CD-ROM Chapter 17
Introduction to
Decision Analysis
Chapter 17 - Chapter Outcomes
After studying the material in this chapter, you
should be able to:
Describe
the decision-making environments of
certainty and uncertainty.
Construct both a payoff table and an opportunity
loss table.
Define the expected value criterion.
Apply the expected value criterion in decision
situations.
Compute the value of perfect information.
Chapter 17 - Chapter Outcomes
(continued)
After studying the material in this chapter, you
should be able to:
Develop a decision tree and explain how it can
aid decision making in an uncertain
environment.
Discuss the difference between risk seeking and
risk avoiding behavior.
Construct an individual risk preference function.
Decision-Making
Environments
Certainty refers to a decision
environment in which the results of
selecting each alternative are known
before the decision is made.
Decision-Making
Environments
Uncertainty refers to a decision
environment in which the decision
maker does not know what outcome will
occur when an alternative is selected.
Decision-Making
Environments
The goal of decision analysis is to focus
on making good decisions, which in the
long run should result in an increased
number of good outcomes.
Decision Criteria
The states of nature are the possible
outcomes in a decision situation
over which the decision maker has
no control.
Decision Criteria
A payoff is the outcome (profit or loss)
for any combination of alternative
states of nature. The outcomes of all
possible combinations of alternatives
and states of nature constitute a payoff
table.
Decision Criteria
(Table 17-2)
DEMAND (STATES OF NATURE)
Alternative
S11 Large Increase
S22 Moderate Increase
S33 Small Increase
A11 Large Investment
$6,000,000
$4,000,000
$-2,600,000
A22 Medium Investment
2,500,000
5,000,000
-1,000,000
A33 Small Investment
2,000,000
1,500,000
1,200,000
Fisher Fabrication Payoff Table
Decision Criteria
The maximax criterion is an optimistic
decision criterion for dealing with
uncertainty without using probability. For
each option, the decision maker finds the
maximum possible payoff and then selects
the option with the greatest maximum
payoff.
Decision Criteria
The maximin criterion is a pessimistic
(conservative) decision criterion for
dealing with uncertainty without using
probability. For each option, the decision
maker finds the minimum possible payoff
and then selects the option with the
greatest minimum payoff.
Decision Criteria
The opportunity loss is the difference
between the actual payoff that occurs
for a decision and the optimal payoff
for the same decision.
Decision Criteria
The minimax regret criterion is a decision
criterion that considers the costs of selecting the
“wrong” alternative. For each sate of nature, the
decision maker finds the difference between the
best payoff and each other alternative and uses
these values to construct an opportunity-loss
table. The decision maker then selects the
alternative with the minimum opportunity loss
(or regret).
Decision Criteria
(Table 17-3)
DEMAND (STATES OF NATURE)
Alternative
S11 Large Increase
A11 Large Investment
S22 Moderate Increase
S33 Small Increase
$0
$1,000,000
$3,800,000
A22 Medium Investment
3,500,000
0
2,200,000
A33 Small Investment
4,000,000
3,500,000
0
Fisher Fabrication Opportunity-Loss Table
Decision Criteria
(Table 17-4)
Alternative
MAXIMUM OPPORTUNITY LOSS, OR REGRET
A11 Large Investment
A22 Medium Investment
A33 Small Investment
$3,800,000
3,500,000 (smallest regret)
4,000,000
Fisher Fabrication Maximum Regret Table
Decision Criteria
The expected-value criterion is a decision
criterion that employs probability to
select the alternative that will produce the
greatest average payoff or minimum
average loss.
Decision Criteria
EXPECTED VALUE
k
E ( x)   xiP( xi )
where:
i 1
xi = The ith outcome of the specified alternative
measured in some units, such as dollars
P(xi) = The probability of outcome xi occurring
k = number of potential outcomes
and:
 P( x )  1.0
i
0.0  P( xi )  1.0
Decision Criteria
CLASSICAL PROBABILITY ASSESSMENT
P( x ) 
Number of ways x can occur
Total number of ways any outcome can occur
Decision Criteria
RELATIVE FREQUENCY OF OCCURRENCE
PROBABILITY
Number of times x occurs
P( x) 
n
where:
n  Number of observances
Decision Criteria
(Table 17-5)
MACHINE A
MACHINE B
Repair Cost
Probability
Repair Cost
Probability
$0
0.1
$0
0.2
1,000
0.5
1,000
0.3
5,000
0.3
5,000
0.4
10,000
0.1
10,000
0.1
Decision Criteria
(Table 17-6)
MACHINE A
MACHINE B
Repair Cost
Probability
xP(x)
Repair Cost
Probability
xP(x)
$0
0.1
$0
$0
0.2
$0
1,000
0.5
500
1,000
0.3
300
5,000
0.3
1,500
5,000
0.4
2,000
10,000
0.1
1,000
10,000
0.1
1,000
$3,000
Expected Repair Cost
Expected Repair Cost
$3,300
Decision-Tree Analysis
A decision tree is a diagram that illustrates
the correct ordering of actions and events
in a decision-analysis problem. Each act or
event is represented by a node on the
decision tree.
