1. To accompany Quantitative Analysis for Management, 8e by Render/Stair/Hanna 3-1 © 2003 by Prentice Hall, Inc. Upper Saddle River, NJ 07458 Chapter 3 Fundamentals of Decision Theory Models

2. To accompany Quantitative Analysis for Management, 8e by Render/Stair/Hanna 3-2 © 2003 by Prentice Hall, Inc. Upper Saddle River, NJ 07458 Learning Objectives Students will be able to: List the steps of the decision- making process Describe the types of decision- making environments Use probability values to make decisions under risk Make decisions under uncertainty, where there is risk but probability values are not known Use computers to solve basic decision-making problems

3. To accompany Quantitative Analysis for Management, 8e by Render/Stair/Hanna 3-3 © 2003 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 Risk 3.5 Decision Making Under Uncertainty 3.6 Marginal Analysis with a Large Number of Alternatives and States of Nature

4. To accompany Quantitative Analysis for Management, 8e by Render/Stair/Hanna 3-4 © 2003 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, 8e by Render/Stair/Hanna 3-5 © 2003 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, 8e by Render/Stair/Hanna 3-6 © 2003 by Prentice Hall, Inc. Upper Saddle River, NJ 07458 Decision Table for Thompson Lumber

7. To accompany Quantitative Analysis for Management, 8e by Render/Stair/Hanna 3-7 © 2003 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

8. To accompany Quantitative Analysis for Management, 8e by Render/Stair/Hanna 3-8 © 2003 by Prentice Hall, Inc. Upper Saddle River, NJ 07458 Tile Replacement on the Space Shuttle

9. To accompany Quantitative Analysis for Management, 8e by Render/Stair/Hanna 3-9 © 2003 by Prentice Hall, Inc. Upper Saddle River, NJ 07458 Critical Decisions in a Nuclear World

10. To accompany Quantitative Analysis for Management, 8e by Render/Stair/Hanna 3-10 © 2003 by Prentice Hall, Inc. Upper Saddle River, NJ 07458 Decision-Making Under Risk Expected Monetary Value

11. To accompany Quantitative Analysis for Management, 8e by Render/Stair/Hanna 3-11 © 2003 by Prentice Hall, Inc. Upper Saddle River, NJ 07458 Decision Table for Thompson Lumber

12. To accompany Quantitative Analysis for Management, 8e by Render/Stair/Hanna 3-12 © 2003 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

13. To accompany Quantitative Analysis for Management, 8e by Render/Stair/Hanna 3-13 © 2003 by Prentice Hall, Inc. Upper Saddle River, NJ 07458 Expected Value With Perfect Information (EV | PI)

14. To accompany Quantitative Analysis for Management, 8e by Render/Stair/Hanna 3-14 © 2003 by Prentice Hall, Inc. Upper Saddle River, NJ 07458 Expected Value of Perfect Information EVPI = EV|PI - maximum EMV

15. To accompany Quantitative Analysis for Management, 8e by Render/Stair/Hanna 3-15 © 2003 by Prentice Hall, Inc. Upper Saddle River, NJ 07458 Expected Value of Perfect Information

16. To accompany Quantitative Analysis for Management, 8e by Render/Stair/Hanna 3-16 © 2003 by Prentice Hall, Inc. Upper Saddle River, NJ 07458 Expected Value of Perfect Information EVPI = expected value with perfect information - max(EMV) = $200,000*0.50 + 0*0.50 - $40,000 = $60,000

17. To accompany Quantitative Analysis for Management, 8e by Render/Stair/Hanna 3-17 © 2003 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

18. To accompany Quantitative Analysis for Management, 8e by Render/Stair/Hanna 3-18 © 2003 by Prentice Hall, Inc. Upper Saddle River, NJ 07458 Computing EOL - The Opportunity Loss Table

19. To accompany Quantitative Analysis for Management, 8e by Render/Stair/Hanna 3-19 © 2003 by Prentice Hall, Inc. Upper Saddle River, NJ 07458 The Opportunity Loss Table continued

20. To accompany Quantitative Analysis for Management, 8e by Render/Stair/Hanna 3-20 © 2003 by Prentice Hall, Inc. Upper Saddle River, NJ 07458 The Opportunity Loss Table - continued

21. To accompany Quantitative Analysis for Management, 8e by Render/Stair/Hanna 3-21 © 2003 by Prentice Hall, Inc. Upper Saddle River, NJ 07458 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)

22. To accompany Quantitative Analysis for Management, 8e by Render/Stair/Hanna 3-22 © 2003 by Prentice Hall, Inc. Upper Saddle River, NJ 07458 Sensitivity Analysis - continued -200000 -150000 -100000 -50000 0 50000 100000 150000 200000 250000 00.20.40.60.81 Values of P EMV Values Point 1 Point 2 Small Plant Large Plant EMV

23. To accompany Quantitative Analysis for Management, 8e by Render/Stair/Hanna 3-23 © 2003 by Prentice Hall, Inc. Upper Saddle River, NJ 07458 Decision Making Under Uncertainty Maximax Maximin Equally likely (Laplace) Criterion of Realism Minimax

24. To accompany Quantitative Analysis for Management, 8e by Render/Stair/Hanna 3-24 © 2003 by Prentice Hall, Inc. Upper Saddle River, NJ 07458 Decision Making Under Uncertainty Maximax - Choose the alternative with the maximum output

