Chapter 3
Decision Analysis
Prepared by Lee Revere and John Large
To accompany Quantitative Analysis
for Management, 9e
by Render/Stair/Hanna
3-1
© 2006 by Prentice Hall, Inc.
Upper Saddle River, NJ 07458
Learning Objectives
Students will be able to:
1. List the steps of the decision-making
process.
2. Describe the types of decision-making
environments.
3. Make decisions under uncertainty.
4. Use probability values to make decisions
under risk.
5. Understand the importance and use of utility
theory in decision theory.
To accompany Quantitative Analysis
for Management, 9e
by Render/Stair/Hanna
3-2
© 2006 by Prentice Hall, Inc.
Upper Saddle River, NJ 07458
Chapter Outline
3.1
3.2
3.3
3.4
3.5
3.7
3.8
Introduction
The Six Steps in Decision Theory
Types of Decision-Making
Environments
Decision Making under Uncertainty
Decision Making under Risk
How Probability Values Are
Estimated by Bayesian Analysis
Utility Theory
To accompany Quantitative Analysis
for Management, 9e
by Render/Stair/Hanna
3-3
© 2006 by Prentice Hall, Inc.
Upper Saddle River, NJ 07458
Introduction
 Decision theory is an analytical and
systematic way to tackle problems.
 A good decision is based on logic.
To accompany Quantitative Analysis
for Management, 9e
by Render/Stair/Hanna
3-4
© 2006 by Prentice Hall, Inc.
Upper Saddle River, NJ 07458
The Six Steps in
Decision Theory
1.
2.
3.
4.
Clearly define the problem at hand.
List the possible alternatives.
Identify the possible outcomes.
List the payoff or profit of each
combination of alternatives and
outcomes.
5. Select one of the mathematical
decision theory models.
6. Apply the model and make your
decision.
To accompany Quantitative Analysis
for Management, 9e
by Render/Stair/Hanna
3-5
© 2006 by Prentice Hall, Inc.
Upper Saddle River, NJ 07458
John Thompson’s
Backyard Storage
Sheds
Define problem
To manufacture or market
backyard storage sheds
List alternatives
1.
2.
3.
Identify outcomes
The market could be favorable or
unfavorable for storage sheds
List payoffs
List the payoff for each state of
nature/decision alternative
combination
Select a model
Decision tables can be used to solve
the problem
Apply model and
make decision
Solutions can be obtained and a
sensitivity analysis used to make a
decision
To accompany Quantitative Analysis
for Management, 9e
by Render/Stair/Hanna
Construct a large new plant
A small plant
No plant at all
3-6
© 2006 by Prentice Hall, Inc.
Upper Saddle River, NJ 07458
Decision Table
for Thompson Lumber
State of Nature
Alternative
Favorable Unfavorable
Market ($) Market ($)
Construct a
large plant
200,000
-180,000
Construct a
small plant
100,000
-20,000
Do nothing
0
0
To accompany Quantitative Analysis
for Management, 9e
by Render/Stair/Hanna
3-7
© 2006 by Prentice Hall, Inc.
Upper Saddle River, NJ 07458
Types of DecisionMaking Environments
 Type 1: Decision making under
certainty.
 Decision maker knows with certainty
the consequences of every alternative or
decision choice.
 Type 2: Decision making under risk.
 The decision maker does know the
probabilities of the various outcomes.
 Decision making under uncertainty.
 The decision maker does not know the
probabilities of the various outcomes.
To accompany Quantitative Analysis
for Management, 9e
by Render/Stair/Hanna
3-8
© 2006 by Prentice Hall, Inc.
Upper Saddle River, NJ 07458
Decision Making
under Uncertainty
 Maximax
 Maximin
 Equally likely (Laplace)
 Criterion of realism
 Minimax
To accompany Quantitative Analysis
for Management, 9e
by Render/Stair/Hanna
3-9
© 2006 by Prentice Hall, Inc.
Upper Saddle River, NJ 07458
Decision Table for
Thompson Lumber
 Maximax: Optimistic Approach
 Find the alternative that maximizes the maximum
outcome for every alternative.
