1. To accompany Quantitative Analysis for Management, 8e by Render/Stair/Hanna 4-1 © 2003 by Prentice Hall, Inc. Upper Saddle River, NJ 07458 PERTEMUAN 13

2. To accompany Quantitative Analysis for Management, 8e by Render/Stair/Hanna 4-2 © 2003 by Prentice Hall, Inc. Upper Saddle River, NJ 07458 Decision Trees and Utility Theory

3. To accompany Quantitative Analysis for Management, 8e by Render/Stair/Hanna 4-3 © 2003 by Prentice Hall, Inc. Upper Saddle River, NJ 07458 Learning Objectives Students will be able to: Develop accurate and useful decision trees Revise probability estimates using Bayesian Analysis Understand the importance and use of utility theory in decision making Use computers to solve more complex decision problems

4. To accompany Quantitative Analysis for Management, 8e by Render/Stair/Hanna 4-4 © 2003 by Prentice Hall, Inc. Upper Saddle River, NJ 07458 Chapter Outline 4.1 Introduction 4.2 Decision Trees 4.3 How Probability Values Are Estimated by Bayesian Analysis 4.4 Utility Theory 4.5 Sensitivity Analysis

5. To accompany Quantitative Analysis for Management, 8e by Render/Stair/Hanna 4-5 © 2003 by Prentice Hall, Inc. Upper Saddle River, NJ 07458 Introduction Decision trees enable one to look at decisions: with many alternatives and states of nature which must be made in sequence

6. To accompany Quantitative Analysis for Management, 8e by Render/Stair/Hanna 4-6 © 2003 by Prentice Hall, Inc. Upper Saddle River, NJ 07458 Decision Trees A graphical representation where: a decision node from which one of several alternatives may be chosen l a state-of-nature node out of which one state of nature will occur

7. To accompany Quantitative Analysis for Management, 8e by Render/Stair/Hanna 4-7 © 2003 by Prentice Hall, Inc. Upper Saddle River, NJ 07458 Thompson’s Decision Tree Fig. 4.1 1 2 A Decision Node A State of Nature Node Favorable Market Unfavorable Market Favorable Market Unfavorable Market Construct Large Plant Construct Small Plant Do Nothing

8. To accompany Quantitative Analysis for Management, 8e by Render/Stair/Hanna 4-8 © 2003 by Prentice Hall, Inc. Upper Saddle River, NJ 07458 Five Steps to Decision Tree Analysis 1.Define the problem 2.Structure or draw the decision tree 3.Assign probabilities to the states of nature 4.Estimate payoffs for each possible combination of alternatives and states of nature 5.Solve the problem by computing expected monetary values (EMVs) for each state of nature node.

9. To accompany Quantitative Analysis for Management, 8e by Render/Stair/Hanna 4-9 © 2003 by Prentice Hall, Inc. Upper Saddle River, NJ 07458 Thompson’s Decision Tree Fig. 4.2 A Decision Node A State of Nature Node Favorable Market (0.5) Unfavorable Market (0.5) Favorable Market (0.5) Unfavorable Market (0.5) Construct Large Plant Construct Small Plant Do Nothing $200,000 -$180,000 $100,000 -$20,000 0 EMV =$40,000 EMV =$10,000 1 2

10. To accompany Quantitative Analysis for Management, 8e by Render/Stair/Hanna 4-10 © 2003 by Prentice Hall, Inc. Upper Saddle River, NJ 07458 Decision Tree Analysis on R&D Projects

11. To accompany Quantitative Analysis for Management, 8e by Render/Stair/Hanna 4-11 © 2003 by Prentice Hall, Inc. Upper Saddle River, NJ 07458 Thompson’s Decision Tree -Fig. 4.3

12. To accompany Quantitative Analysis for Management, 8e by Render/Stair/Hanna 4-12 © 2003 by Prentice Hall, Inc. Upper Saddle River, NJ 07458 Thompson’s Decision Tree -Fig. 4.4

13. To accompany Quantitative Analysis for Management, 8e by Render/Stair/Hanna 4-13 © 2003 by Prentice Hall, Inc. Upper Saddle River, NJ 07458 Thompson Decision Tree Problem Using QM for Windows

14. To accompany Quantitative Analysis for Management, 8e by Render/Stair/Hanna 4-14 © 2003 by Prentice Hall, Inc. Upper Saddle River, NJ 07458 Thompson Decision Tree Problem using Excel

15. To accompany Quantitative Analysis for Management, 8e by Render/Stair/Hanna 4-15 © 2003 by Prentice Hall, Inc. Upper Saddle River, NJ 07458 Expected Value of Sample Information Expected value of best decision with sample information, assuming no cost to gather it Expected value of best decision without sample information EVSI =

16. To accompany Quantitative Analysis for Management, 8e by Render/Stair/Hanna 4-16 © 2003 by Prentice Hall, Inc. Upper Saddle River, NJ 07458 Estimating Probability Values by Bayesian Analysis Management experience or intuition History Existing data Need to be able to revise probabilities based upon new data Posterior probabilities Prior probabilities New data Bayes Theorem

