1. 12-1 Copyright © 2010 Pearson Education, Inc. Publishing as Prentice Hall Decision Analysis Chapter 12

2. 12-2 ■Components of Decision Making ■Decision Making without Probabilities ■Decision Making with Probabilities ■Decision Analysis with Additional Information ■Utility Chapter Topics Copyright © 2010 Pearson Education, Inc. Publishing as Prentice Hall

3. 12-3 Table 12.1 Payoff Table ■A state of nature is an actual event that may occur in the future. ■A payoff table is a means of organizing a decision situation, presenting the payoffs from different decisions given the various states of nature. Decision Analysis Components of Decision Making Copyright © 2010 Pearson Education, Inc. Publishing as Prentice Hall

4. 12-4 Decision Analysis Decision Making Without Probabilities Copyright © 2010 Pearson Education, Inc. Publishing as Prentice Hall Figure 12.1

5. 12-5 Decision-Making Criteria maximaxmaximinminimax minimax regretHurwiczequal likelihood Decision Analysis Decision Making without Probabilities Table 12.2 Copyright © 2010 Pearson Education, Inc. Publishing as Prentice Hall

6. 12-6 Table 12.3 Payoff Table Illustrating a Maximax Decision In the maximax criterion the decision maker selects the decision that will result in the maximum of maximum payoffs; an optimistic criterion. Decision Making without Probabilities Maximax Criterion Copyright © 2010 Pearson Education, Inc. Publishing as Prentice Hall

7. 12-7 Table 12.4 Payoff Table Illustrating a Maximin Decision In the maximin criterion the decision maker selects the decision that will reflect the maximum of the minimum payoffs; a pessimistic criterion. Decision Making without Probabilities Maximin Criterion Copyright © 2010 Pearson Education, Inc. Publishing as Prentice Hall

8. 12-8 Table 12.6 Regret Table Illustrating the Minimax Regret Decision Regret is the difference between the payoff from the best decision and all other decision payoffs. The decision maker attempts to avoid regret by selecting the decision alternative that minimizes the maximum regret. Decision Making without Probabilities Minimax Regret Criterion Copyright © 2010 Pearson Education, Inc. Publishing as Prentice Hall

9. 12-9 The Hurwicz criterion is a compromise between the maximax and maximin criterion. A coefficient of optimism, , is a measure of the decision maker’s optimism. The Hurwicz criterion multiplies the best payoff by  and the worst payoff by 1- ., for each decision, and the best result is selected. Decision Values Apartment building $50,000(.4) + 30,000(.6) = 38,000 Office building $100,000(.4) - 40,000(.6) = 16,000 Warehouse $30,000(.4) + 10,000(.6) = 18,000 Decision Making without Probabilities Hurwicz Criterion Copyright © 2010 Pearson Education, Inc. Publishing as Prentice Hall

10. 12-10 The equal likelihood ( or Laplace) criterion multiplies the decision payoff for each state of nature by an equal weight, thus assuming that the states of nature are equally likely to occur. Decision Values Apartment building $50,000(.5) + 30,000(.5) = 40,000 Office building $100,000(.5) - 40,000(.5) = 30,000 Warehouse $30,000(.5) + 10,000(.5) = 20,000 Decision Making without Probabilities Equal Likelihood Criterion Copyright © 2010 Pearson Education, Inc. Publishing as Prentice Hall

11. 12-11 ■A dominant decision is one that has a better payoff than another decision under each state of nature. ■The appropriate criterion is dependent on the “risk” personality and philosophy of the decision maker. Criterion Decision (Purchase) MaximaxOffice building MaximinApartment building Minimax regretApartment building HurwiczApartment building Equal likelihoodApartment building Decision Making without Probabilities Summary of Criteria Results Copyright © 2010 Pearson Education, Inc. Publishing as Prentice Hall

12. 12-12 Exhibit 12.1 Decision Making without Probabilities Solution with QM for Windows (1 of 3) Copyright © 2010 Pearson Education, Inc. Publishing as Prentice Hall

