Transcript Decision Making Under Uncertainty

Chapter 3
Fundamentals of
Decision Theory
Models
To accompany Quantitative Analysis
for Management, 8e
by Render/Stair/Hanna
3-1
© 2003 by Prentice Hall, Inc.
Upper Saddle River, NJ 07458
Learning Objectives
Students will be able to:
• List the steps of the decisionmaking process
• Describe the types of decisionmaking environments
• Use probability values to make
decisions under risk
• Make decisions under uncertainty,
where there is risk but probability
values are not known
• Use computers to solve basic
decision-making problems
To accompany Quantitative Analysis
for Management, 8e
by Render/Stair/Hanna
3-2
© 2003 by Prentice Hall, Inc.
Upper Saddle River, NJ 07458
Chapter Outline
3.1 Introduction
3.2 The Six Steps in Decision
Theory
3.3 Types of Decision-Making
Environments
3.4 Decision Making Under Risk
3.5 Decision Making Under
Uncertainty
3.6 Marginal Analysis with a
Large Number of Alternatives
and States of Nature
To accompany Quantitative Analysis
for Management, 8e
by Render/Stair/Hanna
3-3
© 2003 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.
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by Render/Stair/Hanna
3-4
© 2003 by Prentice Hall, Inc.
Upper Saddle River, NJ 07458
The Six Steps in
Decision Theory
1) Clearly define the problem at
hand
2) List the possible alternatives
3) Identify the possible outcomes
4) 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
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by Render/Stair/Hanna
3-5
© 2003 by Prentice Hall, Inc.
Upper Saddle River, NJ 07458
Decision Table
for Thompson Lumber
Alternative
Construct a
large plant
Construct a
small plant
Do nothing
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for Management, 8e
by Render/Stair/Hanna
State of Nature
Favorable Unfavorable
Market
Market
$200,000
-$180,000
$100,000
-$20,000
$0
0
3-6
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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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by Render/Stair/Hanna
3-7
© 2003 by Prentice Hall, Inc.
Upper Saddle River, NJ 07458
Tile Replacement on the
Space Shuttle
Define problem
Develop solution
Replacement of tiles on
space shuttle
Decision-making model:
partitions on shuttle
surface
Probability values:
debonding, loss of
adjacent tile, burnthrough, critical failure
Risk-criticality scale
Test solution
Test of model
Analyze results
Improved maintenance
would help
New maintenance model
implemented
Develop model
Acquire data
Implement results
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by Render/Stair/Hanna
3-8
© 2003 by Prentice Hall, Inc.
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Critical Decisions in a
Nuclear World
Define problem
Develop model
Acquire data
Develop solution
Tritium replacement: supply exhausted in 2011;
how to produce additional
11 alternatives
U.S. Dept. of Energy, Secretary of Energy, Office of
Defense Programs, Weapons Complex
Reconfiguration Program
Further investigate two alternatives
Test solution
Test: schedule, capacity, availability, cost,
environmental analysis
Analyze results
Two new offices: Commercial Reactor Production,
Accelerator Production
Implement results Result to be implement
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© 2003 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.
To accompany Quantitative Analysis
for Management, 8e
by Render/Stair/Hanna
3-10
© 2003 by Prentice Hall, Inc.
Upper Saddle River, NJ 07458
Decision Table
for Thompson Lumber
Favorable Unfavorable
Market
Market
Alternative
State of Nature
Construct a $200,000 -$180,000 $10,000
large plant
Construct a $100,000 -$20,000 $40,000
small plant
Do nothing
$0
0
0.50
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for Management, 8e
by Render/Stair/Hanna
0.50
3-11
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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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by Render/Stair/Hanna
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© 2003 by Prentice Hall, Inc.
Upper Saddle River, NJ 07458
Expected Value With
Perfect Information
(EV | PI)
n
EV | P I   (Best outcomefor st at eof nature)* P (Sj )
j1
n  number of st at esof nature.
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for Management, 8e
by Render/Stair/Hanna
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© 2003 by Prentice Hall, Inc.
Upper Saddle River, NJ 07458
Expected Value of
Perfect Information
• EVPI = EV|PI - maximum EMV
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for Management, 8e
by Render/Stair/Hanna
3-14
© 2003 by Prentice Hall, Inc.
