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Quantitative Analysis Quantitative Analysis for Managementfor Management

Chapter 4Chapter 4Decision Trees Decision Trees

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Chapter OutlineChapter Outline4.1 Introduction

4.2 Decision Trees

4.3 How Probability Values Are Estimated by Bayesian Analysis

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Learning ObjectivesLearning ObjectivesStudents will be able to:

Develop accurate and useful decision treesRevise probability estimates using Bayesian

Analysis

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IntroductionIntroductionDecision treesDecision trees enable one to look at

decisions: with many alternativesalternatives and states of states of

naturenature which must be made in sequence

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Decision TreesDecision TreesA 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

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Thompson’s Decision Tree Thompson’s Decision Tree Fig. 4.1Fig. 4.1

1

2

A Decision A Decision NodeNode

A State of A State of Nature NodeNature Node

Favorable Market

Unfavorable Market

Favorable Market

Unfavorable Market

Construct

Large Plant

Construct Small PlantDo Nothing

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Five Steps toFive Steps toDecision Tree AnalysisDecision 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.

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Thompson’s Decision Tree Thompson’s Decision Tree Fig. 4.2Fig. 4.2

1

2

A Decision A Decision NodeNode

A State of A State of Nature NodeNature Node Favorable (0.5)

Market

Unfavorable (0.5) MarketFavorable (0.5) Market

Unfavorable (0.5) Market

Construct

Large Plant

Construct Small PlantDo Nothing

$200,000$200,000

-$180,000-$180,000

$100,000$100,000

-$20,000-$20,000

00

EMV EMV =$40,000=$40,000

EMVEMV=$10,000=$10,000

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Example: Using Decision Tree Example: Using Decision Tree Analysis on R&D ProjectsAnalysis on R&D Projects

Define problem Discovery of a new, unpatentable processDevelop model Traditional decision tree with expected net

present values (ENPV) as outcomesAcquire data Collected both probability and monetary

values: technical success, significantmarket, commercial success

Develop solution Traditional decision tree analysisTest solution Analyzed risks of the processAnalyze results ENPV was $3.2 millionImplement results Decision made to investigate further.

Field testing resulted in cancellation

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Thompson’s Decision TreeThompson’s Decision TreeFig. 4.3Fig. 4.3

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Thompson’s Decision TreeThompson’s Decision TreeFig. 4.4Fig. 4.4

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Thompson Decision Tree Problem Thompson Decision Tree Problem Using QM for WindowsUsing QM for Windows

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Thompson Decision Tree Thompson Decision Tree Problem using ExcelProblem using Excel

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Expected Value of Sample Expected Value of Sample InformationInformation

Expected value of best decision withwith sample information, assuming no cost to gather it

Expected value of best decision withoutwithout sample information

EVSIEVSI =

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Estimating Probability Estimating Probability Values by Bayesian AnalysisValues by Bayesian Analysis

Management experience or intuition History Existing data

Need to be able to reviserevise probabilities based upon new data

Priorprobabilities New data Posterior

probabilities

Bayes Theorem

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Table 4.1Table 4.1Market Survey Reliability in Predicting ActualStates of Nature

Actual States of Nature

Result of Survey FavorableMarket (FM)

UnfavorableMarket (UM)

Positive (predictsfavorable marketfor product)

P(surveypositive|FM) =0.70

P(surveypositive|UM) =0.20

Negative (predictsunfavorablemarket forproduct)

P(surveynegative|FM) =0.30

P(surveynegative|UM) =0.80

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Table 4.2Table 4.2Probability Revisions Given a Positive Survey

ConditionalProbability

PosteriorProbability

StateofNature

P(Surveypositive|State ofNature)

PriorProbability

JointProbability

FM 0.70 * 0.50 0.350.450.35 = 0.78

UM 0.20 * 0.500.450.10 0.10 = 0.22

0.45 1.00

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Table 4.3Table 4.3Probability Revisions Given a Negative Survey

ConditionalProbability

PosteriorProbability

Stateof

Nature

P(Surveynegative|Stateof Nature)

PriorProbability

JointProbability

FM 0.30 * 0.50 0.150.550.15 = 0.27

UM 0.80 * 0.50 0.400.550.40 = 0.73

0.55 1.00