Introduction to
Management Science
with Spreadsheets
Stevenson and Ozgur
First Edition
Part 3 Probabilistic Decision Models
Chapter 11
Decision Theory
McGraw-Hill/Irwin
Copyright © 2007 by The McGraw-Hill Companies, Inc. All rights reserved.
Learning Objectives
After completing this chapter, you should be able to:
1. Outline the characteristics of a decision theory
approach to decision making.
2. Describe and give examples of decisions under
certainty, risk, and complete uncertainty.
3. Make decisions using maximin, maximax, minimax
regret, Hurwicz, equally likely, and expected value
criteria and use Excel to solve problems involving
these techniques.
4. Use Excel to solve decision-making problems under
risk using the expected value criterion.
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McGraw-Hill/Irwin 11–2
Learning Objectives (cont’d)
After completing this chapter, you should be able to:
5. Develop decision trees that consist of a
combination of decision alternatives and events.
6. Use TreePlan to develop decision trees with Excel.
7. Determine if acquiring additional information in a
decision problem will be worth the cost.
8. Calculate revised probabilities manually and with
Excel.
9. Analyze the sensitivity of decisions to probability
estimates.
10. Describe how utilities can be used in lieu of
monetary value in making decisions.
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McGraw-Hill/Irwin 11–3
Decision Theory
• Decision theory problems are characterized by
the following:
1. A list of alternatives.
2. A list of possible future states of nature.
3. Payoffs associated with each alternative/state of
nature combination.
4. An assessment of the degree of certainty of possible
future events.
5. A decision criterion.
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McGraw-Hill/Irwin 11–4
Example 11-1
Suppose that a real estate developer must decide on a
plan for developing a certain piece of property. After
careful consideration, the developer has ruled out “do
nothing” and is left with the following list of acceptable
alternatives:
1. Residential proposal.
2. Commercial proposal #1.
3. Commercial proposal #2.
Suppose that the developer views the possibilities as
1. No shopping center.
2. Medium-sized shopping center.
3. Large shopping center.
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Table 11–1
General Format of a Decision Table
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McGraw-Hill/Irwin 11–6
Table 11–2
Payoff Table for Real Estate Developer
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McGraw-Hill/Irwin 11–7
Table 11–3
If It Is Known That No Shopping Center Will be Built, Only the
First Column Payoffs Would Be Relevant
Decision Making under Certainty
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McGraw-Hill/Irwin 11–8
Decision Making under
Complete Uncertainty
• Approaches to decision making under complete
uncertainty:
1.
2.
3.
4.
5.
Maximin
Maximax.
Minimax regret.
Hurwicz
Equal likelihood
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McGraw-Hill/Irwin 11–9
Table 11–4
Maximin Solution for Real Estate Problem
Maximin
The maximin strategy is a conservative one; it consists of identifying
the worst (minimum) payoff for each alternative and then selecting the
alternative that has the best (maximum) of the worst payoffs. In effect,
the decision maker is setting a floor for the potential payoff; the actual
payoff cannot be less than this amount.
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McGraw-Hill/Irwin 11–10
Table 11–5
Maximax Solution for Real Estate Problem
Maximax
The maximax approach is the opposite of the previous one: The
best payoff for each alternative is identified, and the alternative with
the maximum of these is the designated decision.
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McGraw-Hill/Irwin 11–11
Table 11–6
Payoff Table with Similar Maximum Payoffs
Minimax Regret
An approach that takes all payoffs into account. To use this approach,
it is necessary to develop an opportunity loss table that reflects the
difference between each payoff and the best possible payoff in a
column (i.e., given a state of nature). Hence, opportunity loss
amounts are found by identifying the best payoff in a column and then
subtracting each of the other values in the column from that payoff.
