Chapter 1 Supplement
Decision Analysis Support
Tools and Processes
Supplement 1-1
Decision Analysis
• Quantitative methods
• a set of tools for operations manager
• Decision analysis
• a set of quantitative decision-making
techniques for decision situations in which
uncertainty exists
• Example of an uncertain situation
• demand for a product may vary between 0 and 200
units, depending on the state of market
Copyright 2011 John Wiley & Sons, Inc.
Supplement 1-2
Decision Making Without Probabilities
• States of nature
• Events that may occur in the future
• Examples of states of nature:
• high or low demand for a product
• good or bad economic conditions
• Decision making under risk
• probabilities can be assigned to the occurrence of
states of nature in the future
• Decision making under uncertainty
• probabilities can NOT be assigned to the
occurrence of states of nature in the future
Copyright 2011 John Wiley & Sons, Inc.
Supplement 1-3
Payoff Table
• Payoff table
• method for organizing and illustrating payoffs from
different decisions given various states of nature
• Payoff
• outcome of a decision
Decision
1
2
Copyright 2011 John Wiley & Sons, Inc.
States Of Nature
a
b
Payoff 1a
Payoff 1b
Payoff 2a
Payoff 2b
Supplement 1-4
Decision Making Criteria Under
Uncertainty
• Maximax
• choose decision with the maximum of the
maximum payoffs
• Maximin
• choose decision with the maximum of the
minimum payoffs
• Minimax regret
• choose decision with the minimum of the
maximum regrets for each alternative
Copyright 2011 John Wiley & Sons, Inc.
Supplement 1-5
Decision Making Criteria Under
Uncertainty
• Hurwicz
• choose decision in which decision payoffs are
weighted by a coefficient of optimism, alpha
• coefficient of optimism is a measure of a
decision maker’s optimism, from 0 (completely
pessimistic) to 1 (completely optimistic)
• Equal likelihood (La Place)
• choose decision in which each state of nature is
weighted equally
Copyright 2011 John Wiley & Sons, Inc.
Supplement 1-6
Southern Textile Company
STATES OF NATURE
DECISION
Expand
Maintain status quo
Sell now
Copyright 2011 John Wiley & Sons, Inc.
Good Foreign
Poor Foreign
Competitive Conditions
Competitive Conditions
$ 800,000
1,300,000
320,000
$ 500,000
-150,000
320,000
Supplement 1-7
Maximax Solution
STATES OF NATURE
DECISION
Expand
Maintain status quo
Sell now
Expand:
Status quo:
Sell:
Good Foreign
Poor Foreign
Competitive Conditions
Competitive Conditions
$ 800,000
1,300,000
320,000
$ 500,000
-150,000
320,000
$800,000
1,300,000  Maximum
320,000
Decision: Maintain status quo
Copyright 2011 John Wiley & Sons, Inc.
Supplement 1-8
Maximin Solution
STATES OF NATURE
DECISION
Expand
Maintain status quo
Sell now
Expand:
Status quo:
Sell:
Copyright 2011 John Wiley & Sons, Inc.
Good Foreign
Poor Foreign
Competitive Conditions
Competitive Conditions
$ 800,000
1,300,000
320,000
$ 500,000
-150,000
320,000
$500,000  Maximum
-150,000
320,000
Decision: Expand
Supplement 1-9
Minimax Regret Solution
States of Nature
Good Foreign
Poor Foreign
Competitive Conditions
Competitive Conditions
$1,300,000 - 800,000 = 500,000
$500,000 - 500,000 = 0
1,300,000 - 1,300,000 = 0
500,000 - (-150,000)= 650,000
1,300,000 - 320,000 = 980,000
500,000 - 320,000= 180,000
Expand:
Status quo:
Sell:
Copyright 2011 John Wiley & Sons, Inc.
$500,000  Minimum
650,000
980,000
Decision: Expand
Supplement 1-10
Hurwicz Criteria
STATES OF NATURE
DECISION
Expand
Maintain status quo
Sell now
 = 0.3
Good Foreign
Poor Foreign
Competitive Conditions
Competitive Conditions
$ 800,000
1,300,000
320,000
$ 500,000
-150,000
320,000
1 -  = 0.7
Expand: $800,000(0.3) + 500,000(0.7) = $590,000  Maximum
Status quo: 1,300,000(0.3) -150,000(0.7) = 285,000
Sell: 320,000(0.3) + 320,000(0.7) = 320,000
Decision: Expand
Copyright 2011 John Wiley & Sons, Inc.
Supplement 1-11
Equal Likelihood Criteria
STATES OF NATURE
DECISION
Expand
Maintain status quo
Sell now
Good Foreign
Poor Foreign
Competitive Conditions
Competitive Conditions
$ 800,000
1,300,000
320,000
$ 500,000
-150,000
320,000
Two states of nature each weighted 0.50
Expand: $800,000(0.5) + 500,000(0.5) = $650,000  Maximum
Status quo: 1,300,000(0.5) -150,000(0.5) = 575,000
Sell: 320,000(0.5) + 320,000(0.5) = 320,000
Decision: Expand
Copyright 2011 John Wiley & Sons, Inc.
