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. Develop accurate and useful decision trees.
6. Revise probabilities using Bayesian analysis.
7. Use computers to solve basic decisionmaking problems.
8. 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
3.6
3.7
3.8
Introduction
The Six Steps in Decision Theory
Types of Decision-Making
Environments
Decision Making under Uncertainty
Decision Making under Risk
Decision Trees
How Probability Values Are
Estimated by Bayesian Analysis
Utility Theory
To accompany Quantitative Analysis
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by Render/Stair/Hanna
3-3
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Introduction
 Decision theory is an analytical and
systematic way to tackle problems.
 A good decision is based on logic.
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3-4
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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
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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 and/or trees 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
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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.
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Decision Making
under Uncertainty
 Maximax
 Maximin
 Equally likely (Laplace)
 Criterion of realism
 Minimax
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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
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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
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by Render/Stair/Hanna
3-11
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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
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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
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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
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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 ($)
Construct a
large plant
200,000
-180,000
124,000
Construct a
small plant
100,000
-20,000
76,000
Do nothing
0
0
0
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3-15
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Decision Making
under Uncertainty
 Equally likely (Laplace)
 Assume all states of nature to be
equally likely, choose maximum
Average.
State of Nature
Alternative
Favorable
Market ($)
Unfavorable
Market ($)
Construct a
large plant
200,000
-180,000
Construct a
small plant
100,000
-20,000
Do nothing
0
0
To accompany Quantitative Analysis
for Management, 9e
by Render/Stair/Hanna
3-16
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Upper Saddle River, NJ 07458
Decision Making
under Uncertainty
State of Nature
Alternative
Avg.
Favorable
Market ($)
Unfavorable
Market ($)
Construct a
large plant
200,000
-180,000
10,000
Construct a
small plant
100,000
-20,000
40,000
Do nothing
0
0
0
To accompany Quantitative Analysis
for Management, 9e
by Render/Stair/Hanna
3-17
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Upper Saddle River, NJ 07458
Thompson Lumber;
Minimax Regret
 Minimax Regret:
 Choose the alternative that minimizes the
maximum opportunity loss .
State of Nature
Alternative
Favorable
Market ($)
Unfavorable
Market ($)
Construct a large
plant
200,000
-180,000
Construct a small
plant
100,000
-20,000
0
0
Do nothing
To accompany Quantitative Analysis
for Management, 9e
by Render/Stair/Hanna
3-18
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Upper Saddle River, NJ 07458
Thompson Lumber:
Opportunity Loss
Table
State of Nature
Alternative
Favorable
Market ($)
Unfavorable
Market ($)
Construct a large
plant
200,000 –
200,000 = 0
0- (-180,000) =
180,000
Construct a small
plant
200,000 100,000 =
100,000
0- (-20,000) =
20,000
200,000 – 0 = 0
0–0=0
Do nothing
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3-19
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Thompson Lumber:
Minimax Regret
Solution
State of Nature
Alternative
Maximum
Opportunity
Loss
Favorable
Market ($)
Unfavorable
Market ($)
Construct a
large plant
0
180,000
180,000
Construct a
small plant
100,000
20,000
100,000
Do nothing
200,000
0
200,000
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by Render/Stair/Hanna
3-20
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In-Class Example 1
 Let’s practice what we’ve learned. Use
the decision table below to compute
(1) Mazimax (2) Maximin (3) Minimax regret
State of Nature
Good
Market
($)
Average
Market
($)
Poor
Market
($)
Construct a
large plant
75,000
25,000
-40,000
Construct a
small plant
100,000
35,000
-60,000
Do nothing
0
0
0
Alternative
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In-Class Example 1:
Maximax
State of Nature
Good
Market
($)
Average
Market
($)
Poor
Market
($)
Maximax
Construct a
large plant
75,000
25,000
-40,000
75,000
Construct a
small plant
100,000
35,000
-60,000
100,000
Do nothing
0
0
0
0
To accompany Quantitative Analysis
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by Render/Stair/Hanna
3-22
Alternative
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In-Class Example 1:
Maximin
State of Nature
Good
Market
($)
Average
Market
($)
Poor
Market
($)
Maximin
Construct a
large plant
75,000
25,000
-40,000
-40,000
Construct a
small plant
100,000
35,000
-60,000
-60,000
Do nothing
0
0
0
0
Alternative
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by Render/Stair/Hanna
3-23
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In-Class Example 1:
Minimax Regret
Opportunity Loss Table
State of Nature
Good
Market
($)
Average
Market
($)
Poor
Market
($)
Maximum
Opp. Loss
Construct a
large plant
25,000
75,000
40,000
40,000
Construct a
small plant
0
0
60,000
60,000
Do nothing
100,000
35,000
0
100,000
Alternative
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Decision Making under
Risk
Expected Monetary Value:
EMV(Alternative) 
n
 Payoff S
j
* P( S j )
j 1
where n  number of stages of nature.
