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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. • 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 3.7 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. Decision Making under Risk Expected Monetary Value: In other words: EMVAlternative n = Payoff 1 * PAlt. 1 + Payoff 2 * PAlt. 2 + … + Payoff n * PAlt. N EMV= payoff of state of nature* probability of state of nature 3-21

  22. Thompson Lumber:EMV 3-22

  23. Thompson Lumber: EV|PI and EMV Solution 3-23

  24. 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. 3-24

  25. 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 3-25

  26. Expected Value of Perfect Information Expected value with no additional information Expected value with perfect information EVPI = EV|PI - maximum EMV 3-26

  27. Thompson Lumber:EVPI Solution EVPI = expected value with perfect information - max(EMV) = $200,000*0.50 + 0*0.50 - $40,000 = $60,000 • It means that if the cost of information less that 60000 we’ll accept to pay for getting information • Otherwise refuse. From previous slide 3-27

  28. In-Class Example 2 Let’s practice what we’ve learned. Using the table below compute EMV, EV׀PI, and EVPI. 3-28

  29. In-Class Example 2: EMV and EV׀PI Solution 3-29

  30. 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 3-30

  31. Expected Opportunity Loss • EOL is the cost of not picking the best solution.EOL = Expected Regret 3-31

  32. Thompson Lumber: EOLThe Opportunity Loss Table 3-32

  33. Thompson Lumber: EOL Table 3-33

  34. Thompson Lumber: EOL Solution 3-34

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