Upper Saddle River, NJ 07458
Expected Value of
Perfect Information
State of Nature
Alternative Favorable Unfavorable EMV
Market
Market
Construct a $200,000
large plant
Construct a
small plant
$40,000
Do Nothing
0
0.50
To accompany Quantitative Analysis
for Management, 8e
by Render/Stair/Hanna
0.50
3-15
© 2003 by Prentice Hall, Inc.
Upper Saddle River, NJ 07458
Expected Value of
Perfect Information
EVPI = expected value with
perfect information - max(EMV)
= $200,000*0.50 + 0*0.50
- $40,000
= $60,000
To accompany Quantitative Analysis
for Management, 8e
by Render/Stair/Hanna
3-16
© 2003 by Prentice Hall, Inc.
Upper Saddle River, NJ 07458
Expected Opportunity
Loss
• EOL is the cost of not picking
the best solution
• EOL = Expected Regret
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for Management, 8e
by Render/Stair/Hanna
3-17
© 2003 by Prentice Hall, Inc.
Upper Saddle River, NJ 07458
Computing EOL - The
Opportunity Loss Table
State of Nature
Alternative
Large Plant
Favorable Market
($)
200,000 - 200,000
Unfavorable
Market ($)
0 - (-180,000)
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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© 2003 by Prentice Hall, Inc.
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The Opportunity Loss
Table continued
State of Nature
Alternative
Large Plant
Favorable
Market
0
Unfavorable
Market)
$180,000
Small Plant
$100,000
$20,000
Do Nothing
$200,000
0
Probabilities
0.50
0.50
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for Management, 8e
by Render/Stair/Hanna
3-19
© 2003 by Prentice Hall, Inc.
Upper Saddle River, NJ 07458
The Opportunity Loss
Table - continued
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, 8e
by Render/Stair/Hanna
3-20
© 2003 by Prentice Hall, Inc.
Upper Saddle River, NJ 07458
Sensitivity Analysis
EMV(Large Plant) = $200,000P - (1P)$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
3-21
© 2003 by Prentice Hall, Inc.
Upper Saddle River, NJ 07458
Sensitivity Analysis continued
250000
EMV Values
200000
150000
Point 1
Point 2
Small Plant
100000
50000
0
-50000 0
-100000
0.2
0.4
0.6
0.8
Large Plant EMV
-150000
-200000
Values of P
To accompany Quantitative Analysis
for Management, 8e
by Render/Stair/Hanna
3-22
© 2003 by Prentice Hall, Inc.
Upper Saddle River, NJ 07458
1
Decision Making
Under Uncertainty
• Maximax
• Maximin
• Equally likely (Laplace)
• Criterion of Realism
• Minimax
To accompany Quantitative Analysis
for Management, 8e
by Render/Stair/Hanna
3-23
© 2003 by Prentice Hall, Inc.
Upper Saddle River, NJ 07458
Decision Making
Under Uncertainty
Maximax - Choose the alternative
with the maximum output
State of Nature
Alternative Favorable Unfavorable
Market
Market
Construct a 200,000
-180,000
large plant
Construct a 10,000
-20,000
small plant
Do nothing
0
0
Probabilities
To accompany Quantitative Analysis
for Management, 8e
by Render/Stair/Hanna
0.50
3-24
0.50
© 2003 by Prentice Hall, Inc.
Upper Saddle River, NJ 07458
Decision Making
Under Uncertainty
Maximin - Choose the alternative with
the maximum minimum output
Alternative
Construct a
large plant
Construct a
small plant
Do nothing
State of Nature
Favorable Unfavorable
Market
Market
200,000
-180,000
100,000
-20,000
0
0
Probabilities
To accompany Quantitative Analysis
for Management, 8e
by Render/Stair/Hanna
3-25
© 2003 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
Alternative
Construct
Large Plant
Construct
small plant
Do nothing
States of Nature
Favorable Unfavorable Avg.
Market
Market
$200,000
-$180,000
10,000
100,000
-20,000
40,000
0
0
0
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for Management, 8e
by Render/Stair/Hanna
3-26
© 2003 by Prentice Hall, Inc.