Decision-Tree Analysis
(Figure 17-1)
Don’t sign
Sign
Contract
Decision
Decision-Tree Analysis
(Figure 17-2)
Don’t sign
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Review
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Contract
Favorable
Review
Decision
Event
Decision-Tree Analysis
(Figure 17-3)
Don’t sign
Unfavorable
Review
Hardcover
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Contract
Favorable
Review
Paperback
Decision
Event
Decision
Decision-Tree Analysis
Don’t sign
(Figure 17-4)
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100,000 copies
Hardcover
Sign
Contract
1,000,000 copies
Favorable
Review
50,000 copies
Paperback
Decision
Event
Decision 1,500,000 copies
Event
Risk Preference Attitudes
A risk-neutral attitude refers to the
preference for risk under which the
alternative with the highest expected
payoff or lowest expected cost will be
selected.
Risk Preference Attitudes
(Figure 17-11)
Merger
Buy
$10
(0.5)
(0.5)
No Merger
-$5
Don’t Buy
Xircom Stock Purchase Example
$0
Risk Preference Attitudes
(Figure 17-12)
Merger
Buy
$100
(0.5)
(0.5)
No Merger
-$50
Don’t Buy
Xircom Stock Purchase Example
$0
Risk Preference Attitudes
(Figure 17-13)
Merger
Buy
$10,000
(0.5)
(0.5)
No Merger
-$5,000
Don’t Buy
Xircom Stock Purchase Example
$0
Risk Preference Attitudes
A risk-averse attitude refers to the
preference for risk such that the decision
maker could select an alternative with a
lower expected payoff in order to avoid the
possibility of an undesirable outcome.
Risk Preference Attitudes
Certainty equivalent is the value that
would make a decision maker indifferent
between taking an uncertain gamble
versus receiving that value instead of
taking the gamble.
Risk Preference Attitudes
A risk-seeking attitude refers to the
preference for risk such that the
decision maker could select an
alternative with a lower expected
payoff in hopes of achieving an
outcome with a more desirable
result.
Risk Preference Attitudes
The risk preference function is the
graph that describes a decision
maker’s preference for risk over the
range of possible payoffs.
Risk Preference Attitudes
A standard gamble approach is the
approach for assessing risk-preference
functions that involves setting up a series
of 50-50 gambles between two payoffs
and determining the certainty equivalent
for each gamble.
Risk Preference Attitudes
A preference quotient refers to the
measure of the relative utility for the
outcomes of a decision on a scale
between 0.0 and 1.0.
Risk Preference Attitudes
(Figure 17-16)
Play
End Values
q Values
$10,000
1.0
-$2,000
0.0
0.5
0.5
Don’t Play
CE = ?
Assessing the Risk-Preference Function:
Standard Gamble 1
Risk Preference Attitudes
(Figure 17-17)
Play
End Values
q Values
$10,000
1.0
$4,000
0.5
0.5
0.5
Don’t Play
CE = ?
Assessing the Risk-Preference Function:
Standard Gamble 2
Risk Preference Attitudes
(Figure 17-18)
Play
End Values
q Values
$4,000
0.5
-$2,000
0.0
0.5
0.5
Don’t Play
CE = ?
Assessing the Risk-Preference Function:
Standard Gamble 3
Risk Preference Attitudes
Risk premium is the difference between the
expected value of an event and the certainty
equivalent. The risk premium will be zero
for a risk-neutral decision maker, positive
for a risk-averse decision maker, and
negative for a risk-seeking decision maker.
Risk Preference Attitudes
(Figure 17-19)
1
0.75
0.50
0.25
-$2,000
0
$0
$2,000
$4,000 $6,000 $8,000 $10,000
Risk-Neutral Preference Function
Risk Preference Attitudes
(Figure 17-23)
1
0.75
0.50
0.25
-$2,000
0
$0
$2,000
$4,000 $6,000 $8,000 $10,000
Risk-Averse Preference Function
Risk Preference Attitudes
(Figure 17-26)
1
0.75
0.50
0.25
-$2,000
0
$0
$2,000
$4,000 $6,000 $8,000 $10,000
Risk-Seeking Preference Function
Key Terms
• Certainty
• Certainty Equivalent
• Decision Tree
• Expected Value
• Expected-Value
Criterion
• Maximax Criterion
• Maximin Criterion
• Minimax Regret
Criterion
• Opportunity Loss
• Payoff
• Preference Quotient
• Risk-Averse Attitude
• Risk-Neutral Attitude
• Risk-Preference
Function
• Risk Premium
• Risk-Seeking Attitude
Key Terms
(continued)
• Standard Gamble Approach
• State of Nature
• Uncertainty