17. To accompany Quantitative Analysis for Management, 8e by Render/Stair/Hanna 4-17 © 2003 by Prentice Hall, Inc. Upper Saddle River, NJ 07458 Table 4.1 Market Survey Reliability in Predicting Actual States of Nature Actual States of Nature Result of Survey Favorable Market (FM) Unfavorable Market (UM) Positive (predicts favorable market for product) P (survey positive|FM) = 0.70 P (survey positive|UM) = 0.20 Negative (predicts unfavorable market for product) P (survey negative|FM) = 0.30 P (survey negative|UM) = 0.80

18. To accompany Quantitative Analysis for Management, 8e by Render/Stair/Hanna 4-18 © 2003 by Prentice Hall, Inc. Upper Saddle River, NJ 07458 Table 4.2 Probability Revisions Given a Positive Survey Conditional Probability Posterior Probability State of Nature P(Survey positive|State of Nature Prior Probability Joint Probability FM 0.70* 0.50 0.35 0.45 0.35 = 0.78 UM 0.20 * 0.50 0.45 0.10 = 0.22 0.45 1.00

19. To accompany Quantitative Analysis for Management, 8e by Render/Stair/Hanna 4-19 © 2003 by Prentice Hall, Inc. Upper Saddle River, NJ 07458 Table 4.3 Probability Revisions Given a Negative Survey Conditional Probability Posterior Probability State of Nature P(Survey negative|State of Nature) Prior Probability Joint Probability FM 0.30* 0.50 0.15 0.55 0.15 = 0.27 UM0.80* 0.50 0.40 0.55 0.40 = 0.73 0.55 1.00

20. To accompany Quantitative Analysis for Management, 8e by Render/Stair/Hanna 4-20 © 2003 by Prentice Hall, Inc. Upper Saddle River, NJ 07458 Utility Theory $5,000,000 $0 $2,000,000 Accept Offer Reject Offer Heads (0.5) Tails (0.5)

21. To accompany Quantitative Analysis for Management, 8e by Render/Stair/Hanna 4-21 © 2003 by Prentice Hall, Inc. Upper Saddle River, NJ 07458 Utility Assessment Utility assessment assigns the worst outcome a utility of 0, and the best outcome, a utility of 1. A standard gamble is used to determine utility values. When you are indifferent, the utility values are equal.

22. To accompany Quantitative Analysis for Management, 8e by Render/Stair/Hanna 4-22 © 2003 by Prentice Hall, Inc. Upper Saddle River, NJ 07458 Standard Gamble for Utility Assessment - Fig. 4.6 Best outcome Utility = 1 Worst outcome Utility = 0 Other outcome Utility = ?? (p)(p) (1-p) Alternative 1 Alternative 2

23. To accompany Quantitative Analysis for Management, 8e by Render/Stair/Hanna 4-23 © 2003 by Prentice Hall, Inc. Upper Saddle River, NJ 07458 Figure 4.7 $10,000 U($10,000) = 1.0 0 U(0)=0 $5,000 U($5,000)=p =0.80 p= 0.80 (1-p)= 0.20 Invest in Real Estate Invest in Bank

24. To accompany Quantitative Analysis for Management, 8e by Render/Stair/Hanna 4-24 © 2003 by Prentice Hall, Inc. Upper Saddle River, NJ 07458 Utility Curve for Jane Dickson Fig. 4.8

25. To accompany Quantitative Analysis for Management, 8e by Render/Stair/Hanna 4-25 © 2003 by Prentice Hall, Inc. Upper Saddle River, NJ 07458 Preferences for Risk Fig. 4.9 Monetary Outcome Risk Avoider Risk Seeker Risk Indifference Utility

26. To accompany Quantitative Analysis for Management, 8e by Render/Stair/Hanna 4-26 © 2003 by Prentice Hall, Inc. Upper Saddle River, NJ 07458 Decision Facing Mark Simkin Fig. 4.10 Tack lands point up (0.45) Tack lands point down (0.55) $10,000 -$10,000 0 Alternative 1 Mark plays the game Alternative 2 Mark does not play the game

27. To accompany Quantitative Analysis for Management, 8e by Render/Stair/Hanna 4-27 © 2003 by Prentice Hall, Inc. Upper Saddle River, NJ 07458 Utility Curve for Mark Simkin Fig. 4.11

28. To accompany Quantitative Analysis for Management, 8e by Render/Stair/Hanna 4-28 © 2003 by Prentice Hall, Inc. Upper Saddle River, NJ 07458 Using Expected Utilities in Decision Making - Fig. 4.12 Tack lands point up (0.45) Tack lands point down (0.55) 0.30 0.05 0.15 Alternative 1 Play the game Alternative 2 Don’t play Utility

29. To accompany Quantitative Analysis for Management, 8e by Render/Stair/Hanna 4-29 © 2003 by Prentice Hall, Inc. Upper Saddle River, NJ 07458 Calculations for Thompson Lumber Sensitivity Analysis 2,400$104,000 ($2,000)($106,400)1) EMV(node   p )p(p  Equating the EMV(node 1) to the EMV of not conducting the survey, we have $104,000 $37,000 or $37,000$104,000 $40,000$2,400$104,000     p p p