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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 outcome for every alternative. 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) Mazimax (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: EMVAlternative n = Payoff 1 * PAlt. 1 + Payoff 2 * PAlt. 2 + … + Payoff n * PAlt. n 3-25

  26. Thompson Lumber:EMV 3-26

  27. Thompson Lumber: EV|PI and 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 minus the maximum EMV. 3-28

  29. Expected Value with Perfect Information (EV|PI) In other words EV׀PI = Best Outcome of Alt 1 * PAlt. 1 + Best Outcome of Alt 2 * PAlt. 2 +… + Best Outcome of Alt n * PAlt. n 3-29

  30. Expected Value of Perfect Information Expected value with no additional information Expected value with perfect information EVPI = EV|PI - maximum EMV 3-30

  31. Thompson Lumber:EVPI Solution EVPI = expected value with perfect information - max(EMV) = $200,000*0.50 + 0*0.50 - $40,000 = $60,000 From previous slide 3-31

  32. In-Class Example 2 Let’s practice what we’ve learned. Using the table below compute EMV, EV׀PI, and EVPI. 3-32

  33. In-Class Example 2: EMV and EV׀PI Solution 3-33

  34. 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 3-34

  35. Expected Opportunity Loss • EOL is the cost of not picking the best solution.EOL = Expected Regret 3-35

  36. Thompson Lumber: EOLThe Opportunity Loss Table 3-36

  37. Thompson Lumber: EOL Table 3-37

  38. Thompson Lumber: EOL Solution 3-38

  39. Thompson Lumber:Sensitivity Analysis EMV(Large Plant): = $200,000P - (1-P)$180,000 EMV(Small Plant): = $100,000P - $20,000(1-P) EMV(Do Nothing): = $0P + 0(1-P) 3-39

  40. 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 3-40

  41. Marginal Analysis • P= probability that demand > a given supply. • 1-P = probability that demand < supply. • MP = marginal profit. • ML = marginal loss. • Optimal decision rule is: • P*MP  (1-P)*ML or 3-41

  42. Marginal Analysis -Discrete Distributions Steps using Discrete Distributions: • Determine the value forP. • Construct a probability table and add a cumulative probability column. • Keep ordering inventory as long as the probability of selling at least oneadditional unit is greater thanP. 3-42

  43. Café du Donut:Marginal Analysis Café du Donut sells a dozen donuts for $6. It costs $4 to make each dozen. The following table shows the discrete distribution for Café du Donut sales. 3-43

  44. Café du Donut: Marginal Analysis Solution Marginal profit = selling price - cost = $6 - $4 = $2 Marginal loss = cost Therefore: 3-44

  45. Café du Donut: Marginal Analysis Solution 3-45

  46. In-Class Example 3 Let’s practice what we’ve learned. You sell cases of goods for $15/case, the raw materials cost you $4/case, and you pay $1/case commission. 3-46

  47. In-Class Example 3:Solution MP = $15-$4-$1 = $10 per case ML = $4 P>= $4 / $10+$4 = .286 3-47

  48. Marginal AnalysisNormal Distribution • = average or mean sales • = standard deviation of sales • MP = marginal profit • ML = Marginal loss 3-48

  49. Marginal Analysis -Discrete Distributions ML = P + ML MP * - m X = Z s • Steps using Normal Distributions: • Determine the value forP. • Locate P on the normal distribution. For a given area under the curve, we find Zfrom thestandard Normal table. • Using we can now solve for: X* 3-49

  50. Marginal Analysis:Normal Curve Review 3-50

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