1. To accompany Quantitative Analysis for Management, 9e by Render/Stair/Hanna 3-1 © 2006 by Prentice Hall, Inc. Upper Saddle River, NJ 07458 Prepared by Lee Revere and John Large Chapter 3 Decision Analysis

2. To accompany Quantitative Analysis for Management, 9e by Render/Stair/Hanna 3-2 © 2006 by Prentice Hall, Inc. Upper Saddle River, NJ 07458 Learning Objectives Students will be able to: 1.List the steps of the decision-making process. 2.Describe the types of decision-making environments. 3.Make decisions under uncertainty. 4.Use probability values to make decisions under risk. 5.Understand the importance and use of utility theory in decision theory.

3. To accompany Quantitative Analysis for Management, 9e by Render/Stair/Hanna 3-3 © 2006 by Prentice Hall, Inc. Upper Saddle River, NJ 07458 Chapter Outline 3.1 Introduction 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

4. To accompany Quantitative Analysis for Management, 9e by Render/Stair/Hanna 3-4 © 2006 by Prentice Hall, Inc. Upper Saddle River, NJ 07458 Introduction  Decision theory is an analytical and systematic way to tackle problems.  A good decision is based on logic.

5. To accompany Quantitative Analysis for Management, 9e by Render/Stair/Hanna 3-5 © 2006 by Prentice Hall, Inc. Upper Saddle River, NJ 07458 The Six Steps in Decision Theory 1.Clearly define the problem at hand. 2.List the possible alternatives. 3.Identify the possible outcomes. 4.List the payoff or profit of each combination of alternatives and outcomes. 5.Select one of the mathematical decision theory models. 6.Apply the model and make your decision.

6. To accompany Quantitative Analysis for Management, 9e by Render/Stair/Hanna 3-6 © 2006 by Prentice Hall, Inc. Upper Saddle River, NJ 07458 John Thompson’s Backyard Storage Sheds Define problemTo manufacture or market backyard storage sheds List alternatives1.Construct a large new plant 2.A small plant 3.No plant at all Identify outcomesThe market could be favorable or unfavorable for storage sheds List payoffsList the payoff for each state of nature/decision alternative combination Select a modelDecision tables can be used to solve the problem Apply model and make decision Solutions can be obtained and a sensitivity analysis used to make a decision

7. To accompany Quantitative Analysis for Management, 9e by Render/Stair/Hanna 3-7 © 2006 by Prentice Hall, Inc. Upper Saddle River, NJ 07458 Decision Table for Thompson Lumber Alternative State of Nature Favorable Market ($) Unfavorable Market ($) Construct a large plant 200,000-180,000 Construct a small plant 100,000-20,000 Do nothing00

8. To accompany Quantitative Analysis for Management, 9e by Render/Stair/Hanna 3-8 © 2006 by Prentice Hall, Inc. Upper Saddle River, NJ 07458 Types of Decision- Making Environments  Type 1: Decision making under certainty.  Decision maker knows with certainty the consequences of every alternative or decision choice.  Type 2: Decision making under risk.  The decision maker does know the probabilities of the various outcomes.  Decision making under uncertainty.  The decision maker does not know the probabilities of the various outcomes.

9. To accompany Quantitative Analysis for Management, 9e by Render/Stair/Hanna 3-9 © 2006 by Prentice Hall, Inc. Upper Saddle River, NJ 07458 Decision Making under Uncertainty  Maximax  Maximin  Equally likely (Laplace)  Criterion of realism  Minimax

10. To accompany Quantitative Analysis for Management, 9e by Render/Stair/Hanna 3-10 © 2006 by Prentice Hall, Inc. Upper Saddle River, NJ 07458 Decision Table for Thompson Lumber Alternative State of Nature Favorable Market ($) Unfavorable Market ($) Construct a large plant 200,000-180,000 Construct a small plant 100,000-20,000 Do nothing00  Maximax: Optimistic Approach  Find the alternative that maximizes the maximum outcome for every alternative.

11. To accompany Quantitative Analysis for Management, 9e by Render/Stair/Hanna 3-11 © 2006 by Prentice Hall, Inc. Upper Saddle River, NJ 07458 Thompson Lumber: Maximax Solution Alternative State of Nature Maximax Favorable Market ($) Unfavorable Market ($) Construct a large plant 200,000-180,000200,000 Construct a small plant 100,000-20,000100,000 Do nothing000

12. To accompany Quantitative Analysis for Management, 9e by Render/Stair/Hanna 3-12 © 2006 by Prentice Hall, Inc. Upper Saddle River, NJ 07458 Decision Table for Thompson Lumber Alternative State of Nature Favorable Market ($) Unfavorable Market ($) Construct a large plant 200,000-180,000 Construct a small plant 100,000-20,000 Do nothing00  Maximin: Pessimistic Approach  Choose the alternative with maximum minimum output.

