1. 8-1 CHAPTER 8 Decision Analysis

2. 8-2 LEARNING OBJECTIVES 1.List the steps of the decision-making process and describe the different types of decision-making environments. 2.Make decisions under uncertainty and under risk. 3.Use Excel to set up and solve problems involving decision tables. 4.Develop accurate and useful decision trees.

3. 8-3 LEARNING OBJECTIVES 5. Use TreePlan to set up and analyze decision tree problems with Excel. 6. Understand the importance and use of utility theory in decision making.

4. 8-4 Decision Analysis An analytic and systematic approach to the study of decision making Based on logic Considers all possible alternatives Examines all available information about the future Applies the decision modeling approach

5. 8-5 Five Steps 1. Clearly define the problem 2. List all possible alternatives 3. Identify all possible outcomes for each alternative 4. Identify the payoff for each alternative and outcome combination 5. Use a decision modeling technique to choose an alternative

6. 8-6 Thompson Lumber 1.Decision: Should he make and sell storage sheds 2.Alternatives: 1.Build a large plant 2.Build a small plant 3.Do nothing 3.Outcomes: Demand for sheds will be 1.High 2.Moderate 3.Low

7. 8-7 Thompson Lumber 4.Payoff table OUTCOMES HIGHMODERATELOW ALTERNATIVESDEMANDDEMANDDEMAND Build large plant$200,000$100,000–$120,000 Build small plant$ 90,000$ 50,000–$ 20,000 No plant$ 0$ 0 $ 0 Table 8.1 5.Select and apply decision analysis model

8. 8-8 Decision-Making Environments Type 1:Decision making under certainty Type 2:Decision making under uncertainty Type 3:Decision making under risk

9. 8-9 Certainty Consequence of every alternative is known Usually only one outcome for each alternative Seldom occurs in reality

10. 8-10 Uncertainty Probabilities of possible outcomes not known Decision making methods: 1. Maximax 2. Maximin 3. Criterion of realism 4. Equally likely 5. Minimax regret

11. 8-11 Thompson Lumber Maximax Criterion Maximizes the maximum payoff OUTCOMES HIGHMODERATELOW ALTERNATIVESDEMANDDEMANDDEMAND Build large plant$200,000$100,000–$120,000 Build small plant$ 90,000$ 50,000–$ 20,000 No plant$ 0$ 0 $ 0 Table 8.2 Maximax

12. 8-12 Thompson Lumber Maximin Criterion Maximizes the minimum payoff OUTCOMES HIGHMODERATELOW ALTERNATIVESDEMANDDEMANDDEMAND Build large plant$200,000$100,000–$120,000 Build small plant$ 90,000$ 50,000–$ 20,000 No plant$ 0$ 0 $ 0 Table 8.3 Maximin

13. 8-13 Thompson Lumber Criterion of Realism (Hurwicz) Table 8.4 Thompson’s coefficient of realism  = 0.45 Realism payoff for alternative =  x (Maximum payoff for alternative) + (1 –  ) x (Minimum payoff for alternative) OUTCOMES HIGHMODERATELOWWT. AVG. FOR ALTERNATIVESDEMANDDEMANDDEMANDALTERNATIVE Build large plant$200,000$100,000–$120,000$24,000 Build small plant$ 90,000$ 50,000–$ 20,000$29,500 No plant$ 0$ 0 $ 0$ 0 Realism

14. 8-14 Thompson Lumber Equally Likely (Laplace) Criterion Highest average payoff Table 8.5 OUTCOMES HIGHMODERATELOWAVERAGE FOR ALTERNATIVESDEMANDDEMANDDEMANDALTERNATIVE Build large plant$200,000$100,000–$120,000$60,000 Build small plant$ 90,000$ 50,000–$ 20,000$40,000 No plant$ 0$ 0 $ 0$ 0 Equally likely