In other words:
EMVAlternative n = Payoff 1 * PAlt. 1 + Payoff 2
* PAlt. 2 + … + Payoff n *
PAlt. n
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Thompson Lumber:
EMV
State of Nature
Alternative
Construct a
large plant
Favorable
Market ($)
200,000
Unfavorable
Market ($)
EMV
-180,000
200,000*0.5 +
(-180,000)*0.5 =
10,000
Construct a
small plant
100,000
-20,000
100,000*0.5 +
(-20,000)*0.5 =
40,000
Do nothing
0
0
0*0.5 + 0*0.5 = 0
Probabilities
0.50
0.50
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by Render/Stair/Hanna
3-26
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Upper Saddle River, NJ 07458
Thompson Lumber:
EV|PI and EMV
Solution
State of Nature
Alternative
Favorable Unfavorable
Market
Market
($)
($)
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
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3-27
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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.
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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
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Expected Value of
Perfect Information
EVPI = EV|PI - maximum EMV
Expected value
with no additional
information
Expected value
with perfect
information
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by Render/Stair/Hanna
3-30
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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
= $60,000
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3-31
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In-Class Example 2
Let’s practice what we’ve learned. Using
the table below compute EMV, EV‫׀‬PI,
and EVPI.
State of Nature
Good
Market
($)
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
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by Render/Stair/Hanna
0
3-32
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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
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for Management, 9e
by Render/Stair/Hanna
3-33
Alternative
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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
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3-34
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Expected Opportunity
Loss
 EOL is the cost of not picking
the best solution.
EOL = Expected Regret
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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
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by Render/Stair/Hanna
3-36
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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
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by Render/Stair/Hanna
3-37
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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)
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by Render/Stair/Hanna
3-38
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Thompson Lumber:
Sensitivity Analysis
EMV(Large Plant):
= $200,000P - (1-P)$180,000
EMV(Small Plant):
= $100,000P - $20,000(1-P)
EMV(Do Nothing):
= $0P + 0(1-P)
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by Render/Stair/Hanna
3-39
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Thompson Lumber:
Sensitivity Analysis (continued)
EMV Values
250000
200000
150000
Point 1
Point 2
Small Plant
100000
50000
0
-50000 0
-100000
-150000
0.2
0.4
0.6
0.8
Large Plant
EMV
-200000
Values of P
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3-40
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1
Marginal Analysis
 P = probability that demand > a given
supply.
 1-P = probability that demand < supply.
 MP = marginal profit.
 ML = marginal loss.
 Optimal decision rule is:
 P*MP  (1-P)*ML
or
ML
P
MPML
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3-41
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Marginal Analysis Discrete Distributions
Steps using Discrete Distributions:
 Determine the value for P.
 Construct a probability table and add a
cumulative probability column.
 Keep ordering inventory as long as the
probability of selling at least one
additional unit is greater than P.
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3-42
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Café du Donut:
Marginal Analysis
Café du Donut sells a dozen donuts for $6. It costs $4 to
make each dozen. The following table shows the discrete
distribution for Café du Donut sales.