Supplement 1-12
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Supplement 1-13
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Supplement 1-14
Copyright 2011 John Wiley & Sons, Inc.
Supplement 1-15
Copyright 2011 John Wiley & Sons, Inc.
Supplement 1-16
Decision Analysis with Excel
= MAX(C6:D6)
= MIN(C6:D8)
= MAX(D6:D8)-F7
= MAX(F6:F8)
= MAX(G7:H7)
= C19*E7+C20*F7)
= .5*E8+.5*F8
Copyright 2011 John Wiley & Sons, Inc.
Supplement 1-17
Decision Analysis with OM Tools
Copyright 2011 John Wiley & Sons, Inc.
Supplement 1-18
Decision Making with Probabilities
• Risk involves assigning probabilities to states of
nature
• Expected value
• a weighted average of decision outcomes in which
each future state of nature is assigned a probability
of occurrence
Copyright 2011 John Wiley & Sons, Inc.
Supplement 1-19
Expected Value
n
EV (x) =
 p(xi)xi
i =1
where
xi = outcome i
p(xi) = probability of outcome i
Copyright 2011 John Wiley & Sons, Inc.
Supplement 1-20
Decision Making with Probabilities
STATES OF NATURE
DECISION
Expand
Maintain status quo
Sell now
Good Foreign
Poor Foreign
Competitive Conditions
Competitive Conditions
$ 800,000
1,300,000
320,000
p(good) = 0.70
$ 500,000
-150,000
320,000
p(poor) = 0.30
EV(expand): $800,000(0.7) + 500,000(0.3) = $710,000
EV(status quo): 1,300,000(0.7) -150,000(0.3) = 865,000  Maximum
EV(sell):
320,000(0.7) + 320,000(0.3) = 320,000
Decision: Status quo
Copyright 2011 John Wiley & Sons, Inc.
Supplement 1-21
Decision Making with Probabilities: Excel
Expected value
computed
in cell D6
Copyright 2011 John Wiley & Sons, Inc.
Supplement 1-22
Expected Value of Perfect Information
• EVPI
• maximum value of perfect information to the decision
maker
• maximum amount that would be paid to gain
information that would result in a decision better than
the one made without perfect information
Copyright 2011 John Wiley & Sons, Inc.
Supplement 1-23
EVPI
• Good conditions will exist 70% of the time
• choose maintain status quo with payoff of
$1,300,000
• Poor conditions will exist 30% of the time
• choose expand with payoff of $500,000
• Expected value given perfect information
= $1,300,000 (0.70) + 500,000 (0.30)
= $1,060,000
• Recall that expected value without perfect
information was $865,000 (maintain status quo)
• EVPI= $1,060,000 - 865,000 = $195,000
Copyright 2011 John Wiley & Sons, Inc.
Supplement 1-24
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Supplement 1-25
Copyright 2011 John Wiley & Sons, Inc.
Supplement 1-26
Copyright 2011 John Wiley & Sons, Inc.
Supplement 1-28
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Supplement 1-29
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Supplement 1-30
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Supplement 1-31
Sequential Decision Trees
• A graphical method for analyzing decision
situations that require a sequence of decisions
over time
• Decision tree consists of
• Square nodes - indicating decision points
• Circles nodes - indicating states of nature
• Arcs - connecting nodes
Copyright 2011 John Wiley & Sons, Inc.
Supplement 1-32
Copyright 2011 John Wiley & Sons, Inc.
Supplement 1-33
Evaluations at Nodes
• Compute EV at nodes 6 & 7
• EV(node 6)= 0.80($3,000,000) + 0.20($700,000) = $2,540,000
• EV(node 7)= 0.30($2,300,000) + 0.70($1,000,000)= $1,390,000
• Decision at node 4 is between
$2,540,000 for Expand and
$450,000 for Sell land
• Choose Expand
• Repeat expected value calculations and decisions at
remaining nodes
Copyright 2011 John Wiley & Sons, Inc.
Supplement 1-34
Decision Tree Analysis
$2,000,000
$1,290,000
0.60
Market growth
2
0.40
$225,000
$2,540,000
$3,000,000
0.80
$1,740,000
1
6
0.20
4
$1,160,000
$700,000
$450,000
0.60
3
$1,360,000
$1,390,000
0.40
$790,000
$2,300,000
0.30
7
0.70
$1,000,000
5
$210,000
Copyright 2011 John Wiley & Sons, Inc.
Supplement 1-35
Copyright 2011 John Wiley & Sons, Inc.
Supplement 1-36
Since cost of installation ($900,000) is greater than
expected value of not installing ($552,000), do not install an
emergency power generator
Copyright 2011 John Wiley & Sons, Inc.
Supplement 1-37