Quantitative Analysis
for Management
Chapter 4
Decision Trees
To accompany Quantitative Analysis for
Management, 7e by (Render/Stair
4-1
© 2000 by Prentice Hall, Inc., Upper Saddle River,
N.J. 07458
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, 7e by (Render/Stair
4-2
© 2000 by Prentice Hall, Inc., Upper Saddle River,
N.J. 07458
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, 7e by (Render/Stair
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© 2000 by Prentice Hall, Inc., Upper Saddle River,
N.J. 07458
Introduction
Decision trees enable one to look at
decisions:
 with many alternatives and states of
nature
which must be made in sequence
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© 2000 by Prentice Hall, Inc., Upper Saddle River,
N.J. 07458
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
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© 2000 by Prentice Hall, Inc., Upper Saddle River,
N.J. 07458
Thompson’s Decision Tree
Fig. 4.1
A State of
Nature Node
Favorable Market
1
Unfavorable Market
A Decision
Node
Construct
Small Plant 2
Favorable Market
Unfavorable Market
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© 2000 by Prentice Hall, Inc., Upper Saddle River,
N.J. 07458
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, 7e by (Render/Stair
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© 2000 by Prentice Hall, Inc., Upper Saddle River,
N.J. 07458
Thompson’s Decision Tree
Fig. 4.2
A State of
Nature Node
A Decision
Node
Favorable (0.5)
Market
$200,000
1
EMV
Unfavorable (0.5) -$180,000
=$10,000 Market
Favorable (0.5)
$100,000
Construct
Market
Small Plant 2
EMV
Unfavorable (0.5) -$20,000
Market
=$40,000
0
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© 2000 by Prentice Hall, Inc., Upper Saddle River,
N.J. 07458
Example: Using Decision Tree
Analysis on R&D Projects
Define problem
Discovery of a new, unpatentable process
Develop model
Develop solution
Traditional decision tree with expected net
present values (ENPV) as outcomes
Collected both probability and monetary
values: technical success, significant
market, commercial success
Traditional decision tree analysis
Test solution
Analyzed risks of the process
Analyze results
ENPV was $3.2 million
Acquire data
Implement results Decision made to investigate further.
Field testing resulted in cancellation
To accompany Quantitative Analysis for
Management, 7e by (Render/Stair
4-9
© 2000 by Prentice Hall, Inc., Upper Saddle River,
N.J. 07458
Thompson’s Decision Tree
Fig. 4.3
To accompany Quantitative Analysis for
Management, 7e by (Render/Stair
4-10
© 2000 by Prentice Hall, Inc., Upper Saddle River,
N.J. 07458
Thompson’s Decision Tree
Fig. 4.4
To accompany Quantitative Analysis for
Management, 7e by (Render/Stair
4-11
© 2000 by Prentice Hall, Inc., Upper Saddle River,
N.J. 07458
Thompson Decision Tree Problem
Using QM for Windows
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Management, 7e by (Render/Stair
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© 2000 by Prentice Hall, Inc., Upper Saddle River,
N.J. 07458
Thompson Decision Tree
Problem using Excel
To accompany Quantitative Analysis for
Management, 7e by (Render/Stair
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© 2000 by Prentice Hall, Inc., Upper Saddle River,
N.J. 07458
Expected Value of Sample
Information
EVSI =
Expected value of
best decision
with sample
information,
assuming no
cost to gather it
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Management, 7e by (Render/Stair
4-14
Expected value of
best decision
without sample
information
© 2000 by Prentice Hall, Inc., Upper Saddle River,
N.J. 07458
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
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Management, 7e by (Render/Stair
New data
4-15
Posterior
probabilities
© 2000 by Prentice Hall, Inc., Upper Saddle River,
N.J. 07458
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)
Negative (predicts
unfavorable
market for
product)
P(survey
positive|FM) =
0.70
P(survey
negative|FM) =
0.30
P(survey
positive|UM) =
0.20
P(survey
negative|UM) =
0.80
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© 2000 by Prentice Hall, Inc., Upper Saddle River,
N.J. 07458
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
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© 2000 by Prentice Hall, Inc., Upper Saddle River,
N.J. 07458
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 Probability
* 0.50
0.15
* 0.50
0.40
0.55
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0.15
= 0.27
0.55
0.40
= 0.73
0.55
1.00
© 2000 by Prentice Hall, Inc., Upper Saddle River,
N.J. 07458