Daily
Sales
(Cartons)
Probability
of Sales
at this Level
Probability
that Sales Will
Be at this
Level or Greater
4
0.05
1.00
5
0.15
0.95
6
0.15
0. 80
7
0.20
0.65
8
0.25
0.45
9
0.10
0.20
10
0.10
0.10
1.00
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Café du Donut:
Marginal Analysis Solution
Marginal profit = selling price
- cost
= $6 - $4 = $2
Marginal loss = cost
Therefore:
ML
P
ML  MP
4
4

  0.667
42 6
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Café du Donut:
Marginal Analysis Solution
Daily
Sales
(Cartons)
Probability
of Sales
at this Level
Probability
that Sales Will
Be at this
Level or Greater
4
0.05
1.00 ≥ 0.66
5
0.15
0.95 ≥ 0.66
6
0.15
0. 80 ≥ 0.66
7
0.20
0.65
8
0.25
0.45
9
0.10
0.20
10
0.10
0.10
1.00
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In-Class Example 3
Let’s practice what we’ve learned. You sell cases of goods
for $15/case, the raw materials cost you $4/case, and you
pay $1/case commission.
Daily
Probability of Probability that
Sales Sales at this Level Sales Will Be at this
Cases
Level or Greater
4
0.1
5
0.1
6
0.4
7
0.3
8
0.1
1.00
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In-Class Example 3:
Solution
MP = $15-$4-$1 = $10 per case
P>= $4 / $10+$4 = .286
ML = $4
Daily
Probability of Probability that
Sales Sales at this Level Sales Will Be at this
Cases
Level or Greater
4
0.1
1.0 > .286
5
0.1
.9 > .286
6
0.4
.8 > .286
7
0.3
.4 > .286
8
0.1
.1
1.00
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Marginal Analysis
Normal Distribution




 = average or mean sales
 = standard deviation of sales
MP = marginal profit
ML = Marginal loss
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Marginal Analysis Discrete Distributions
• Steps using Normal Distributions:
 Determine the value for P.
P
ML
MLMP
 Locate P on the normal distribution. For a given
area under the curve, we find Z from the standard
Normal table.
 Using we can now solve for:
*
Z
X -
X* 
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Marginal Analysis:
Normal Curve Review
 cumulativeP
 1.00
Z
- Zo
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
x* - 

 Zo
3-50
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Marginal Analysis Normal Curve Review
area = .30
area = .70
.3 

ML
MLMP
X*
Use table to find Z
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Joe’s Newsstand
Example
Joe sells newspapers for $1.00 each.
Papers cost him $.40 each. His average
daily demand is 50 papers with a standard
deviation of 10 papers. Assuming sales
follow a normal distribution, how many
papers should Joe stock?
 ML = $0.40
 MP = $0.60
  = Average demand = 50 papers per
day
  = Standard deviation of demand =
10
To accompany Quantitative Analysis
for Management, 9e
by Render/Stair/Hanna
3-52
© 2006 by Prentice Hall, Inc.
Upper Saddle River, NJ 07458
Joe’s Newsstand Example
(continued)
.40
ML
Step 1: 
0 .40

P
MLMP .40.60
.
To accompany Quantitative Analysis
for Management, 9e
by Render/Stair/Hanna
3-53
© 2006 by Prentice Hall, Inc.
Upper Saddle River, NJ 07458
Joe’s Newsstand Example
(continued)
Step 2: Look on the Normal table
for
P = 0.6 (i.e., 1 - .4)
and
0 25 
 Z = 0.25,
X -50
or:
*
10
X* = 10 * 0.25 + 50 = 52.5 or 53 newspapers
To accompany Quantitative Analysis
for Management, 9e
by Render/Stair/Hanna
3-54
© 2006 by Prentice Hall, Inc.
Upper Saddle River, NJ 07458
Joe’s Newsstand
Example B
 Joe also offers his clients the “Times” for $1.00. This
paper is flown in from out of state, which greatly
increases its costs. Joe pays $.80 for the “Times.”
The “Times” has average daily sales of 100 papers
with a standard deviation of 10. Assuming sales
follow a normal distribution, how many “Times”
papers should Joe stock?




