Introduction to management science 10e by bernard taylor chapter 13

Decision Analysis

Chapter 12

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Chapter Topics

■ Components of Decision Making
■ Decision Making without Probabilities
■ Decision Making with Probabilities
■ Decision Analysis with Additional Information
■ Utility

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Decision Analysis
Components of Decision Making
■ A state of nature is an actual event that may
occur in the future.
■ A payoff table is a means of organizing a decision
situation, presenting the payoffs from different
decisions given the various states of nature.

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Table 12.1 Payoff
Table
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Decision Analysis
Decision Making Without
Probabilities

Figure 12.1

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Decision Analysis
Decision Making without
Probabilities

Table 12.2

Decision-Making Criteria
maximax
minimax

maximin

minimax regret

Hurwicz

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equal
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Decision Making without
Probabilities
In the maximax
criterion the decision maker
Maximax
Criterion

selects the decision that will result in the
maximum of maximum payoffs; an optimistic
criterion.

Table 12.3 Payoff Table Illustrating a
Maximax
Decision
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as

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Decision Making without
Probabilities
Maximin
Criterion
In the maximin
criterion the decision maker
selects the decision that will reflect the
maximum of the minimum payoffs; a
pessimistic criterion.

Table 12.4 Payoff Table Illustrating a
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Maximin Decision
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Decision Making without
Probabilities
Minimax
Regret
Criterion
Regret is the
difference

between the payoff
from the best decision and all other decision
payoffs.
The decision maker attempts to avoid regret by
selecting the decision alternative that
minimizes the maximum regret.

Table 12.6

Regret Table Illustrating the Minimax
Regret Decision

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Decision Making without
Probabilities
Hurwicz Criterion

The Hurwicz criterion is a compromise between
the maximax and maximin criterion.
A coefficient of optimism,  , is a measure of the
decision maker’s optimism.
The Hurwicz criterion multiplies the best payoff
by  and the worst payoff by 1-  ., for each
decision, and the best result is selected.
Decision

Apartment building
30,000(.6) = 38,000
Office building
= 16,000

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Warehouse

Values
$50,000(.4) +
$100,000(.4) - 40,000(.6)
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$30,000(.4) + 10,000(.6)


Decision Making without
Probabilities
Equal Likelihood Criterion

The equal likelihood ( or Laplace) criterion
multiplies the decision payoff for each state of
nature by an equal weight, thus assuming that
the states of nature are equally likely to occur.
Decision
Apartment building
30,000(.5) = 40,000
Office building
= 30,000

Warehouse
= 20,000

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Values
$50,000(.5) +
$100,000(.5) - 40,000(.5)
$30,000(.5) + 10,000(.5)

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Decision Making without
Probabilities
Summary of Criteria Results

■ A dominant decision is one that has a better
payoff than another decision under each state
of nature.
■ The appropriate criterion is dependent on the
“risk” personality and philosophy of the
decision maker.
Criterion
(Purchase)

Decision

Maximax

Office building

Maximin

Apartment building

Minimax regret
building
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Hurwicz

Apartment
Apartment building

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Decision Making without
Probabilities
Solution with QM for Windows (1 of
3)

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Exhibit
12.1

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Decision Making without
Probabilities
Solution with QM for Windows (2 of
3)

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Prentice Hall

Exhibit
12.2

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Decision Making without
Probabilities
Solution with QM for Windows (3 of
3)

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Prentice Hall

Exhibit
12.3
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Decision Making without
Probabilities
Solution with Excel

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Exhibit 12.4

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Decision Making with Probabilities
Expected Value
Expected value is computed by multiplying
each decision outcome under each state of
nature by the probability of its occurrence.

Table
12.7
30,000(.4)
=

EV(Apartment) = $50,000(.6) +
42,000
EV(Office) = $100,000(.6) - 40,000(.4) = 44,000
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= $30,000(.6) + 10,000(.4) =12Prentice EV(Warehouse)
Hall

Decision Making with Probabilities
Expected Opportunity Loss
■ The expected opportunity loss is the expected
value of the regret for each decision.
■ The expected value and expected opportunity
loss criterion result in the same decision.

EOL(Apartment) = $50,000(.6) + 0(.4) = 30,000 Table
EOL(Office) = $0(.6) + 70,000(.4) = 28,000
12.8
EOL(Warehouse) = $70,000(.6) + 20,000(.4) = 50,000
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Expected Value Problems
Solution with QM for Windows

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Exhibit
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Expected Value Problems

Solution with Excel and Excel QM (1
of 2)

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Exhibit
12.6

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Expected Value Problems
Solution with Excel and Excel QM (2
of 2)

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Exhibit 12.7
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Decision Making with Probabilities
Expected Value of Perfect
Information
■ The expected value of perfect information
(EVPI) is the maximum amount a decision
maker would pay for additional information.
■ EVPI equals the expected value given perfect

information minus the expected value without
perfect information.
■ EVPI equals the expected opportunity loss
(EOL) for the best decision.
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Decision Making with Probabilities
EVPI Example (1 of 2)

Table 12.9

Payoff Table with Decisions, Given Perfect
Information

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Decision Making with Probabilities
EVPI Example (2 of 2)
■ Decision with perfect information:
$100,000(.60) + 30,000(.40) = $72,000
■ Decision without perfect information:
EV(office) = $100,000(.60) - 40,000(.40) =

$44,000
EVPI = $72,000 - 44,000 = $28,000
EOL(office) = $0(.60) + 70,000(.4) = $28,000
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Decision Making with Probabilities
EVPI with QM for Windows

Exhibit 12.8
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Decision Making with Probabilities
Decision Trees (1 of 4)
A decision tree is a diagram consisting of
decision nodes (represented as squares),
probability nodes (circles), and decision
alternatives (branches).

Table 12.10 Payoff Table for Real Estate
Investment Example

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