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Quantitative Analysis for Management

Quantitative Analysis for Management. Chapter 4 Decision Trees and Utility Theory. 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. Learning Objectives.

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Quantitative Analysis for Management

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  1. Quantitative Analysis for Management Chapter 4 Decision Trees and Utility Theory 4-1

  2. 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 4-2

  3. 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 4-3

  4. Introduction Decision trees enable one to look at decisions: • with many alternatives and states of nature • which must be made in sequence 4-4

  5. Decision Trees A graphical representation where: • a decision node from which one of several alternatives may be chosen • a state-of-nature node out of which one state of nature will occur 4-5

  6. Thompson’s Decision Tree Fig. 4.1 Favorable Market A State of Nature Node 1 Unfavorable Market Construct Large Plant A Decision Node Favorable Market Construct Small Plant 2 Unfavorable Market Do Nothing 4-6

  7. Five Steps toDecision Tree Analysis • Define the problem • Structure or draw the decision tree • Assign probabilities to the states of nature • Estimate payoffs for each possible combination of alternatives and states of nature • Solve the problem by computing expected monetary values (EMVs) for each state of nature node. 4-7

  8. Thompson’s Decision Tree Fig. 4.2 A State of Nature Node Favorable (0.5) Market $200,000 1 EMV =$10,000 Construct Large Plant -$180,000 Unfavorable (0.5) Market A Decision Node $100,000 Favorable (0.5) Market Construct Small Plant 2 EMV =$40,000 -$20,000 Unfavorable (0.5) Market Do Nothing 0 4-8

  9. Example: Using Decision Tree Analysis on R&D Projects 4-9

  10. Thompson’s Decision TreeFig. 4.3 4-10

  11. Thompson’s Decision TreeFig. 4.4 4-11

  12. Thompson Decision Tree Problem Using QM for Windows 4-12

  13. Thompson Decision Tree Problem using Excel 4-13

  14. Expected value of best decision with sample information, assuming no cost to gather it Expected value of best decision without sample information Expected Value of Sample Information EVSI= 4-14

  15. Estimating Probability Values by Bayesian Analysis Bayes Theorem Prior probabilities Posterior probabilities New data • Management experience or intuition • History • Existing data • Need to be able to revise probabilities based upon new data 4-15

  16. Table 4.1 4-16

  17. Table 4.2 Probability Revisions Given a Positive Survey Conditional Posterior Probability Probability State P(Survey Prior Joint of positive|State of Probability Probability Nature Nature) 0.35 FM 0.70 * 0.50 0.35 = 0.78 0.45 0.10 UM 0.20 * 0.50 0.10 = 0.22 0.45 0.45 1.00 4-17

  18. Table 4.3 Probability Revisions Given a Negative Survey Conditional Posterior Probability Probability State P(Survey Prior Joint of negative|State Probability Probability Nature of Nature) 0.15 FM 0.30 * 0.50 0.15 = 0.27 0.55 0.40 UM 0.80 * 0.50 0.40 = 0.73 0.55 0.55 1.00 4-18

  19. Utility Theory $2,000,000 Accept Offer $0 Heads (0.5) Reject Offer Tails (0.5) $5,000,000 4-19

  20. Utility Assessment • Utility assessment assigns the worst outcome a utility of 0, and the bestoutcome, a utility of 1. • A standard gamble is used to determine utility values. • When you are indifferent, the utility values are equal. 4-20

  21. Standard Gamble for Utility Assessment - Fig. 4.6 (p) Alternative 1 (1-p) Alternative 2 Best outcome Utility = 1 Worst outcome Utility = 0 Other outcome Utility = ?? 4-21

  22. Figure 4.7 p= 0.80 Invest in Real Estate (1-p)= 0.20 Invest in Bank $10,000 U($10,000) = 1.0 0 U(0)=0 $5,000 U($5,000)=p =0.80 4-22

  23. Utility Curve for Jane Dickson Fig. 4.8 4-23

  24. Preferences for RiskFig. 4.9 Risk Avoider Utility Risk Indifference Risk Seeker Monetary Outcome 4-24

  25. Decision Facing Mark SimkinFig. 4.10 Tack lands point up (0.45) $10,000 Alternative 1 Mark plays the game Tack lands point down (0.55) -$10,000 Mark does not play the game Alternative 2 0 4-25

  26. Utility Curve for Mark SimkinFig. 4.11 4-26

  27. Using Expected Utilities in Decision Making - Fig. 4.12 Utility Tack lands point up (0.45) 0.30 Alternative 1 Play the game Tack lands point down (0.55) 0.05 Don’t play Alternative 2 0.15 4-27

  28. Calculations for Thompson Lumber Sensitivity Analysis = + 1 - EMV(node 1) ($106,400) p ( p ) ($2,000) = + $104,000 p 2,400 + = $104,000 p $2,400 $40,000 = $104,000 p $37,000 or $37,000 = 0.36 = p $104,000 Equating the EMV(node 1) to the EMV of not conducting the survey, we have 4-28

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