results) = .78 • Likewise, if the market survey predicts an unfavorable market, there is a 13 % chance of its occurring. P(Unfav. Mkt | Unfav. Survey Results) = .13 • Now that we have redefined the problem (Step 1), let’s use this additional data and redraw Thompson’s decision tree (Step 2). 3-49

  50. Thompson’s Decision Tree 3-50

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