13. 12-13 Exhibit 12.2 Decision Making without Probabilities Solution with QM for Windows (2 of 3) Copyright © 2010 Pearson Education, Inc. Publishing as Prentice Hall

14. 12-14 Exhibit 12.3 Decision Making without Probabilities Solution with QM for Windows (3 of 3) Copyright © 2010 Pearson Education, Inc. Publishing as Prentice Hall

15. 12-15 Decision Making without Probabilities Solution with Excel Exhibit 12.4 Copyright © 2010 Pearson Education, Inc. Publishing as Prentice Hall

16. 12-16 Expected value is computed by multiplying each decision outcome under each state of nature by the probability of its occurrence. EV(Apartment) = $50,000(.6) + 30,000(.4) = 42,000 EV(Office) = $100,000(.6) - 40,000(.4) = 44,000 EV(Warehouse) = $30,000(.6) + 10,000(.4) = 22,000 Table 12.7 Decision Making with Probabilities Expected Value Copyright © 2010 Pearson Education, Inc. Publishing as Prentice Hall

17. 12-17 ■The expected opportunity loss is the expected value of the regret for each decision. ■The expected value and expected opportunity loss criterion result in the same decision. EOL(Apartment) = $50,000(.6) + 0(.4) = 30,000 EOL(Office) = $0(.6) + 70,000(.4) = 28,000 EOL(Warehouse) = $70,000(.6) + 20,000(.4) = 50,000 Table 12.8 Decision Making with Probabilities Expected Opportunity Loss Copyright © 2010 Pearson Education, Inc. Publishing as Prentice Hall

18. 12-18 Exhibit 12.5 Expected Value Problems Solution with QM for Windows Copyright © 2010 Pearson Education, Inc. Publishing as Prentice Hall

19. 12-19 Exhibit 12.6 Expected Value Problems Solution with Excel and Excel QM (1 of 2) Copyright © 2010 Pearson Education, Inc. Publishing as Prentice Hall

20. 12-20 Expected Value Problems Solution with Excel and Excel QM (2 of 2) Copyright © 2010 Pearson Education, Inc. Publishing as Prentice Hall Exhibit 12.7

21. 12-21 ■The expected value of perfect information (EVPI) is the maximum amount a decision maker would pay for additional information. ■EVPI equals the expected value given perfect information minus the expected value without perfect information. ■EVPI equals the expected opportunity loss (EOL) for the best decision. Decision Making with Probabilities Expected Value of Perfect Information Copyright © 2010 Pearson Education, Inc. Publishing as Prentice Hall

22. 12-22 Table 12.9 Payoff Table with Decisions, Given Perfect Information Decision Making with Probabilities EVPI Example (1 of 2) Copyright © 2010 Pearson Education, Inc. Publishing as Prentice Hall

23. 12-23 ■Decision with perfect information: $100,000(.60) + 30,000(.40) = $72,000 ■Decision without perfect information: EV(office) = $100,000(.60) - 40,000(.40) = $44,000 EVPI = $72,000 - 44,000 = $28,000 EOL(office) = $0(.60) + 70,000(.4) = $28,000 Decision Making with Probabilities EVPI Example (2 of 2) Copyright © 2010 Pearson Education, Inc. Publishing as Prentice Hall

24. 12-24 Exhibit 12.8 Decision Making with Probabilities EVPI with QM for Windows Copyright © 2010 Pearson Education, Inc. Publishing as Prentice Hall

25. 12-25 A decision tree is a diagram consisting of decision nodes (represented as squares), probability nodes (circles), and decision alternatives (branches). Table 12.10 Payoff Table for Real Estate Investment Example Decision Making with Probabilities Decision Trees (1 of 4) Copyright © 2010 Pearson Education, Inc. Publishing as Prentice Hall

26. 12-26 Figure 12.2 Decision Tree for Real Estate Investment Example Decision Making with Probabilities Decision Trees (2 of 4) Copyright © 2010 Pearson Education, Inc. Publishing as Prentice Hall