13. To accompany Quantitative Analysis for Management, 9e by Render/Stair/Hanna 3-13 © 2006 by Prentice Hall, Inc. Upper Saddle River, NJ 07458 Thompson Lumber: Maximin Solution Alternative State of Nature Maximin Favorable Market ($) Unfavorable Market ($) Construct a large plant 200,000-180,000 Construct a small plant 100,000-20,000 Do nothing000

14. To accompany Quantitative Analysis for Management, 9e by Render/Stair/Hanna 3-14 © 2006 by Prentice Hall, Inc. Upper Saddle River, NJ 07458 Thompson Lumber: Hurwicz  Criterion of Realism (Hurwicz)  Decision maker uses a weighted average based on optimism of the future. Alternative State of Nature Favorable Market ($) Unfavorable Market ($) Construct a large plant 200,000-180,000 Construct a small plant 100,000-20,000 Do nothing00

15. To accompany Quantitative Analysis for Management, 9e by Render/Stair/Hanna 3-15 © 2006 by Prentice Hall, Inc. Upper Saddle River, NJ 07458 Thompson Lumber: Hurwicz Solution CR = α*(row max)+(1- α)*(row min) Alternative State of Nature Criterion of Realism or Weighted Average (α = 0.8) ($) Favorable Market ($) Unfavorable Market ($) Construct a large plant 200,000-180,000124,000 Construct a small plant 100,000-20,00076,000 Do nothing000

16. To accompany Quantitative Analysis for Management, 9e by Render/Stair/Hanna 3-16 © 2006 by Prentice Hall, Inc. Upper Saddle River, NJ 07458 Decision Making under Uncertainty  Equally likely (Laplace)  Assume all states of nature to be equally likely, choose maximum Average. Alternative State of Nature Favorable Market ($) Unfavorable Market ($) Construct a large plant 200,000-180,000 Construct a small plant 100,000-20,000 Do nothing00

17. To accompany Quantitative Analysis for Management, 9e by Render/Stair/Hanna 3-17 © 2006 by Prentice Hall, Inc. Upper Saddle River, NJ 07458 Decision Making under Uncertainty Alternative State of Nature Avg. Favorable Market ($) Unfavorable Market ($) Construct a large plant 200,000-180,00010,000 Construct a small plant 100,000-20,00040,000 Do nothing000

18. To accompany Quantitative Analysis for Management, 9e by Render/Stair/Hanna 3-18 © 2006 by Prentice Hall, Inc. Upper Saddle River, NJ 07458 Thompson Lumber; Minimax Regret  Minimax Regret:  Choose the alternative that minimizes the maximum opportunity loss. Alternative State of Nature Favorable Market ($) Unfavorable Market ($) Construct a large plant 200,000-180,000 Construct a small plant 100,000-20,000 Do nothing00

19. To accompany Quantitative Analysis for Management, 9e by Render/Stair/Hanna 3-19 © 2006 by Prentice Hall, Inc. Upper Saddle River, NJ 07458 Thompson Lumber: Opportunity Loss Table Alternative State of Nature Favorable Market ($) Unfavorable Market ($) Construct a large plant 200,000 – 200,000 = 0 0- (-180,000) = 180,000 Construct a small plant 200,000 - 100,000 = 100,000 0- (-20,000) = 20,000 Do nothing 200,000 – 0 = 200000 0 – 0 = 0

20. To accompany Quantitative Analysis for Management, 9e by Render/Stair/Hanna 3-20 © 2006 by Prentice Hall, Inc. Upper Saddle River, NJ 07458 Thompson Lumber: Minimax Regret Solution Alternative State of Nature Maximum Opportunity Loss Favorable Market ($) Unfavorable Market ($) Construct a large plant 0180,000 Construct a small plant 100,00020,000100,000 Do nothing200,0000

21. To accompany Quantitative Analysis for Management, 9e by Render/Stair/Hanna 3-21 © 2006 by Prentice Hall, Inc. Upper Saddle River, NJ 07458 Decision Making under Risk Expected Monetary Value: In other words: EMV Alternative n = Payoff 1 * P Alt. 1 + Payoff 2 * P Alt. 2 + … + Payoff n * P Alt. N EMV= payoff of state of nature* probability of state of nature