ML = $0.80
MP = $0.20
 = Average demand = 100 papers per day
 = Standard deviation of demand = 10
To accompany Quantitative Analysis
for Management, 9e
by Render/Stair/Hanna
3-55
© 2006 by Prentice Hall, Inc.
Upper Saddle River, NJ 07458
Joe’s Newsstand
Example B (continued)
ML
Step 1:
.8

0. 80
P
ML MP .8 .2
.
To accompany Quantitative Analysis
for Management, 9e
by Render/Stair/Hanna
3-56
© 2006 by Prentice Hall, Inc.
Upper Saddle River, NJ 07458
Joe’s Newsstand
Example B (continued)
Step 2:
Z = 0.80
= -0.84 for an area of 0.80
And
X -100
-0 .84 
*
10
or: X=-8.4+100 or 92 newspapers
To accompany Quantitative Analysis
for Management, 9e
by Render/Stair/Hanna
3-57
© 2006 by Prentice Hall, Inc.
Upper Saddle River, NJ 07458
Decision Making with
Uncertainty: Using the
Decision Trees
Decision trees enable one to look at
decisions:
 With many alternatives and states of
nature,
 which must be made in sequence.
To accompany Quantitative Analysis
for Management, 9e
by Render/Stair/Hanna
3-58
© 2006 by Prentice Hall, Inc.
Upper Saddle River, NJ 07458
Five Steps to
Decision Tree Analysis
1. Define the problem.
2. Structure or draw the decision tree.
3. Assign probabilities to the states of
nature.
4. Estimate payoffs for each possible
combination of alternatives and states
of nature.
5. Solve the problem by computing
expected monetary values (EMVs) for
each state of nature node.
To accompany Quantitative Analysis
for Management, 9e
by Render/Stair/Hanna
3-59
© 2006 by Prentice Hall, Inc.
Upper Saddle River, NJ 07458
Structure of Decision
Trees
A graphical representation where:
 A decision node from which one of
several alternatives may be chosen.
 A state-of-nature node out of which
one state of nature will occur.
To accompany Quantitative Analysis
for Management, 9e
by Render/Stair/Hanna
3-60
© 2006 by Prentice Hall, Inc.
Upper Saddle River, NJ 07458
Thompson’s Decision
Tree
Step 1: Define the problem
Lets re-look at John Thompson’s decision regarding
storage sheds. This simple problem can be depicted
using a decision tree.
Step 2: Draw the tree
A State of
Nature
Node
Favorable Market
1
Unfavorable Market
A
Decision
Node
Favorable Market
Construct
Small
Plant
2
Unfavorable Market
To accompany Quantitative Analysis
for Management, 9e
by Render/Stair/Hanna
3-61
© 2006 by Prentice Hall, Inc.
Upper Saddle River, NJ 07458
Thompson’s Decision
Tree
Step 3: Assign probabilities to the states
of nature.
Step 4: Estimate payoffs.
A State of
Nature Node
Favorable (0.5)
Market
$200,000
1
Unfavorable (0.5)-$180,000
Market
A
Decision
Node
Favorable (0.5) $100,000
Market
Construct
Small
Plant
2
Unfavorable (0.5)-$20,000
Market
To accompany Quantitative Analysis
for Management, 9e
by Render/Stair/Hanna
3-62
0
© 2006 by Prentice Hall, Inc.
Upper Saddle River, NJ 07458
Thompson’s Decision
Tree
Step 5: Compute EMVs and make
decision.
A State
of Nature
Favorable (0.5) $200,000
Node
Market
1
EMV
Unfavorable (0.5)
=$10,000 Market
-$180,000
A Decision
Node
Favorable (0.5)
$100,000
Market
Construct
Small
Plant
2
EMV
Unfavorable (0.5)
-$20,000
=$40,000 Market
0
To accompany Quantitative Analysis
for Management, 9e
by Render/Stair/Hanna
3-63
© 2006 by Prentice Hall, Inc.