15. 8-15 Thompson Lumber Minimax Regret Criterion Table 8.6 OUTCOMES ALTERNATIVESHIGH DEMAND Build large plant$200,000 – $200,000 = $ 0 Build small plant$200,000 – $ 90,000 = $110,000 No plant$200,000 – $ 0 = $200,000 MODERATE DEMAND Build large plant$100,000 – $100,000 = $ 0 Build small plant$100,000 – $ 50,000 = $ 50,000 No plant$100,000 – $ 0 = $100,000 LOW DEMAND Build large plant$0 – (–$120,000) = $120,000 Build small plant$0 – (–$ 20,000) = $ 20,000 No plant $0 – $ 0 = $ 0

16. 8-16 Minimax Regret Criterion Thompson Lumber Table 8.7 Minimax OUTCOMES HIGHMODERATELOWMAXIMUM FOR ALTERNATIVESDEMANDDEMANDDEMANDALTERNATIVE Build large plant$ 0$ 0$120,000$120,000 Build small plant$110,000$ 50,000$ 20,000$110,000 No plant$200,000$100,000$ 0$200,000

17. 8-17 Using Excel Screenshot 8-1A

18. 8-18 Using Excel Screenshot 8-1B

19. 8-19 Under Risk Expected Monetary Value (EMV) EMV (Alternative i ) =(Payoff of first outcome) x (Probability of first outcome) + (Payoff of second outcome) x (Probability of second outcome) + … + (Payoff of last outcome) x (Probability of last outcome)

20. 8-20 Thompson Lumber OUTCOMES HIGHMODERATELOWEMV FOR ALTERNATIVESDEMANDDEMANDDEMANDALTERNATIVE Build large plant$200,000$100,000–$120,000$200,000 x 0.3 + $100,000 x 0.5 + (–$120,000) x 0.2 = $86,000 Build small plant$ 90,000$ 50,000–$ 20,000$90,000 x 0.3 + $50,000 x 0.5 + (–$20,000) x 0.2 = $48,000 No plant$ 0$ 0 $ 0$0 x 0.3 + $0 x 0.5 + $0 x 0.2 = $ 0 Probabilities0.30.50.2 Table 8.8

21. 8-21 Under Risk Expected Opportunity Loss (EOL) EOL (Alternative i ) =(Regret of first outcome) x (Probability of first outcome) + (Regret of second outcome) x (Probability of second outcome) + … + (Regret of last outcome) x (Probability of last outcome)

22. 8-22 Thompson Lumber Table 8.9 OUTCOMES HIGHMODERATELOWEOL FOR ALTERNATIVESDEMANDDEMANDDEMANDALTERNATIVE Build large plant$ 0$ 0$120,000$0 x 0.3 + $0 x 0.5 + $120,000 x 0.2 = $24,000 Build small plant$110,000$ 50,000$ 20,000$110,000 x 0.3 + $50,000 x 0.5 + $20,000 x 0.2 = $62,000 No plant$200,000$100,000$ 0$200,000 x 0.3 + $100,000 x 0.5 + $0 x 0.2 = $110,000 Probabilities0.30.50.2

23. 8-23 Decision Trees Presents decision alternatives and outcomes in a sequential manner Decision node Outcome node

24. 8-24 High Demand Moderate Demand Low Demand High Demand Moderate Demand Low Demand All Demands $200,000 $100,000 –$120,000 Payoffs $90,000 $50,000 –$20,000 $0 Decision Trees Thompson Lumber 1 2 3 Large Plant Small Plant No Plant Decision Node Outcome Node Figure 8.1

25. 8-25 Decision Trees Thompson Lumber High Demand (0.30) Moderate Demand (0.50) Low Demand (0.20) High Demand (0.30) Moderate Demand (0.50) Low Demand (0.20) All Demands $200,000 $100,000 –$120,000 Payoffs $90,000 $50,000 –$20,000 $0 1 2 3 Large Plant Small Plant No Plant Decision Node Outcome Node Figure 8.2 Probability $86,000 $48,000 $0 1 EMV = $200,000 x 0.3 + $100,000 x 0.05 + (–$120,000) x 0.2 = $86,000 2 EMV = $90,000 x 0.3 + $50,000 x 0.05 + (–$20,000) x 0.2 = $48,000