State of Nature
Alternative
Favorable Unfavorable
Market ($) Market ($)
Construct a
large plant
200,000
-180,000
Construct a
small plant
100,000
-20,000
Do nothing
0
0
To accompany Quantitative Analysis
for Management, 9e
by Render/Stair/Hanna
3-10
© 2006 by Prentice Hall, Inc.
Upper Saddle River, NJ 07458
Thompson Lumber:
Maximax Solution
State of Nature
Alternative
Maximax
Favorable
Market ($)
Unfavorable
Market ($)
Construct a
large plant
200,000
-180,000
200,000
Construct a
small plant
100,000
-20,000
100,000
Do nothing
0
0
0
To accompany Quantitative Analysis
for Management, 9e
by Render/Stair/Hanna
3-11
© 2006 by Prentice Hall, Inc.
Upper Saddle River, NJ 07458
Decision Table for
Thompson Lumber
 Maximin: Pessimistic Approach
 Choose the alternative with maximum
minimum output.
State of Nature
Alternative
Favorable Unfavorable
Market ($) Market ($)
Construct a
large plant
200,000
-180,000
Construct a
small plant
100,000
-20,000
Do nothing
0
0
To accompany Quantitative Analysis
for Management, 9e
by Render/Stair/Hanna
3-12
© 2006 by Prentice Hall, Inc.
Upper Saddle River, NJ 07458
Thompson Lumber:
Maximin Solution
State of Nature
Alternative
Maximin
Favorable
Market ($)
Unfavorable
Market ($)
Construct a
large plant
200,000
-180,000
-180,000
Construct a
small plant
100,000
-20,000
-20,000
Do nothing
0
0
0
To accompany Quantitative Analysis
for Management, 9e
by Render/Stair/Hanna
3-13
© 2006 by Prentice Hall, Inc.
Upper Saddle River, NJ 07458
Thompson Lumber:
Hurwicz
 Criterion of Realism (Hurwicz)
 Decision maker uses a weighted average based
on optimism of the future.
State of Nature
Alternative
Favorable
Market ($)
Unfavorable
Market ($)
Construct a
large plant
200,000
-180,000
Construct a
small plant
100,000
-20,000
Do nothing
0
0
3-14
© 2006 by Prentice Hall, Inc.
Upper Saddle River, NJ 07458
To accompany Quantitative Analysis
for Management, 9e
by Render/Stair/Hanna
Thompson Lumber:
Hurwicz Solution
CR = α*(row max)+(1- α)*(row min)
State of Nature
Alternative
Criterion
of Realism
or
Weighted
Average (α
= 0.8) ($)
Favorable
Market ($)
Unfavorable
Market ($)
Construct a
large plant
200,000
-180,000
124,000
Construct a
small plant
100,000
-20,000
76,000
Do nothing
0
0
0
To accompany Quantitative Analysis
for Management, 9e
by Render/Stair/Hanna
3-15
© 2006 by Prentice Hall, Inc.
Upper Saddle River, NJ 07458
Decision Making
under Uncertainty
 Equally likely (Laplace)
 Assume all states of nature to be
equally likely, choose maximum
Average.
State of Nature
Alternative
Favorable
Market ($)
Unfavorable
Market ($)
Construct a
large plant
200,000
-180,000
Construct a
small plant
100,000
-20,000
Do nothing
0
0
To accompany Quantitative Analysis
for Management, 9e
by Render/Stair/Hanna
3-16
© 2006 by Prentice Hall, Inc.
Upper Saddle River, NJ 07458
Decision Making
under Uncertainty
State of Nature
Alternative
Avg.
Favorable
Market ($)
Unfavorable
Market ($)
Construct a
large plant
200,000
-180,000
10,000
Construct a
small plant
100,000
-20,000
40,000
Do nothing
0
0
0
To accompany Quantitative Analysis
for Management, 9e
by Render/Stair/Hanna
3-17
© 2006 by Prentice Hall, Inc.
Upper Saddle River, NJ 07458
Thompson Lumber;
Minimax Regret
 Minimax Regret:
 Choose the alternative that minimizes the
maximum opportunity loss .