Upper Saddle River, NJ 07458
Thompson’s Decision:
A More Complex
Problem
 John Thompson has the opportunity of
obtaining a market survey that will give
additional information on the probable state
of nature. Results of the market survey will
likely indicate there is a percent change of a
favorable market. Historical data show
market surveys accurately predict favorable
markets 78 % of the time. Thus P(Fav. Mkt /
Fav. Survey Results) = .78
 Likewise, if the market survey predicts an
unfavorable market, there is a 13 % chance
of its occurring. P(Unfav. Mkt / Unfav.
Survey Results) = .13
 Now that we have redefined the problem
(Step 1), let’s use this additional data and
redraw Thompson’s decision tree (Step 2).
To accompany Quantitative Analysis
for Management, 9e
by Render/Stair/Hanna
3-64
© 2006 by Prentice Hall, Inc.
Upper Saddle River, NJ 07458
Thompson’s Decision
Tree
To accompany Quantitative Analysis
for Management, 9e
by Render/Stair/Hanna
3-65
© 2006 by Prentice Hall, Inc.
Upper Saddle River, NJ 07458
Thompson’s Decision
Tree
Step 3: Assign the new probabilities to the states of
nature.
Step 4: Estimate the payoffs.
To accompany Quantitative Analysis
for Management, 9e
by Render/Stair/Hanna
3-66
© 2006 by Prentice Hall, Inc.
Upper Saddle River, NJ 07458
Thompson’s Decision
Tree
Step 5: Compute the EMVs and make decision.
To accompany Quantitative Analysis
for Management, 9e
by Render/Stair/Hanna
3-67
© 2006 by Prentice Hall, Inc.
Upper Saddle River, NJ 07458
John Thompson Dilemma
John Thompson is not sure how much value
to place on market survey. He wants to
determine the monetary worth of the survey.
John Thompson is also interested in how
sensitive his decision is to changes in the
market survey results. What should he do?
Expected Value of Sample Information
Sensitivity Analysis
To accompany Quantitative Analysis
for Management, 9e
by Render/Stair/Hanna
3-68
© 2006 by Prentice Hall, Inc.
Upper Saddle River, NJ 07458
Expected Value of
Sample Information
Expected value of
best decision
EVSI =
with sample
information,
assuming no
cost to gather it
Expected value of
best decision
without sample
information
EVSI for Thompson Lumber = $59,200
- $40,000
= $19,200
Thompson could pay up to $19,200 and
come out ahead.
To accompany Quantitative Analysis
for Management, 9e
by Render/Stair/Hanna
3-69
© 2006 by Prentice Hall, Inc.
Upper Saddle River, NJ 07458
Calculations for Thompson
Lumber Sensitivity
Analysis
EMV(node 1)  ($106,400) p  ( 1 - p )($2,400)
 $104,000 p  2,400
Equating the EMV(node 1) to the EMV of not
conducting the survey, we have
$104,000 p  $2,400  $40,000
$104,000 p  $37,600
or
p
To accompany Quantitative Analysis
for Management, 9e
by Render/Stair/Hanna
3-70
$37,600
 0.36
$104,000
© 2006 by Prentice Hall, Inc.
Upper Saddle River, NJ 07458
In-Class Problem 3
Let’s practice what we’ve learned
Leo can purchase a historic home for $200,000 or land in a
growing area for $50,000. There is a 60% chance the
economy will grow and a 40% change it will not. If it grows,
the historic home will appreciate in value by 15% yielding a
$30,00 profit. If it does not grow, the profit is only $10,000.
If Leo purchases the land he will hold it for 1 year to assess
the economic growth. If the economy grew during the first
year, there is an 80% chance it will continue to grow. If it did
not grow during the first year, there is a 30% chance it will
grow in the next 4 years. After a year, if the economy grew,
Leo will decide either to build and sell a house or simply sell
the land. It will cost Leo $75,000 to build a house that will
sell for a profit of $55,000 if the economy grows, or $15,000
if it does not grow. Leo can sell the land for a profit of
$15,000. If, after a year, the economy does not grow, Leo will
either develop the land, which will cost $75,000, or sell the
land for a profit of $5,000. If he develops the land and the
economy begins to grow, he will make $45,000. If he
develops the land and the economy does not grow, he will
make $5,000.