27. 12-27 ■The expected value is computed at each probability node: EV(node 2) =.60($50,000) +.40(30,000) = $42,000 EV(node 3) =.60($100,000) +.40(-40,000) = $44,000 EV(node 4) =.60($30,000) +.40(10,000) = $22,000 ■Branches with the greatest expected value are selected. Decision Making with Probabilities Decision Trees (3 of 4) Copyright © 2010 Pearson Education, Inc. Publishing as Prentice Hall

28. 12-28 Figure 12.3 Decision Tree with Expected Value at Probability Nodes Decision Making with Probabilities Decision Trees (4 of 4) Copyright © 2010 Pearson Education, Inc. Publishing as Prentice Hall

29. 12-29 Exhibit 12.9 Decision Making with Probabilities Decision Trees with QM for Windows Copyright © 2010 Pearson Education, Inc. Publishing as Prentice Hall

30. 12-30 Decision Making with Probabilities Decision Trees with Excel and TreePlan (1 of 4) Copyright © 2010 Pearson Education, Inc. Publishing as Prentice Hall Exhibit 12.10

31. 12-31 Exhibit 12.11 Decision Making with Probabilities Decision Trees with Excel and TreePlan (2 of 4) Copyright © 2010 Pearson Education, Inc. Publishing as Prentice Hall

32. 12-32 Exhibit 12.12 Decision Making with Probabilities Decision Trees with Excel and TreePlan (3 of 4) Copyright © 2010 Pearson Education, Inc. Publishing as Prentice Hall

33. 12-33 Exhibit 12.13 Decision Making with Probabilities Decision Trees with Excel and TreePlan (4 of 4) Copyright © 2010 Pearson Education, Inc. Publishing as Prentice Hall

34. 12-34 Decision Making with Probabilities Sequential Decision Trees (1 of 4) ■A sequential decision tree is used to illustrate a situation requiring a series of decisions. ■Used where a payoff table, limited to a single decision, cannot be used. ■Real estate investment example modified to encompass a ten- year period in which several decisions must be made: Copyright © 2010 Pearson Education, Inc. Publishing as Prentice Hall

35. 12-35 Figure 12.4 Sequential Decision Tree Decision Making with Probabilities Sequential Decision Trees (2 of 4) Copyright © 2010 Pearson Education, Inc. Publishing as Prentice Hall

36. 12-36 Decision Making with Probabilities Sequential Decision Trees (3 of 4) ■Decision is to purchase land; highest net expected value ($1,160,000). ■Payoff of the decision is $1,160,000. Copyright © 2010 Pearson Education, Inc. Publishing as Prentice Hall

37. 12-37 Figure 12.5 Sequential Decision Tree with Nodal Expected Values Decision Making with Probabilities Sequential Decision Trees (4 of 4) Copyright © 2010 Pearson Education, Inc. Publishing as Prentice Hall

38. 12-38 Exhibit 12.14 Sequential Decision Tree Analysis Solution with QM for Windows Copyright © 2010 Pearson Education, Inc. Publishing as Prentice Hall

39. 12-39 Exhibit 12.15 Sequential Decision Tree Analysis Solution with Excel and TreePlan Copyright © 2010 Pearson Education, Inc. Publishing as Prentice Hall

40. 12-40 ■Bayesian analysis uses additional information to alter the marginal probability of the occurrence of an event. ■In real estate investment example, using expected value criterion, best decision was to purchase office building with expected value of $444,000, and EVPI of $28,000. Table 12.11 Decision Analysis with Additional Information Bayesian Analysis (1 of 3) Copyright © 2010 Pearson Education, Inc. Publishing as Prentice Hall

41. 12-41 ■A conditional probability is the probability that an event will occur given that another event has already occurred. ■Economic analyst provides additional information for real estate investment decision, forming conditional probabilities: g = good economic conditions p = poor economic conditions P = positive economic report N = negative economic report P(P  g) =.80P(N  G) =.20 P(P  p) =.10P(N  p) =.90 Decision Analysis with Additional Information Bayesian Analysis (2 of 3) Copyright © 2010 Pearson Education, Inc. Publishing as Prentice Hall