State of Nature
Alternative
Favorable
Market ($)
Unfavorable
Market ($)
Construct a large
plant
200,000
-180,000
Construct a small
plant
100,000
-20,000
0
0
Do nothing
To accompany Quantitative Analysis
for Management, 9e
by Render/Stair/Hanna
3-18
© 2006 by Prentice Hall, Inc.
Upper Saddle River, NJ 07458
Thompson Lumber:
Opportunity Loss
Table
State of Nature
Alternative
Favorable
Market ($)
Unfavorable
Market ($)
Construct a large
plant
200,000 –
200,000 = 0
0- (-180,000) =
180,000
Construct a small
plant
200,000 100,000 =
100,000
0- (-20,000) =
20,000
200,000 – 0 =
200000
0–0=0
Do nothing
To accompany Quantitative Analysis
for Management, 9e
by Render/Stair/Hanna
3-19
© 2006 by Prentice Hall, Inc.
Upper Saddle River, NJ 07458
Thompson Lumber:
Minimax Regret
Solution
State of Nature
Alternative
Maximum
Opportunity
Loss
Favorable
Market ($)
Unfavorable
Market ($)
Construct a
large plant
0
180,000
180,000
Construct a
small plant
100,000
20,000
100,000
Do nothing
200,000
0
200,000
To accompany Quantitative Analysis
for Management, 9e
by Render/Stair/Hanna
3-20
© 2006 by Prentice Hall, Inc.
Upper Saddle River, NJ 07458
Decision Making under
Risk
Expected Monetary Value:
EMV(Alternative) 
n
 Payoff S
j
* P( S j )
j 1
where n  number of stages of nature.
In other words:
EMVAlternative n = Payoff 1 * PAlt. 1 + Payoff 2 * PAlt. 2 +
… + Payoff n * PAlt. N
EMV= payoff of state of nature*
probability of state of nature
To accompany Quantitative Analysis
for Management, 9e
by Render/Stair/Hanna
3-21
© 2006 by Prentice Hall, Inc.
Upper Saddle River, NJ 07458
Thompson Lumber:
EMV
State of Nature
Alternative
Construct a
large plant
Favorable
Market ($)
200,000
Unfavorable
Market ($)
EMV
-180,000
200,000*0.5 +
(-180,000)*0.5 =
10,000
Construct a
small plant
100,000
-20,000
100,000*0.5 +
(-20,000)*0.5 =
40,000
Do nothing
0
0
0*0.5 + 0*0.5 = 0
Probabilities
0.50
0.50
To accompany Quantitative Analysis
for Management, 9e
by Render/Stair/Hanna
3-22
© 2006 by Prentice Hall, Inc.
Upper Saddle River, NJ 07458
Thompson Lumber:
EV|PI and EMV
Solution
State of Nature
Alternative
Favorable Unfavorable
Market
Market
($)
($)
EMV
Construct a
large plant
200,000
-180,000
10,000
Construct a
small plant
100,000
-20,000
40,000
Do nothing
0
0
0
200,000*
0.5 =
100,000
0*0.5 = 0
EV‫׀‬PI
To accompany Quantitative Analysis
for Management, 9e
by Render/Stair/Hanna
3-23
© 2006 by Prentice Hall, Inc.
Upper Saddle River, NJ 07458
Expected Value of
Perfect Information
(EVPI)
 EVPI places an upper bound on what
one would pay for additional
information.
 EVPI is the expected value with
perfect information minus the
maximum EMV.
To accompany Quantitative Analysis
for Management, 9e
by Render/Stair/Hanna
3-24
© 2006 by Prentice Hall, Inc.
Upper Saddle River, NJ 07458
Expected Value with
Perfect Information
(EV|PI)
n
EV | PI   (Best outcome for state of nature) * P(S j )
j1
n  number of states of nature.
In other words
EV‫׀‬PI = Best Outcome of Alt 1 * PAlt. 1 +
Best Outcome of Alt 2 * PAlt. 2 +… +
Best Outcome of Alt n * PAlt. n
To accompany Quantitative Analysis
for Management, 9e
by Render/Stair/Hanna
3-25
© 2006 by Prentice Hall, Inc.