To accompany Quantitative Analysis
for Management, 9e
by Render/Stair/Hanna
3-71
© 2006 by Prentice Hall, Inc.
Upper Saddle River, NJ 07458
In-Class Problem 3:
Solution
Economy grows (.6)
2
No
growth
(.4)
Purchase
historic
home
Economy
grows (.8)
Build
house
1
6
No growth
(.2)
4
Purchase
land
Sell
land
Economy
grows (.6)
Economy
grows (.3)
3
Develop
land
No
growth
(.4)
7
No growth
(.7)
5
Sell
land
To accompany Quantitative Analysis
for Management, 9e
by Render/Stair/Hanna
3-72
© 2006 by Prentice Hall, Inc.
Upper Saddle River, NJ 07458
In-Class Problem 3:
Solution
$22,000
2
Economy grows (.6)
No
growth
(.4)
$10,000
Purchase
historic
home
Economy
grows (.8)
6
$35,000
No growth
(.2)
4
Purchase
land
$55,000
$47,000
Build
house
1
$30,000
Economy
grows (.6)
$47,000
Sell
land
$15,000
$15,000
3
$17,000
Economy
grows (.3)
$45,000
$35,000
Develop
land
No
growth
(.4)
7
No growth
(.7)
5
$17,000
To accompany Quantitative Analysis
for Management, 9e
by Render/Stair/Hanna
Sell
land
3-73
$5,000
© 2006 by Prentice Hall, Inc.
Upper Saddle River, NJ 07458
$5,000
Estimating Probability
Values with Bayesian




Management experience or intuition
History
Existing data
Need to be able to revise
probabilities based upon new data
Baye’s Theorem
Prior
probabilities
To accompany Quantitative Analysis
for Management, 9e
by Render/Stair/Hanna
New data
3-74
Posterior
probabilities
© 2006 by Prentice Hall, Inc.
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Bayesian Analysis
The probabilities of a favorable / unfavorable state of
nature can be obtained by analyzing the Market Survey
Reliability in Predicting Actual States of Nature.
Market Survey Reliability in Predicting
Actual States of Nature
Actual States of Nature
Result of Survey
Favorable
Market (FM)
Unfavorable
Market (UM)
Positive (predicts
favorable market
for product)
P(survey positive|FM)
= 0.70
P(survey positive|UM)
= 0.20
Negative (predicts
unfavorable
market for
product)
P(survey
negative|FM) = 0.30
P(survey negative|UM)
= 0.80
To accompany Quantitative Analysis
for Management, 9e
by Render/Stair/Hanna
3-75
© 2006 by Prentice Hall, Inc.
Upper Saddle River, NJ 07458
Bayesian Analysis (continued):
Favorable Survey
Probability Revisions Given a Favorable Survey
Conditional
Probability
State P(Survey
positive|State
of
of Nature
Nature
0.35
FM
0.70
* 0.50
0.35
UM
0.20
* 0.50
0.10
= 0.78
0.45
0.10
= 0.22
0.45
0.45
To accompany Quantitative Analysis
for Management, 9e
by Render/Stair/Hanna
3-76
© 2006 by Prentice Hall, Inc.
Upper Saddle River, NJ 07458
1.00
Bayesian Analysis (continued):
Unfavorable Survey
Probability Revisions Given an
Unfavorable Survey
Conditional
Probability
State P(Survey
of
negative|State
Nature of Nature)
0.15
FM
0.30
* 0.50
0.15
= 0.27
0.55
0.40
UM
0.80
* 0.50
0.40
= 0.73
0.55
1.00
0.55
To accompany Quantitative Analysis
for Management, 9e
by Render/Stair/Hanna
3-77
© 2006 by Prentice Hall, Inc.
Upper Saddle River, NJ 07458
Decision Making Using
Utility Theory
 Utility assessment assigns the worst
outcome a utility of 0, and the best
outcome, a utility of 1.
