Quantitative Analysis for Management Chapter 4 Decision Trees

Chapter Outline 4. 1 Introduction 4. 2 Decision Trees 4. 3 How Probability Values

Learning Objectives Students will be able to: § Develop accurate and useful decision trees

Introduction Decision trees enable one to look at decisions: ¨ with many alternatives and

Decision Trees A graphical representation where: na decision node from which one of several

Thompson’s Decision Tree Fig. 4. 1 A Decision Node A State of Nature Node

Five Steps to Decision Tree Analysis ¨ Define the problem ¨ Structure or draw

Thompson’s Decision Tree Fig. 4. 2 A State of Nature Node A Decision Node

Example: Using Decision Tree Analysis on R&D Projects To accompany Quantitative Analysis for Management,

Thompson’s Decision Tree Fig. 4. 3 To accompany Quantitative Analysis for Management, 7 e

Thompson’s Decision Tree Fig. 4. 4 To accompany Quantitative Analysis for Management, 7 e

Thompson Decision Tree Problem Using QM for Windows To accompany Quantitative Analysis for Management,

Thompson Decision Tree Problem using Excel To accompany Quantitative Analysis for Management, 7 e

Expected Value of Sample Information EVSI = Expected value of best decision with sample

Estimating Probability Values by Bayesian Analysis ¨ Management experience or intuition ¨ History ¨

Table 4. 1 To accompany Quantitative Analysis for Management, 7 e by (Render/Stair 4

Table 4. 2 Probability Revisions Given a Positive Survey Conditional Posterior Probability State P(Survey

Table 4. 3 Probability Revisions Given a Negative Survey Conditional Probability State P(Survey of

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Quantitative Analysis for Management Chapter 4 Decision Trees To accompany Quantitative Analysis for Management, 7 e by (Render/Stair 4 -1 1

Chapter Outline 4. 1 Introduction 4. 2 Decision Trees 4. 3 How Probability Values Are Estimated by Bayesian Analysis To accompany Quantitative Analysis for Management, 7 e by (Render/Stair 4 -2 2

Learning Objectives Students will be able to: § Develop accurate and useful decision trees § Revise probability estimates using Bayesian Analysis To accompany Quantitative Analysis for Management, 7 e by (Render/Stair 4 -3 3

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, 7 e by (Render/Stair 4 -4 4

Decision Trees A graphical representation where: na 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, 7 e by (Render/Stair 4 -5 5

Thompson’s Decision Tree Fig. 4. 1 A Decision Node A State of Nature Node 1 ct nt u tr Pla s n Co arge L Construct Small Plant 2 Do No thi ng To accompany Quantitative Analysis for Management, 7 e by (Render/Stair 4 -6 Favorable Market Unfavorable Market 6

Five Steps to Decision 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. To accompany Quantitative Analysis for Management, 7 e by (Render/Stair 4 -7 7

Thompson’s Decision Tree Fig. 4. 2 A State of Nature Node A Decision Node Favorable (0. 5) Market $200, 000 1 ct nt EMV Unfavorable (0. 5) -$180, 000 u r t a ns e Pl =$10, 000 Market o C arg Favorable (0. 5) L Construct $100, 000 Market Small Plant 2 EMV Do Unfavorable (0. 5) -$20, 000 No Market thi =$40, 000 ng 0 To accompany Quantitative Analysis for Management, 7 e by (Render/Stair 4 -8 8

Example: Using Decision Tree Analysis on R&D Projects To accompany Quantitative Analysis for Management, 7 e by (Render/Stair 4 -9 9

Thompson’s Decision Tree Fig. 4. 3 To accompany Quantitative Analysis for Management, 7 e by (Render/Stair 4 -10 10

Thompson’s Decision Tree Fig. 4. 4 To accompany Quantitative Analysis for Management, 7 e by (Render/Stair 4 -11 11

Thompson Decision Tree Problem Using QM for Windows To accompany Quantitative Analysis for Management, 7 e by (Render/Stair 4 -12 12

Thompson Decision Tree Problem using Excel To accompany Quantitative Analysis for Management, 7 e by (Render/Stair 4 -13 13

Expected Value of Sample Information EVSI = Expected value of best decision with sample information, assuming no cost to gather it To accompany Quantitative Analysis for Management, 7 e by (Render/Stair 4 -14 Expected value of best decision without sample information 14

Estimating Probability Values by Bayesian Analysis ¨ Management experience or intuition ¨ History ¨ Existing data ¨ Need to be able to revise probabilities based upon new data Bayes Theorem Prior probabilities To accompany Quantitative Analysis for Management, 7 e by (Render/Stair Posterior probabilities New data 4 -15 15

Table 4. 1 To accompany Quantitative Analysis for Management, 7 e by (Render/Stair 4 -16 16

Table 4. 2 Probability Revisions Given a Positive Survey Conditional Posterior Probability State P(Survey Prior Joint of positive|State of Probability 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 1. 00 To accompany Quantitative Analysis for Management, 7 e by (Render/Stair 4 -17 17

Table 4. 3 Probability Revisions Given a Negative Survey Conditional Probability State P(Survey of negative|State Nature of Nature) FM 0. 30 UM 0. 80 Posterior Probability Prior Joint Probability * 0. 50 0. 15 * 0. 50 0. 40 0. 55 To accompany Quantitative Analysis for Management, 7 e by (Render/Stair 4 -18 18 0. 15 = 0. 27 0. 55 0. 40 = 0. 73 0. 55 1. 00