1 / 28

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.

tender
Télécharger la présentation

Quantitative Analysis for Management

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  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

More Related