26. 8-26 Decision Trees Thompson Lumber Figure 8.3 1 2 3 Large Plant Small Plant No Plant Decision Node EMV = $86,000 EMV = $48,000 $0 EMV = $0

27. 8-27 Using TreePlan With Excel Screenshot 8-3A

28. 8-28 Using TreePlan With Excel Screenshot 8-3B (a) (b)

29. 8-29 Using TreePlan With Excel Screenshot 8-3B

30. 8-30 Using TreePlan With Excel Screenshot 8-3C

31. 8-31 Using TreePlan With Excel Screenshot 8-3D

32. 8-32 Utility Theory An alternative to EMV Incorporates a person’s attitude toward risk A utility function converts a person’s attitude toward money and risk into a number between 0 and 1

33. 8-33 Utility Theory = $100,000 x 0.5 + $0 x 0.5 Figure 8.6 $35,000 $50,000 Tails (0.5) Heads (0.5) $35,000 Payoffs $100,000 $0 $50,000 Accept Offer Reject Offer

34. 8-34 Jane’s Utility Function Figure 8.7 Certainty Equivalent EMV = $25,000 $50,000 Outcome 2 (0.5) Outcome 1 (0.5) $50,000 ? $0 Alternative Alternative 2

35. 8-35 Jane’s Utility Function Worst payoff utility = 0 Best payoff utility = 1 Certainty equivalent – the minimum guaranteed amount you are willing to accept to avoid the risk associated with a gamble U ($15,000)= U ($0) x 0.5 + U ($50,000) x 0.5 = 0 x 0.5 + 1 x 0.5 = 0.5

36. 8-36 Jane’s Utility Function Repeat for multiple amounts Utility Value 1.00 – 0.80 – 0.60 – 0.40 – 0.20 – 0.00 – |||||| $0$10,000$20,000$30,000$40,000$50,000 Monetary Value U ($27,000) = 0.75 U ($50,000) = 1.00 U ($6,000) = 0.25 U ($15,000) = 0.50 U ($50) = 0.00 Figure 8.8

37. 8-37 Jane’s Utility Function Risk premium The EMV a person is willing to give up to avoid the risk associated with a gamble Risk premium =(EMV of gamble) – (Certainty equivalent) Risk avoider/risk adverse: Risk premium > 0 Risk indifferent/risk-neutral: Risk premium = 0 Risk seeker/risk-prone: Risk premium < 0

38. 8-38 Exponential Utility Function Risk avoider U ( X ) = 1 – e – X / R Risk Indifferent Risk Seeker Risk Avoider Monetary Outcome Utility Figure 8.9

39. 8-39 Utility as a Criteria Utility replaces monetary values in decision tree Best Choice Figure 8.10 EMV = –$4,000 $0 | $0 Invest Do Not Invest $0 Big Success (0.2) $40,000 Payoffs $10,000 –$30,000 Failure (0.5) Moderate Success (0.3) 1 2

40. 8-40 Utility as a Criteria Figure 8.11 U ($40,000) = 1.00 U ($0) = 0.15 U ($10,000) = 0.30 U ($30,000) = 0.00 |||||||| –$30,000$–20,000–$10,000$0$10,000$20,000$30,000$40,000 Utility Value 1.00 – 0.80 – 0.60 – 0.40 – 0.20 – 0.00 – Monetary Value

41. 8-41 Utility as a Criteria Utility replaces monetary values in decision tree Best Choice Figure 8.10 0.29 0.15 0.29 | Invest Do Not Invest 0.15 Big Success (0.2) 1.00 Utilities 0.30 0.00 Failure (0.5) Moderate Success (0.3) 1 2 Expected Utility