### Introduction to

```Chapter 5 supplement
Decision Theory
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1
The Decision-Making Process
Quantitative Analysis
Problem
Logic
Historical Data
Marketing Research
Scientific Analysis
Modeling
Decision
Qualitative Analysis
Emotions
Intuition
Personal Experience
Personal Motivation
Rumors
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2
Decision Environments
CERTAINTY:
When all parameters (like cost, distance, capacity, time ...) are known.
UNCERTAINTY:
When it is impossible to assess the probability of possible outcomes.
RISK:
When there exists a certain probability level associated with possible outcomes.
What environment is investing in drilling a new oil well?
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3
Typical Example
A building contractor has to make a decision regarding the capacity of his
operation for next year. He has estimated profits (in \$1,000) under each of
the states of nature he believes might occur, as shown in the table below:
Alternative
Do nothing
Expand
Subcontract
Next year’s demand
Low
High
\$50
\$60
\$20
\$80
\$40
\$70
What decisions will he make under different environments and different decision
making approaches?
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4
Decision Making Under Certainty
Alternative
Do nothing
Expand
Subcontract
Next year’s demand
Low
High
\$50
\$60
\$20
\$80
\$40
\$70
In this case, we assume that we know, with certainty, the outcome
for next year (high or low demand).
Therefore, the manager should do nothing if he/she believes that
next year's demand will be low, and the manager should expand
if he/she believes that next year's demand will be high.
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5
Decisions Under Uncertainty (1/2)
1. MAXIMIN: Determine the worst payoff for each alternative, and then select the best
among these worst alternatives. (pessimistic, guaranteed minimum)
Next year demand
Alternative
Low
High
Worst
Do nothing
\$50
\$60
50
Expand
\$20
\$80
20
Subcontract
\$40
\$70
40
Therefore select to do nothing.
2. MAXIMAX: Determine the best payoff for each alternative, and then select the best
among these best alternatives. (optimistic, greedy)
Next year demand
Alternative
Low
High
Do nothing
\$50
\$60
Expand
\$20
\$80
Subcontract
\$40
\$70
Therefore select to expand.
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Best
60
80
70
6
Decisions Under Uncertainty (2/2)
3. Equally Likely (LaPlace): Determine the average payoff for each alternative, and choose the
alternative with the best average.
Next year demand
Alternative
Low
High
Average
Do nothing
\$50
\$60
(50+60)/2 = 55
Expand
\$20
\$80
(20+80)/2 = 50
Subcontract
\$40
\$70
(40+70)/2 = 55
Therefore select either to do nothing or to subcontract the work.
4. Minimax Regret:
Alternative
Do nothing
Expand
Subcontract
Next year demand
Low
High
\$50
\$60
\$20
\$80
\$40
\$70
Regrets
Low
High
\$00
\$20
\$30
\$00
\$10
\$10
Max.
\$20
\$30
\$10 (min.)
Therefore select to subcontract the work.
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7
Decision Theory Elements
• A set of possible future conditions exists that will have a
bearing on the results of the decision
• A list of alternatives for the decision maker to choose from
• A known payoff for each alternative under each possible
future condition
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8
Decision Making Under Risk (1/2)
1. EXPECTED MONETARY VALUE (EMV): Determine the expected payoff of each
alternative, and then select the best alternative.
Assume P(low)=.3 and P(high)=.7,
the expected monetary value for each alternative is:
Next year demand
Low
High
Alternative
Probability:
Do nothing
Expand
Subcontract
Therefore select to expand.
.3
.7
\$50
\$20
\$40
\$60
\$80
\$70
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EMV
.3x50 + .7x60 = 57
.3x20 + .7x80 = 62
.3x40 + .7x70 = 61
9
Decision Making Under Risk (2/2)
DECISION TREES:
Low .3
\$50
Low .3
\$50
High .7
\$60
High
.7
\$60
Low .3
\$20
High .7
\$80
Low .3
\$40
High .7
\$70
\$57
Low .3
\$20
Expand
Expand
\$62
High .7
\$80
Low .3
\$40
High .7
\$70
\$61
- Branches leaving square nodes represent alternatives.
- Branches leaving circular nodes represent outcomes.
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10
Expected Value of Perfect Information (EVPI)
Expected value of perfect information: the difference between the
expected payoff under certainty and the expected payoff under risk
EVPI = Expected payoff under certainty (EPUC) - Expected payoff under risk (EPUR)
Alternative
Probability:
Do nothing
Expand
Subcontract
Next year demand
Low
High
.3
.7
\$50
\$60
\$20
\$80
\$40
\$70
E M V (or EPUR)
.3x50 + .7x60 = 57
.3x20 + .7x80 = 62
.3x40 + .7x70 = 61
EVPI = Expected payoff under certainty (EPUC) - Expected payoff under risk (EPUR)
EVPI =
(.3 x 50) + (.7 x 80)
62
EVPI =
9
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11
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12
Sensitivity Analysis
80
70
60
Do N.
50
Sub.
40
Exp.
Payoff in case of high demand
Payoff in case of low demand
Probabilities associated with each outcome are estimates. What happens if they were different?
Equations:
Do nothing:
Expand:
Subcontract:
50 + 10P
20 + 60P
40 + 30P
After solving pairs of equations with two
unknown:
Do nothing for:
0.00 < P < 0.50
Subcontract for:
0.50 < P < 0.67
Expand for:
0.67 < P < 1.00
20
0
.50 .67
Probability of high demand
1.0
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13
```