Spreadsheet Modeling & Decision Analysis. A Practical Introduction to Management Science 5 th edition Cliff T. Ragsdale. Chapter 15. Decision Analysis. Introduction to Decision Analysis. Models help managers gain insight and understanding, but they can’t make decisions.
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A Practical Introduction to Management Science
5th edition
Cliff T. Ragsdale
1) Buy the parcel of land at location A.
2) Buy the parcel of land at location B.
3) Buy both parcels.
4) Buy nothing.
1) The new airport is built at location A.
2) The new airport is built at location B.
See file Fig151.xls
Decision 1 2 MAX
A 30 10000 30 <maximum
B 29 29 29
The Maximax Decision RuleState of Nature
Decision 1 2 MIN
A 1000 28 28
B 29 29 29 <maximum
The Maximin Decision RuleConsider the following payoff matrix
State of Nature
Decision 1 2
A 9 2
B 4 6
State of Nature
Decision 1 2 MAX
A 0 4 4 <minimum
B 5 0 5
Anomalies with the Minimax Regret RuleDecision 1 2
A 9 2
B 4 6
C 3 9
State of Nature
Decision 1 2 MAX
A 0 7 7
B 5 3 5 <minimum
C 6 0 6
Adding an AlternativeState of Nature
Decision 1 2 EMV
A 15,000 5,000 5,000 <maximum
B 5,000 4,000 4,500
Probability 0.5 0.5
EMV CautionEV with PI = 0.4*$13 + 0.6*$11 = $11.8 (in millions)
EV of PI = $11.8  $3.4 = $8.4 (in millions)
EV of PI = EV with PI  maximum EMV
EV of PI = minimum EOL
Airport Location
Payoff
13
A
31
Buy A
1
18
6
12
B
A
8
4
Buy B
2
12
23
B
11
0
5
A
35
Buy A&B
3
30
29
1
B
A
0
0
Buy nothing
4
0
0
B
0
A Decision Tree for Magnolia InnsAirport Location
Payoff
0.4
13
A
31
Buy A
1
EMV=2
18
6
12
B
0.6
0.4
A
8
4
Buy B
2
12
EMV=3.4
23
B
11
0.6
0
0.4
5
A
35
Buy A&B
EMV=3.4
3
30
EMV=1.4
29
1
B
0.6
0.4
A
0
0
Buy nothing
4
EMV= 0
0
0
B
0
0.6
Rolling Back A Decision TreeLand Purchase Decision
Airport Location
Payoff
0.4
13
A
31
Buy A
1
EMV=2
18
6
12
B
0.6
0.4
A
8
4
Buy B
2
12
EMV=3.4
23
B
11
0.6
0
0.4
5
A
35
Buy A&B
EMV=3.4
3
30
EMV=1.4
29
1
B
0.6
Buy nothing
0
0
Microwave $4,000
Cellular $5,000
Infrared $4,000
continued...
MultiStage Decision Example: COMTECHSteve knows he will also spend money in R&D, but he doesn’t know exactly what the R&D costs will be. Steve estimates the following best case and worst case R&D costs and probabilities, based on his expertise in each area.
Best Case Worst Case
Cost Prob. Cost Prob.
Microwave $30,000 0.4 $60,000 0.6
Cellular $40,000 0.8 $70,000 0.2
Infrared $40,000 0.9 $80,000 0.1
COMTECH(continued)The $13,500 EMV for COMTECH was created as follows:
Event Probability Payoff
Receive grant, Low R&D costs 0.5*0.9=0.45 $36,000
Receive grant, High R&D costs 0.5*0.1=0.05 $4,000
Don’t receive grant 0.5 $5,000
EMV $13,500
Risk ProfilesThe payoffs (in millions of dollars) are summarized below.
P(favorable response) = 0.67
P(unfavorable response) = 0.33
P(high demand  favorable response)=0.9
P(low demand  favorable response)=0.1
P(low demand  unfavorable response)=0.7
P(high demand  unfavorable response)=0.3
Expected Value of Sample Information
Expected Value with Sample Information
Expected Value without Sample Information

=
The Expected Value of Sample InformationDemand Demand Total
Favorable Response 0.600 0.067 0.667
Unfavorable Response 0.100 0.233 0.333
Total 0.700 0.300 1.000
Demand Demand Total
Favorable Response 0.600 0.067 0.667
Unfavorable Response 0.100 0.233 0.333
Total 0.700 0.300 1.000
Consider the following payoff table,
State of Nature
Decision 1 2 EMV
A 150,000 30,000 60,000 <maximum
B 70,000 40,000 55,000
Probability 0.5 0.5
Utility TheoryU($30,000)=0 and U($150,000)=1
Alternative 1: Receive $70,000 with certainty.
Alternative 2: Receive $150,000 with probability p and lose $30,000 with probability (1p).
(e.g., $70,000 was equivalent to Alternative 2 with p = 0.8)
(e.g., Risk premium = $114,000$70,000 = $44,000)
Consider the utility table from the earlier example,
State of Nature Expected
Decision 1 2 Utility
A 1 0 0.500
B 0.8 0.65 0.725 <maximum
Probability 0.5 0.5
Using Utilities to Make Decisions1.00
0.80
R=200
R=100
0.60
0.40
R=300
0.20
0.00
0.20
0.40
0.60
0.80
50
25
0
25
50
75
100
125
150
175
200
225
250
275
300
325
350
x
The Exponential Utility FunctionWin $Y with probability 0.5,
Lose $Y/2 with probability 0.5.
‘Use Exponential Utility Function’
For each alternative j, compute a weighted average score as:
wi = weight for criterion i
sij = score for alternative i on criterion j
The Multicriteria Scoring Model1 Equally Preferred
2 Equally to Moderately Preferred
3 Moderately Preferred
4 Moderately to Strongly Preferred
5 Strongly Preferred
6 Strongly to Very Strongly Preferred
7 Very Strongly Preferred
8 Very Strongly to Extremely Preferred
9 Extremely Preferred
Pairwise Comparisons1) Compute the sum of each column,
2) Divide each entry in the matrix by its column sum.
The consistency measure for alternative i is:
where
Pij = pairwise comparison of alternative i to j
sj = score for alternative j
ConsistencyThe inconsistency is not deemed a problem provided the Consistency Ratio (CR) is no more than 10%
where,
RI = 0.00 0.58 0.90 1.12 1.24 1.32 1.41
for n = 2 3 4 5 6 7 8
Consistency (cont’d)