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McGraw-Hill/Irwin 11–12
Table 11–7
Opportunity Loss Table for Real Estate Problem
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McGraw-Hill/Irwin 11–13
Table 11–8
Identifying the Minimax Regret Alternative
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McGraw-Hill/Irwin 11–14
Table 11–9
Minimax Regret Can Lead in a Poor Decision
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McGraw-Hill/Irwin 11–15
The Hurwicz (Realism) Criterion (Weighted
Average or Realism Criterion)
• The approach offers the decision maker a compromise
between the maximax and the maximin criteria.
– Requires the decision maker to specify a degree of optimism, in
the form of a coefficient of optimism α, with possible values of
α ranging from 0 to 1.00.
– The closer the selected value of α is to 1.00, the more optimistic
the decision maker is, and the closer the value of α is to 0, the
more pessimistic the decision maker is.
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McGraw-Hill/Irwin 11–16
Table 11–10
Equal Likelihood Criterion
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McGraw-Hill/Irwin 11–17
Table 11–11
Summary of Methods for Decision Making under Complete
Uncertainty
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McGraw-Hill/Irwin 11–18
Exhibit 11-1
Using Excel to Make Decisions under Complete Uncertainty
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McGraw-Hill/Irwin 11–19
Decision Making under Risk
• Decision making under partial uncertainty
–Distinguished by the present of probabilities for the
occurrence of the various states of nature under
partial uncertainty.
–The term risk is often used in conjunction with partial
uncertainty.
• Sources of probabilities
–Subjective estimates
–Expert opinions
–Historical frequencies
Copyright © 2007 The McGraw-Hill Companies. All rights reserved.
McGraw-Hill/Irwin 11–20
Table 11–12
Real Estate Payoff Table with Probabilities
Expected Monetary Value (EMV) approach
Provides the decision maker with a value that represents an average
payoff for each alternative. The best alternative is, then, the one that
has the highest expected monetary value. The average or expected
payoff of each alternative is a weighted average: the state of nature
probabilities are used to weight the respective payoffs.
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McGraw-Hill/Irwin 11–21
Approaches to Incorporating Probabilities in
the Decision Making Process
• Expected Monetary Value (EMV) approach
– Provides the decision maker with a value that represents an
average payoff for each alternative.
• Expected Opportunity Loss (EOL)
– The opportunity losses for each alternative are weighted by the
probabilities of their respective states of nature to compute a
long-run average opportunity loss, and the alternative with the
smallest expected loss is selected as the best choice.
• Expected Value of Perfect Information (EVPI)
– A measure of the difference between the certain payoff that could
be realized under a condition of certainty and the expected payoff
under a condition involving risk.
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McGraw-Hill/Irwin 11–22
Exhibit 11-2
Using Excel to Make Decisions under Risk
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McGraw-Hill/Irwin 11–23
Figure 11–1
Decision Tree Format
Decision trees are used by decision
makers to obtain a visual portrayal of
decision alternatives and their
possible consequences.
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McGraw-Hill/Irwin 11–24
Figure 11–2
Decision Tree for Real Estate Developer Problem
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McGraw-Hill/Irwin 11–25
Figure 11–3
Real Estate Problem with a Second Possible Decision
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McGraw-Hill/Irwin 11–26
Exhibit 11–3
Initial TreePlan Dialog Box
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McGraw-Hill/Irwin 11–27
Exhibit 11–4
Decision Tree Initially Developed by TreePlan
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McGraw-Hill/Irwin 11–28
Exhibit 11–5
TreePlan Dialog Box to Add Branches, Decision Nodes,
or Events
Copyright © 2007 The McGraw-Hill Companies. All rights reserved.
McGraw-Hill/Irwin 11–29
Exhibit 11–6
Modified Decision Tree with Three Branches
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McGraw-Hill/Irwin 11–30
Exhibit 11–7
TreePlan Dialog Box to Add or Change Decision Nodes
or Events
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McGraw-Hill/Irwin 11–31
Exhibit 11–8
Modified Decision Tree with Three Branches and the Added
Event Node with Three Nodes
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McGraw-Hill/Irwin 11–32
Exhibit 11–9
Excel Solution to the Real Estate Developer Decision Tree
Problem
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McGraw-Hill/Irwin 11–33
Figure 11–4
Sequential Decision Tree for Unicom Inc.