42. 12-42 ■A posterior probability is the altered marginal probability of an event based on additional information. ■Prior probabilities for good or poor economic conditions in real estate decision: P(g) =.60; P(p) =.40 ■Posterior probabilities by Bayes’ rule: (g  P) = P(P  G)P(g)/[P(P  g)P(g) + P(P  p)P(p)] = (.80)(.60)/[(.80)(.60) + (.10)(.40)] =.923 ■Posterior (revised) probabilities for decision: P(g  N) =.250P(p  P) =.077P(p  N) =.750 Decision Analysis with Additional Information Bayesian Analysis (3 of 3) Copyright © 2010 Pearson Education, Inc. Publishing as Prentice Hall

43. 12-43 Decision Analysis with Additional Information Decision Trees with Posterior Probabilities (1 of 4) Decision tree with posterior probabilities differ from earlier versions in that: ■ Two new branches at beginning of tree represent report outcomes. ■ Probabilities of each state of nature are posterior probabilities from Bayes’ rule. Copyright © 2010 Pearson Education, Inc. Publishing as Prentice Hall

44. 12-44 Figure 12.6 Decision Tree with Posterior Probabilities Decision Analysis with Additional Information Decision Trees with Posterior Probabilities (2 of 4) Copyright © 2010 Pearson Education, Inc. Publishing as Prentice Hall

45. 12-45 Decision Analysis with Additional Information Decision Trees with Posterior Probabilities (3 of 4) EV (apartment building) = $50,000(.923) + 30,000(.077) = $48,460 EV (strategy) = $89,220(.52) + 35,000(.48) = $63,194 Copyright © 2010 Pearson Education, Inc. Publishing as Prentice Hall

46. 12-46 Figure 12.7 Decision Tree Analysis Decision Analysis with Additional Information Decision Trees with Posterior Probabilities (4 of 4) Copyright © 2010 Pearson Education, Inc. Publishing as Prentice Hall

47. 12-47 Table 12.12 Computation of Posterior Probabilities Decision Analysis with Additional Information Computing Posterior Probabilities with Tables Copyright © 2010 Pearson Education, Inc. Publishing as Prentice Hall

48. 12-48 Decision Analysis with Additional Information Computing Posterior Probabilities with Excel Exhibit 12.16 Copyright © 2010 Pearson Education, Inc. Publishing as Prentice Hall

49. 12-49 ■The expected value of sample information (EVSI) is the difference between the expected value with and without information: For example problem, EVSI = $63,194 - 44,000 = $19,194 ■The efficiency of sample information is the ratio of the expected value of sample information to the expected value of perfect information: efficiency = EVSI /EVPI = $19,194/ 28,000 =.68 Decision Analysis with Additional Information Expected Value of Sample Information Copyright © 2010 Pearson Education, Inc. Publishing as Prentice Hall

50. 12-50 Table 12.13 Payoff Table for Auto Insurance Example Decision Analysis with Additional Information Utility (1 of 2) Copyright © 2010 Pearson Education, Inc. Publishing as Prentice Hall

51. 12-51 Expected Cost (insurance) =.992($500) +.008(500) = $500 Expected Cost (no insurance) =.992($0) +.008(10,000) = $80 Decision should be do not purchase insurance, but people almost always do purchase insurance. ■Utility is a measure of personal satisfaction derived from money. ■Utiles are units of subjective measures of utility. ■Risk averters forgo a high expected value to avoid a low- probability disaster. ■Risk takers take a chance for a bonanza on a very low- probability event in lieu of a sure thing. Decision Analysis with Additional Information Utility (2 of 2) Copyright © 2010 Pearson Education, Inc. Publishing as Prentice Hall

52. 12-52 Decision Analysis Example Problem Solution (1 of 9) Copyright © 2010 Pearson Education, Inc. Publishing as Prentice Hall