Upper Saddle River, NJ 07458
Expected Value of
Perfect Information
EVPI = EV|PI - maximum EMV
Expected value
with no additional
information
Expected value
with perfect
information
To accompany Quantitative Analysis
for Management, 9e
by Render/Stair/Hanna
3-26
© 2006 by Prentice Hall, Inc.
Upper Saddle River, NJ 07458
Thompson Lumber:
EVPI Solution
EVPI = expected value with perfect
information - max(EMV)
= $200,000*0.50 + 0*0.50 - $40,000
From previous slide
= $60,000
• It means that if the cost of
information less that 60000 we’ll
accept to pay for getting
information
• Otherwise refuse.
To accompany Quantitative Analysis
for Management, 9e
by Render/Stair/Hanna
3-27
© 2006 by Prentice Hall, Inc.
Upper Saddle River, NJ 07458
In-Class Example 2
Let’s practice what we’ve learned. Using
the table below compute EMV, EV‫׀‬PI,
and EVPI.
State of Nature
Good
Market
($)
Average
Market
($)
Poor
Market
($)
75,000
25,000
-40,000
Construct a
100,000
small plant
35,000
-60,000
0
0
Alternative
Construct a
large plant
Do nothing
To accompany Quantitative Analysis
for Management, 9e
by Render/Stair/Hanna
0
3-28
© 2006 by Prentice Hall, Inc.
Upper Saddle River, NJ 07458
In-Class Example 2:
EMV and EV‫׀‬PI
Solution
State of Nature
Good
Market
($)
Average
Market
($)
Poor
Market
($)
EMV
Construct a
large plant
75,000
25,000
-40,000
21,250
Construct a
small plant
100,000
35,000
-60,000
27,500
Do nothing
0
0
0
0
0.25
0.50
0.25
Alternative
To accompany Quantitative Analysis
for Management, 9e
by Render/Stair/Hanna
3-29
© 2006 by Prentice Hall, Inc.
Upper Saddle River, NJ 07458
In-Class Example 2:
EVPI Solution
EVPI = expected value with perfect
information - max(EMV)
= $100,000*0.25 + 35,000*0.50 +0*0.25
= $ 42,500 - 27,500
= $ 15,000
To accompany Quantitative Analysis
for Management, 9e
by Render/Stair/Hanna
3-30
© 2006 by Prentice Hall, Inc.
Upper Saddle River, NJ 07458
Expected Opportunity
Loss
 EOL is the cost of not picking
the best solution.
EOL = Expected Regret
To accompany Quantitative Analysis
for Management, 9e
by Render/Stair/Hanna
3-31
© 2006 by Prentice Hall, Inc.
Upper Saddle River, NJ 07458
Thompson Lumber: EOL
The Opportunity Loss Table
State of Nature
Alternative
Favorable
Market ($)
Unfavorable
Market ($)
Construct a
large plant
200,000 –
200,000
0- (-180,000)
Construct a
small plant
200,000 100,000
0 – (-20,000)
Do nothing
200,000 - 0
0-0
Probabilities
0.50
0.50
To accompany Quantitative Analysis
for Management, 9e
by Render/Stair/Hanna
3-32
© 2006 by Prentice Hall, Inc.
Upper Saddle River, NJ 07458
Thompson Lumber:
EOL Table
State of Nature
Alternative
Favorable Unfavorable
Market ($) Market ($)
Construct a
large plant
200,000
-180,000
Construct a
small plant
100,000
-20,000
Do nothing
0
0
Probabilities
0.50
0.50
To accompany Quantitative Analysis
for Management, 9e
by Render/Stair/Hanna
3-33
© 2006 by Prentice Hall, Inc.
Upper Saddle River, NJ 07458
Thompson Lumber:
EOL Solution
Alternative
Large Plant
Small Plant
Do Nothing
EOL
(0.50)*$0 +
$90,000
(0.50)*($180,000)
(0.50)*($100,000) $60,000
+ (0.50)(*$20,000)
(0.50)*($200,000) $100,000
+ (0.50)*($0)
To accompany Quantitative Analysis
for Management, 9e
by Render/Stair/Hanna
3-34
© 2006 by Prentice Hall, Inc.
Upper Saddle River, NJ 07458