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

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

To accompany Quantitative Analysis for Management, 8e by Render/Stair/Hanna 4-3 © 2003 by Prentice Hall, Inc. Upper Saddle River, NJ 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

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

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

To accompany Quantitative Analysis for Management, 8e by Render/Stair/Hanna 4-6 © 2003 by Prentice Hall, Inc. Upper Saddle River, NJ 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

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

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

To accompany Quantitative Analysis for Management, 8e by Render/Stair/Hanna 4-9 © 2003 by Prentice Hall, Inc. Upper Saddle River, NJ 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,

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

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

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

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

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

To accompany Quantitative Analysis for Management, 8e by Render/Stair/Hanna 4-15 © 2003 by Prentice Hall, Inc. Upper Saddle River, NJ 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 =

To accompany Quantitative Analysis for Management, 8e by Render/Stair/Hanna 4-16 © 2003 by Prentice Hall, Inc. Upper Saddle River, NJ 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

To accompany Quantitative Analysis for Management, 8e by Render/Stair/Hanna 4-17 © 2003 by Prentice Hall, Inc. Upper Saddle River, NJ 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

To accompany Quantitative Analysis for Management, 8e by Render/Stair/Hanna 4-18 © 2003 by Prentice Hall, Inc. Upper Saddle River, NJ 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* = 0.78 UM 0.20 * =

To accompany Quantitative Analysis for Management, 8e by Render/Stair/Hanna 4-19 © 2003 by Prentice Hall, Inc. Upper Saddle River, NJ 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* = 0.27 UM0.80* =

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

To accompany Quantitative Analysis for Management, 8e by Render/Stair/Hanna 4-21 © 2003 by Prentice Hall, Inc. Upper Saddle River, NJ 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.

To accompany Quantitative Analysis for Management, 8e by Render/Stair/Hanna 4-22 © 2003 by Prentice Hall, Inc. Upper Saddle River, NJ 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

To accompany Quantitative Analysis for Management, 8e by Render/Stair/Hanna 4-23 © 2003 by Prentice Hall, Inc. Upper Saddle River, NJ Figure 4.7 $10,000 U($10,000) = 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

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

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

To accompany Quantitative Analysis for Management, 8e by Render/Stair/Hanna 4-26 © 2003 by Prentice Hall, Inc. Upper Saddle River, NJ Decision Facing Mark Simkin Fig 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

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

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

To accompany Quantitative Analysis for Management, 8e by Render/Stair/Hanna 4-29 © 2003 by Prentice Hall, Inc. Upper Saddle River, NJ 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