25. To accompany Quantitative Analysis for Management, 8e by Render/Stair/Hanna 3-25 © 2003 by Prentice Hall, Inc. Upper Saddle River, NJ 07458 Decision Making Under Uncertainty Maximin - Choose the alternative with the maximum minimum output

26. To accompany Quantitative Analysis for Management, 8e by Render/Stair/Hanna 3-26 © 2003 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 States of Nature AlternativeFavorable Market Unfavorable Market Avg. Construct Large Plant $200,000-$180,00010,000 Construct small plant 100,000-20,00040,000 Do nothing 000

27. To accompany Quantitative Analysis for Management, 8e by Render/Stair/Hanna 3-27 © 2003 by Prentice Hall, Inc. Upper Saddle River, NJ 07458 Decision Making Under Uncertainty Criterion of Realism (Hurwicz): CR =  *(row max) + (1-  )*(row min) State of Nature AlternativeFavorable Market Unfavorable Market CR Construct large plant $200,000-180,000124,000 Construct small plant $100,000-20,00076,000 Do nothing000 0.800.20

28. To accompany Quantitative Analysis for Management, 8e by Render/Stair/Hanna 3-28 © 2003 by Prentice Hall, Inc. Upper Saddle River, NJ 07458 Decision Making Under Uncertainty Minimax - choose the alternative with the minimum maximum Opportunity Loss States of Nature Alternative Favorable Market Unfavorable Market CR Construct a large plant 0$$180,000 Construct a small plant $100,00020,000100,000 Do nothing200,0000

29. To accompany Quantitative Analysis for Management, 8e by Render/Stair/Hanna 3-29 © 2003 by Prentice Hall, Inc. Upper Saddle River, NJ 07458 Marginal Analysis P = probability that demand is greater that or equal to a given supply 1-P = probability that demand will be less than supply MP = marginal profit ML = marginal loss Optimal decision rule is: P*MP  (1-P)*ML or

30. To accompany Quantitative Analysis for Management, 8e by Render/Stair/Hanna 3-30 © 2003 by Prentice Hall, Inc. Upper Saddle River, NJ 07458 Marginal Analysis - Discrete Distributions Steps using Discrete Distributions : PDetermine the value for P Construct a probability table and add a cumulative probability column PKeep ordering inventory as long as the probability of selling at least one additional unit is greater than P

31. To accompany Quantitative Analysis for Management, 8e by Render/Stair/Hanna 3-31 © 2003 by Prentice Hall, Inc. Upper Saddle River, NJ 07458 Café du Donut Example

32. To accompany Quantitative Analysis for Management, 8e by Render/Stair/Hanna 3-32 © 2003 by Prentice Hall, Inc. Upper Saddle River, NJ 07458 Café du Donut Example continued Marginal profit = selling price - cost = $6 - $4 = $2 Marginal loss = cost Therefore:

33. To accompany Quantitative Analysis for Management, 8e by Render/Stair/Hanna 3-33 © 2003 by Prentice Hall, Inc. Upper Saddle River, NJ 07458 Café du Donut Example continued

34. To accompany Quantitative Analysis for Management, 8e by Render/Stair/Hanna 3-34 © 2003 by Prentice Hall, Inc. Upper Saddle River, NJ 07458 Marginal Analysis Normal Distribution   = average or mean sales   = standard deviation of sales MPMP = marginal profit MLML = Marginal loss

35. To accompany Quantitative Analysis for Management, 8e by Render/Stair/Hanna 3-35 © 2003 by Prentice Hall, Inc. Upper Saddle River, NJ 07458 Marginal Analysis - Discrete Distributions Steps using Normal Distributions: Determine the value for P. Locate P on the normal distribution. For a given area under the curve, we find Z from the standard Normal table. Using we can now solve for X *    * X Z MPML P  

36. To accompany Quantitative Analysis for Management, 8e by Render/Stair/Hanna 3-36 © 2003 by Prentice Hall, Inc. Upper Saddle River, NJ 07458 Joe’s Newsstand Example A MLML = 4 MPMP = 6   = Average demand = 50 papers per day   = Standard deviation of demand = 10

37. To accompany Quantitative Analysis for Management, 8e by Render/Stair/Hanna 3-37 © 2003 by Prentice Hall, Inc. Upper Saddle River, NJ 07458 Joe’s Newsstand Example A - continued Step 1: P Step 2: Look in the Normal table for P = 0.6 (i.e., 1 – 0.4).

38. To accompany Quantitative Analysis for Management, 8e by Render/Stair/Hanna 3-38 © 2003 by Prentice Hall, Inc. Upper Saddle River, NJ 07458 Joe’s Newsstand Example A continued

39. To accompany Quantitative Analysis for Management, 8e by Render/Stair/Hanna 3-39 © 2003 by Prentice Hall, Inc. Upper Saddle River, NJ 07458 Joe’s Newsstand Example B MLML = 8 MPMP = 2   = Average demand = 100 papers per day   = Standard deviation of demand = 10

40. To accompany Quantitative Analysis for Management, 8e by Render/Stair/Hanna 3-40 © 2003 by Prentice Hall, Inc. Upper Saddle River, NJ 07458 Joe’s Newsstand Example B - continued Step 1: Step 2: Z Z = -0.84 for an area of 0.80 and or:

41. To accompany Quantitative Analysis for Management, 8e by Render/Stair/Hanna 3-41 © 2003 by Prentice Hall, Inc. Upper Saddle River, NJ 07458 Joe’s Newsstand Example B continued