Chapter 1 Supplement
Decision Analysis
Operations Management - 6th Edition
Roberta Russell & Bernard W. Taylor, III
Copyright 2009 John Wiley & Sons, Inc.
Beni Asllani
University of Tennessee at Chattanooga
Lecture Outline
 Decision Analysis
 Decision Making without Probabilities
 Decision Making with Probabilities
 Expected Value of Perfect Information
 Sequential Decision Tree
Copyright 2009 John Wiley & Sons, Inc.
Supplement 1-2
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 2009 John Wiley & Sons, Inc.
Supplement 1-3
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 2009 John Wiley & Sons, Inc.
Supplement 1-4
Payoff Table
 Payoff table

method for organizing and illustrating payoffs from different
decisions given various states of nature
 Payoff

outcome of a decision
States Of Nature
Decision
a
b
1
Payoff 1a
Payoff 1b
2
Payoff 2a
Payoff 2b
Copyright 2009 John Wiley & Sons, Inc.
Supplement 1-5
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 2009 John Wiley & Sons, Inc.
Supplement 1-6
Decision Making Criteria Under
Uncertainty (cont.)
 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 2009 John Wiley & Sons, Inc.
Supplement 1-7
Southern Textile
Company
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
Copyright 2009 John Wiley & Sons, Inc.
$ 500,000
-150,000
320,000
Supplement 1-8
Maximax Solution
STATES OF NATURE
DECISION
Good Foreign
Poor Foreign
Competitive Conditions
Competitive Conditions
Expand
Maintain status quo
Sell now
Expand:
Status quo:
Sell:
$ 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 2009 John Wiley & Sons, Inc.
Supplement 1-9
Maximin Solution
STATES OF NATURE
DECISION
Good Foreign
Poor Foreign
Competitive Conditions
Competitive Conditions
Expand
Maintain status quo
Sell now
Expand:
Status quo:
Sell:
$ 800,000
1,300,000
320,000
$ 500,000
-150,000
320,000
$500,000  Maximum
-150,000
320,000
Decision: Expand
Copyright 2009 John Wiley & Sons, Inc.
Supplement 1-10
Minimax Regret Solution
Good Foreign
Competitive Conditions
Poor Foreign
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 2009 John Wiley & Sons, Inc.
$500,000  Minimum
650,000
980,000
Decision: Expand
Supplement 1-11
Hurwicz Criteria
STATES OF NATURE
DECISION
Good Foreign
Poor Foreign
Competitive Conditions
Competitive Conditions
Expand
Maintain status quo
Sell now
 = 0.3
$ 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 2009 John Wiley & Sons, Inc.
Supplement 1-12
Equal Likelihood Criteria
STATES OF NATURE
DECISION
Good Foreign
Poor Foreign
Competitive Conditions
Competitive Conditions
Expand
Maintain status quo
Sell now
$ 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 2009 John Wiley & Sons, Inc.
Supplement 1-13
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 2009 John Wiley & Sons, Inc.
Supplement 1-14
Expected value
n
EV (x) =
 p(xi)xi
i =1
where
xi = outcome i
p(xi) = probability of outcome i
Copyright 2009 John Wiley & Sons, Inc.
Supplement 1-15
Decision Making with
Probabilities: Example
STATES OF NATURE
DECISION
Good Foreign
Poor Foreign
Competitive Conditions
Competitive Conditions
Expand
Maintain status quo
Sell now
$ 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 2009 John Wiley & Sons, Inc.
Supplement 1-16
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 2009 John Wiley & Sons, Inc.
Supplement 1-17
EVPI Example
 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 2009 John Wiley & Sons, Inc.
Supplement 1-18
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 2009 John Wiley & Sons, Inc.
Supplement 1-19
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 2009 John Wiley & Sons, Inc.
Supplement 1-20
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 2009 John Wiley & Sons, Inc.
Supplement 1-21