(Example 11-3, part a)
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McGraw-Hill/Irwin 11–34
Exhibit 11–10
Excel Solution to the Unicom Inc. Sequential Decision Tree
Problem
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McGraw-Hill/Irwin 11–35
Figure 11–5
Conceptual Portrayal of Market Test Example
Copyright © 2007 The McGraw-Hill Companies. All rights reserved.
McGraw-Hill/Irwin 11–36
Test Market Payoffs
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McGraw-Hill/Irwin 11–37
Figure 11–6
Summary of Analysis of Market Test Example
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McGraw-Hill/Irwin 11–38
Table 11–13
Reliability of Market Test
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McGraw-Hill/Irwin 11–39
Table 11–14
Probability Calculations Given the Market Test Indicates a
Strong Market
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McGraw-Hill/Irwin 11–40
Table 11–15
Probability Calculations Given the Market Test Indicates a
Weak Market
Conditional probabilities express the reliability of
the sampling device (e.g., market test) given the
condition of actual market type.
Copyright © 2007 The McGraw-Hill Companies. All rights reserved.
McGraw-Hill/Irwin 11–41
Exhibit 11–11
Calculation of the Revised Probabilities for the Market Test
Example
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McGraw-Hill/Irwin 11–42
Figure 11–7
Format of Graph for Sensitivity Analysis
Sensitivity Analysis enables decision makers to identify a range
of probabilities over which a particular alternative would be optimal.
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McGraw-Hill/Irwin 11–43
Figure 11–8
The Expected Value Line for Alternative a.
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McGraw-Hill/Irwin 11–44
Figure 11–9
Example of Finding the Expected Value for Alternative a when
P(#2) Is .50
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McGraw-Hill/Irwin 11–45
Figure 11–10
All Three Alternatives Are Plotted on a Single Graph
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McGraw-Hill/Irwin 11–46
Figure 11–11
The Line with the Highest Expected Profit Is Optimal for a
Given Value of P(#2)
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McGraw-Hill/Irwin 11–47
Utility
• Utility (of a payoff)
– A measure of the personal satisfaction associated with a payoff.
• Risk
– A decision problem in which the states of nature have
probabilities associated with their occurrence.
• Risk Averters
– Individuals that avoid taking risks. The decision maker has less
utility for greater risk.
• Risk Takers
– Individuals that like taking risks and that have a greater utility for
the potential winnings even though their chances of winning are
very low.
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McGraw-Hill/Irwin 11–48
Figure 11–12
Converting P(#2) Ranges into P(#1) Ranges
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McGraw-Hill/Irwin 11–49
Exhibit 11–12
Solved Problem 1: Decision Making under Complete
Uncertainty—A Profit Maximization Problem (Part f)
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McGraw-Hill/Irwin 11–50
Exhibit 11–13
Solved Problem 2: Decision Making under Complete
Uncertainty—A Cost Minimization Problem (part f)
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McGraw-Hill/Irwin 11–51
Exhibit 11–14
Calculation of the Revised Probabilities and Expected Value of
Perfect Information for Solved Problem 3 (part c)
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McGraw-Hill/Irwin 11–52
Exhibit 11–15
Calculation of the Revised Probabilities for Solved Problem 5
(part c)
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McGraw-Hill/Irwin 11–53
Exhibit 11–16
TreePlan Dialog Box to Add Branches, Decision Nodes, or Events
Exhibit 11–17
TreePlan Dialog Box to Add or Change Decision Nodes or Events
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McGraw-Hill/Irwin 11–54
Exhibit 11–18
Decision Tree for Solved Problem 5 (part c)
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McGraw-Hill/Irwin 11–55