1. Decision Analysis Support Tools and Processes
Chapter 1 Supplement
Decision Analysis Support Tools and Processes

2. Decision Analysis Quantitative methods Decision analysis
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

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

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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 2011 John Wiley & Sons, Inc.

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 2011 John Wiley & Sons, Inc.

6. Decision Making Criteria Under Uncertainty
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 2011 John Wiley & Sons, Inc.

7. Southern Textile Company
STATES OF NATURE
Good Foreign Poor Foreign
DECISION Competitive Conditions Competitive Conditions
Expand $ 800,000 $ 500,000
Maintain status quo 1,300, ,000
Sell now 320, ,000
Copyright 2011 John Wiley & Sons, Inc.

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Maximax Solution
STATES OF NATURE
Good Foreign Poor Foreign
DECISION Competitive Conditions Competitive Conditions
Expand $ 800,000 $ 500,000
Maintain status quo 1,300, ,000
Sell now 320, ,000
Expand: $800,000
Status quo: 1,300,000  Maximum
Sell: 320,000
Decision: Maintain status quo
Copyright 2011 John Wiley & Sons, Inc.

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Maximin Solution
STATES OF NATURE
Good Foreign Poor Foreign
DECISION Competitive Conditions Competitive Conditions
Expand $ 800,000 $ 500,000
Maintain status quo 1,300, ,000
Sell now 320, ,000
Expand: $500,000  Maximum
Status quo: -150,000
Sell: 320,000
Decision: Expand
Copyright 2011 John Wiley & Sons, Inc.

10. Minimax Regret Solution
States of Nature
Good Foreign Poor Foreign
Competitive Conditions Competitive Conditions
$1,300, ,000 = 500, $500, ,000 = 0
1,300, ,300,000 = ,000 - (-150,000)= 650,000
1,300, ,000 = 980, , ,000= 180,000
Expand: $500,000  Minimum
Status quo: 650,000
Sell: 980,000
Decision: Expand
Copyright 2011 John Wiley & Sons, Inc.

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Hurwicz Criteria
STATES OF NATURE
Good Foreign Poor Foreign
DECISION Competitive Conditions Competitive Conditions
Expand $ 800,000 $ 500,000
Maintain status quo 1,300, ,000
Sell now 320, ,000
 =  = 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 2011 John Wiley & Sons, Inc.

12. Equal Likelihood Criteria
STATES OF NATURE
Good Foreign Poor Foreign
DECISION Competitive Conditions Competitive Conditions
Expand $ 800,000 $ 500,000
Maintain status quo 1,300, ,000
Sell now 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 2011 John Wiley & Sons, Inc.

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17. Decision Analysis with Excel
= MAX(C6:D6)
= MAX(D6:D8)-F7
= MIN(C6:D8)
= MAX(F6:F8)
= MAX(G7:H7)
= C19*E7+C20*F7)
= .5*E8+.5*F8
Copyright 2011 John Wiley & Sons, Inc.

18. Decision Analysis with OM Tools
Copyright 2011 John Wiley & Sons, Inc.

19. 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

20.  Expected Value EV (x) = p(xi)xi n i =1 where xi = outcome i
p(xi) = probability of outcome i

21. Decision Making with Probabilities
STATES OF NATURE
Good Foreign Poor Foreign
DECISION Competitive Conditions Competitive Conditions
Expand $ 800,000 $ 500,000
Maintain status quo 1,300, ,000
Sell now 320, ,000
p(good) = 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): ,000(0.7) + 320,000(0.3) = 320,000
Decision: Status quo
Copyright 2011 John Wiley & Sons, Inc.

22. Decision Making with Probabilities: Excel
Expected value computed in cell D6
Copyright 2011 John Wiley & Sons, Inc.

23. 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 2011 John Wiley & Sons, Inc.

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EVPI
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 = $195,000
Copyright 2011 John Wiley & Sons, Inc.

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32. 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
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Evaluations at Nodes
Compute EV at nodes 6 & 7
EV(node 6)= 0.80($3,000,000) ($700,000) = $2,540,000
EV(node 7)= 0.30($2,300,000) ($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 2011 John Wiley & Sons, Inc.

35. Decision Tree Analysis6 7 2 1 3 4 5
Expand
(-$800,000)
Purchase Land
(-$200,000)
$1,160,000
$1,360,000
$790,000
$1,390,000
$1,740,000
$2,540,000
Warehouse
(-$600,000)
0.60
0.40
No market
growth
$225,000
Market growth
$2,000,000
$3,000,000
$700,000
$2,300,000
$1,000,000
$210,000
Market
Sell land
0.80
0.70
0.30
growth (3 years,
$0 payoff)
$1,290,000
0.20
$450,000
Copyright 2011 John Wiley & Sons, Inc.

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Since cost of installation ($900,000) is greater than expected value of not installing ($552,000), do not install an emergency power generator
Copyright 2011 John Wiley & Sons, Inc.