22. To accompany Quantitative Analysis for Management, 9e by Render/Stair/Hanna 3-22 © 2006 by Prentice Hall, Inc. Upper Saddle River, NJ 07458 Thompson Lumber: EMV Alternative State of Nature EMV Favorable Market ($) Unfavorable Market ($) Construct a large plant 200,000-180,000 200,000*0.5 + (-180,000)*0.5 = 10,000 Construct a small plant 100,000-20,000 100,000*0.5 + (-20,000)*0.5 = 40,000 Do nothing000*0.5 + 0*0.5 = 0 Probabilities0.50

23. To accompany Quantitative Analysis for Management, 9e by Render/Stair/Hanna 3-23 © 2006 by Prentice Hall, Inc. Upper Saddle River, NJ 07458 Thompson Lumber: EV|PI and EMV Solution Alternative State of Nature EMV Favorable Market ($) Unfavorable Market ($) Construct a large plant 200,000-180,00010,000 Construct a small plant 100,000-20,00040,000 Do nothing000 EV ׀ PI 200,000* 0.5 = 100,000 0*0.5 = 0

24. To accompany Quantitative Analysis for Management, 9e by Render/Stair/Hanna 3-24 © 2006 by Prentice Hall, Inc. Upper Saddle River, NJ 07458 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.

25. To accompany Quantitative Analysis for Management, 9e by Render/Stair/Hanna 3-25 © 2006 by Prentice Hall, Inc. Upper Saddle River, NJ 07458 Expected Value with Perfect Information (EV|PI) In other words EV ׀ PI = Best Outcome of Alt 1 * P Alt. 1 + Best Outcome of Alt 2 * P Alt. 2 +… + Best Outcome of Alt n * P Alt. n

26. To accompany Quantitative Analysis for Management, 9e by Render/Stair/Hanna 3-26 © 2006 by Prentice Hall, Inc. Upper Saddle River, NJ 07458 Expected Value of Perfect Information EVPI = EV|PI - maximum EMV Expected value with perfect information Expected value with no additional information

27. To accompany Quantitative Analysis for Management, 9e by Render/Stair/Hanna 3-27 © 2006 by Prentice Hall, Inc. Upper Saddle River, NJ 07458 Thompson Lumber: EVPI Solution EVPI EMV 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

28. To accompany Quantitative Analysis for Management, 9e by Render/Stair/Hanna 3-28 © 2006 by Prentice Hall, Inc. Upper Saddle River, NJ 07458 In-Class Example 2 Let’s practice what we’ve learned. Using the table below compute EMV, EV ׀ PI, and EVPI. Alternative State of Nature Good Market ($) Average Market ($) Poor Market ($) Construct a large plant 75,00025,000-40,000 Construct a small plant 100,00035,000-60,000 Do nothing000

29. To accompany Quantitative Analysis for Management, 9e by Render/Stair/Hanna 3-29 © 2006 by Prentice Hall, Inc. Upper Saddle River, NJ 07458 In-Class Example 2: EMV and EV׀PI Solution Alternative State of Nature EMV Good Market ($) Average Market ($) Poor Market ($) Construct a large plant 75,00025,000-40,00021,250 Construct a small plant 100,00035,000-60,00027,500 Do nothing0000 0.250.500.25

30. To accompany Quantitative Analysis for Management, 9e by Render/Stair/Hanna 3-30 © 2006 by Prentice Hall, Inc. Upper Saddle River, NJ 07458 In-Class Example 2: EVPI Solution EVPI EMV 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

31. To accompany Quantitative Analysis for Management, 9e by Render/Stair/Hanna 3-31 © 2006 by Prentice Hall, Inc. Upper Saddle River, NJ 07458 Expected Opportunity Loss  EOL is the cost of not picking the best solution. EOL = Expected Regret

32. To accompany Quantitative Analysis for Management, 9e by Render/Stair/Hanna 3-32 © 2006 by Prentice Hall, Inc. Upper Saddle River, NJ 07458 Thompson Lumber: EOL The Opportunity Loss Table Alternative State of Nature Favorable Market ($) Unfavorable Market ($) Construct a large plant 200,000 – 200,000 0- (-180,000) Construct a small plant 200,000 - 100,000 0 – (-20,000) Do nothing200,000 - 00-0 Probabilities0.50

33. To accompany Quantitative Analysis for Management, 9e by Render/Stair/Hanna 3-33 © 2006 by Prentice Hall, Inc. Upper Saddle River, NJ 07458 Thompson Lumber: EOL Table Alternative State of Nature Favorable Market ($) Unfavorable Market ($) Construct a large plant 200,000-180,000 Construct a small plant 100,000-20,000 Do nothing00 Probabilities0.50

34. To accompany Quantitative Analysis for Management, 9e by Render/Stair/Hanna 3-34 © 2006 by Prentice Hall, Inc. Upper Saddle River, NJ 07458 Thompson Lumber: EOL Solution