Upper Saddle River, NJ 07458
Decision Making
Under Uncertainty
Criterion of Realism (Hurwicz):
CR = *(row max) + (1-)*(row min)
State of Nature
Alternative Favorable Unfavorable
Market
Market
CR
Construct
large plant
$200,000
-180,000
124,000
Construct
small plant
Do nothing
$100,000
-20,000
76,000
0
0
0
0.80
0.20
To accompany Quantitative Analysis
for Management, 8e
by Render/Stair/Hanna
3-27
© 2003 by Prentice Hall, Inc.
Upper Saddle River, NJ 07458
Decision Making
Under Uncertainty
Minimax - choose the alternative with
the minimum maximum Opportunity
Loss
States of Nature
Alternative Favorable Unfavorable
CR
Market
0$
Market
$180,000
$180,000
$100,000
20,000
100,000
200,000
0
200,000
Construct a
large plant
Construct a
small plant
Do nothing
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for Management, 8e
by Render/Stair/Hanna
3-28
© 2003 by Prentice Hall, Inc.
Upper Saddle River, NJ 07458
Marginal Analysis
• P = probability that demand is
greater that or equal to a given
supply
• 1-P = probability that demand will
be less than 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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for Management, 8e
by Render/Stair/Hanna
3-29
© 2003 by Prentice Hall, Inc.
Upper Saddle River, NJ 07458
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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for Management, 8e
by Render/Stair/Hanna
3-30
© 2003 by Prentice Hall, Inc.
Upper Saddle River, NJ 07458
Café du Donut
Example
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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for Management, 8e
by Render/Stair/Hanna
3-31
© 2003 by Prentice Hall, Inc.
Upper Saddle River, NJ 07458
Café du Donut Example
continued
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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for Management, 8e
by Render/Stair/Hanna
3-32
© 2003 by Prentice Hall, Inc.
Upper Saddle River, NJ 07458
Café du Donut Example
continued
Daily Sales
Probability of
Probability that Sales
(Cartons) Sales at this Level Will Be at this Level
or Greater
4
5
6
7
8
9
10
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by Render/Stair/Hanna
1.00  0.66
0.95  0.66
0. 80  0.66
0.65
0.45
0.20
0.10
0.05
0.15
0.15
0.20
0.25
0.10
0.10
1.00
3-33
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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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for Management, 8e
by Render/Stair/Hanna
3-34
© 2003 by Prentice Hall, Inc.
Upper Saddle River, NJ 07458
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.
X -
*
•
Using
Z

we can now
solve for X*
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Joe’s Newsstand
Example A
• ML = 4
• MP = 6
•  = Average demand = 50
papers per day
•  = Standard deviation of
demand = 10
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© 2003 by Prentice Hall, Inc.
Upper Saddle River, NJ 07458
Joe’s Newsstand
Example A - continued
ML
4
Step 1: p 

 0.40
ML  MP 4  6
Step 2: Look in the Normal table
for P = 0.6 (i.e., 1 – 0.4)
X * - 50
Z  0.25 
10
.
or
X  10 * 0.25 50
*
 52.5 or 53 newspapers
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for Management, 8e
by Render/Stair/Hanna
3-37
© 2003 by Prentice Hall, Inc.
Upper Saddle River, NJ 07458
Joe’s Newsstand
Example A continued
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© 2003 by Prentice Hall, Inc.
Upper Saddle River, NJ 07458
Joe’s Newsstand
Example B
• ML = 8
• MP = 2
•  = Average demand = 100
papers per day
•  = Standard deviation of
demand = 10
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by Render/Stair/Hanna
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© 2003 by Prentice Hall, Inc.
Upper Saddle River, NJ 07458
Joe’s Newsstand
Example B - continued
ML
8

 0.80
• Step 1: p 
ML  MP 8  2
• Step 2:
Z = -0.84 for an area of 0.80
and
or:
X - 1000
- 0.84 
10
*
X *  0 - 0.84(10)  100
 91.6 or 92 newspapers
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by Render/Stair/Hanna
3-40
© 2003 by Prentice Hall, Inc.
Upper Saddle River, NJ 07458
Joe’s Newsstand
Example B continued
To accompany Quantitative Analysis
for Management, 8e
by Render/Stair/Hanna
3-41
© 2003 by Prentice Hall, Inc.
Upper Saddle River, NJ 07458