53. 12-53 Decision Analysis Example Problem Solution (2 of 9) a.Determine the best decision without probabilities using the 5 criteria of the chapter. b.Determine best decision with probabilities assuming.70 probability of good conditions,.30 of poor conditions. Use expected value and expected opportunity loss criteria. c.Compute expected value of perfect information. d.Develop a decision tree with expected value at the nodes. e.Given following, P(P  g) =.70, P(N  g) =.30, P(P  p) = 20, P(N  p) =.80, determine posterior probabilities using Bayes’ rule. f.Perform a decision tree analysis using the posterior probability obtained in part e. Copyright © 2010 Pearson Education, Inc. Publishing as Prentice Hall

54. 12-54 Step 1 (part a): Determine decisions without probabilities. Maximax Decision: Maintain status quo DecisionsMaximum Payoffs Expand $800,000 Status quo1,300,000 (maximum) Sell 320,000 Maximin Decision: Expand DecisionsMinimum Payoffs Expand$500,000 (maximum) Status quo-150,000 Sell 320,000 Decision Analysis Example Problem Solution (3 of 9) Copyright © 2010 Pearson Education, Inc. Publishing as Prentice Hall

55. 12-55 Minimax Regret Decision: Expand DecisionsMaximum Regrets Expand$500,000 (minimum) Status quo650,000 Sell 980,000 Hurwicz (  =.3) Decision: Expand Expand $800,000(.3) + 500,000(.7) = $590,000 Status quo$1,300,000(.3) - 150,000(.7) = $285,000 Sell $320,000(.3) + 320,000(.7) = $320,000 Decision Analysis Example Problem Solution (4 of 9) Copyright © 2010 Pearson Education, Inc. Publishing as Prentice Hall

56. 12-56 Equal Likelihood Decision: Expand Expand $800,000(.5) + 500,000(.5) = $650,000 Status quo $1,300,000(.5) - 150,000(.5) = $575,000 Sell $320,000(.5) + 320,000(.5) = $320,000 Step 2 (part b): Determine Decisions with EV and EOL. Expected value decision: Maintain status quo Expand $800,000(.7) + 500,000(.3) = $710,000 Status quo $1,300,000(.7) - 150,000(.3) = $865,000 Sell $320,000(.7) + 320,000(.3) = $320,000 Decision Analysis Example Problem Solution (5 of 9) Copyright © 2010 Pearson Education, Inc. Publishing as Prentice Hall

57. 12-57 Expected opportunity loss decision: Maintain status quo Expand $500,000(.7) + 0(.3) = $350,000 Status quo 0(.7) + 650,000(.3) = $195,000 Sell $980,000(.7) + 180,000(.3) = $740,000 Step 3 (part c): Compute EVPI. EV given perfect information = 1,300,000(.7) + 500,000(.3) = $1,060,000 EV without perfect information = $1,300,000(.7) - 150,000(.3) = $865,000 EVPI = $1.060,000 - 865,000 = $195,000 Decision Analysis Example Problem Solution (6 of 9) Copyright © 2010 Pearson Education, Inc. Publishing as Prentice Hall

58. 12-58 Step 4 (part d): Develop a decision tree. Decision Analysis Example Problem Solution (7 of 9) Copyright © 2010 Pearson Education, Inc. Publishing as Prentice Hall

59. 12-59 Step 5 (part e): Determine posterior probabilities. P(g  P) = P(P  g)P(g)/[P(P  g)P(g) + P(P  p)P(p)] = (.70)(.70)/[(.70)(.70) + (.20)(.30)] =.891 P(p  P) =.109 P(g  N) = P(N  g)P(g)/[P(N  g)P(g) + P(N  p)P(p)] = (.30)(.70)/[(.30)(.70) + (.80)(.30)] =.467 P(p  N) =.533 Decision Analysis Example Problem Solution (8 of 9) Copyright © 2010 Pearson Education, Inc. Publishing as Prentice Hall

60. 12-60 Step 6 (part f): Decision tree analysis. Decision Analysis Example Problem Solution (9 of 9) Copyright © 2010 Pearson Education, Inc. Publishing as Prentice Hall

61. 12-61 Copyright © 2010 Pearson Education, Inc. Publishing as Prentice Hall