 A standard gamble is used to
determine utility values.
 When you are indifferent, the utility
values are equal.
To accompany Quantitative Analysis
for Management, 9e
by Render/Stair/Hanna
3-78
© 2006 by Prentice Hall, Inc.
Upper Saddle River, NJ 07458
Standard Gamble for
Utility Assessment
(p)
Best outcome
Utility = 1
(1-p)
Worst outcome
Utility = 0
Other outcome
Utility = ??
To accompany Quantitative Analysis
for Management, 9e
by Render/Stair/Hanna
3-79
© 2006 by Prentice Hall, Inc.
Upper Saddle River, NJ 07458
Simple Example: Utility
Theory
Let’s say you were offered $2,000,000 right now on
a chance to win $5,000,000. The $5,000,000 is won
only if you flip a coin and get tails. If you get heads
you lose and get $0. What should you do?
$2,000,000
$0
Heads
(0.5)
Tails
(0.5)
$5,000,000
To accompany Quantitative Analysis
for Management, 9e
by Render/Stair/Hanna
3-80
© 2006 by Prentice Hall, Inc.
Upper Saddle River, NJ 07458
Real Estate Example:
Utility Theory
Jane Dickson is considering a 3-year real
estate investment. There is an 80 %
chance the real estate market will soar
and a 20 % chance it will bust. In a good
market the real estate investment will
pay $10,000, in an unfavorable market it
is $0. Of course, she could leave her
money in the bank and earn a $5,000
return. What should she do?
To accompany Quantitative Analysis
for Management, 9e
by Render/Stair/Hanna
3-81
© 2006 by Prentice Hall, Inc.
Upper Saddle River, NJ 07458
Real Estate Example:
Solution
p= 0.80 $10,000
U($10,000) = 1.0
(1-p)= 0.20 0
U(0)=0
$5,000
U($5,000)=p
=0.80
To accompany Quantitative Analysis
for Management, 9e
by Render/Stair/Hanna
3-82
© 2006 by Prentice Hall, Inc.
Upper Saddle River, NJ 07458
Utility
Utility Curve for Jane
Dickson
1
0.9
0.8
0.7
0.6
0.5
0.4
0.3
0.2
0.1
0
$-
$2,000
$4,000
$6,000
$8,000
$10,000
Monetary Value
To accompany Quantitative Analysis
for Management, 9e
by Render/Stair/Hanna
3-83
© 2006 by Prentice Hall, Inc.
Upper Saddle River, NJ 07458
Utility
Preferences for Risk
Monetary Outcome
To accompany Quantitative Analysis
for Management, 9e
by Render/Stair/Hanna
3-84
© 2006 by Prentice Hall, Inc.
Upper Saddle River, NJ 07458
Decision Facing Mark
Simkin
Tack lands
point up (0.45)
$10,000
Tack lands
point down (0.55)
-$10,000
Mark does not play the game
0
To accompany Quantitative Analysis
for Management, 9e
by Render/Stair/Hanna
3-85
© 2006 by Prentice Hall, Inc.
Upper Saddle River, NJ 07458
Utility Curve for Mark
Simkin
1
0.9
0.8
0.7
0.6
0.5
0.4
0.3
0.2
0.1
0
-$20,000
-$10,000
To accompany Quantitative Analysis
for Management, 9e
by Render/Stair/Hanna
$0
$10,000
3-86
$20,000
$30,000
© 2006 by Prentice Hall, Inc.
Upper Saddle River, NJ 07458
Thompson Decision Tree
Problem Using QM for
Windows
To accompany Quantitative Analysis
for Management, 9e
by Render/Stair/Hanna
3-87
© 2006 by Prentice Hall, Inc.
Upper Saddle River, NJ 07458
Thompson Decision Tree
Problem Using Excel
To accompany Quantitative Analysis
for Management, 9e
by Render/Stair/Hanna
3-88
© 2006 by Prentice Hall, Inc.
Upper Saddle River, NJ 07458