Chapter 5 supplement
Saba Bahouth – UCO 1

Problem
Quantitative Analysis
Logic
Historical Data
Marketing Research
Scientific Analysis
Modeling
Qualitative Analysis
Emotions
Intuition
Personal Experience
Personal Motivation
Rumors
Saba Bahouth – UCO
Decision
2

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?
Saba Bahouth – UCO 3

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
$20
$40
$60
$80
$70
What decisions will he make under different environments and different decision making approaches?
Saba Bahouth – UCO 4

Alternative
Do nothing
Expand
Subcontract
Next year’s demand
Low High
$50
$20
$40
$60
$80
$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.
Saba Bahouth – UCO 5

1. MAXIMIN : Determine the worst payoff for each alternative, and then select the best among these worst alternatives. (pessimistic, guaranteed minimum)
Alternative
Do nothing
Expand
Subcontract
Therefore select to do nothing.
Next year demand
Low High
$50
$20
$40
$60
$80
$70
Worst
50
20
40
2. MAXIMAX : Determine the best payoff for each alternative, and then select the best among these best alternatives. (optimistic, greedy)
Alternative
Do nothing
Expand
Subcontract
Therefore select to expand .
Next year demand
Low
$50
High
$60
$20
$40
$80
$70
Best
60
80
70
Saba Bahouth – UCO 6

3. Equally Likely (LaPlace): Determine the average payoff for each alternative, and choose the alternative with the best average.
Next year demand
Alternative
Do nothing
Expand
Low
$50
$20
High
$60
$80
Average
(50+60)/2 = 55
(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
$50
$20
$40
High
$60
$80
$70
Therefore select to subcontract the work.
Regrets
Low High
$00 $20
$30 $00
$10 $10
Max.
$20
$30
$10 (min.)
Saba Bahouth – UCO 7

• 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
Saba Bahouth – UCO 8

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:
Alternative
Next year demand
Low
Probability : .3
High
.7
Do nothing
Expand
Subcontract
Therefore select to expand.
$50
$20
$40
$60
$80
$70
E M V
.3x50 + .7x60 = 57
.3x20 + .7x80 = 62
.3x40 + .7x70 = 61
Saba Bahouth – UCO 9

Expand
DECISION TREES:
Low .3
$50
Low .3
$50
High .7
$60
Low .3
$20
$57
High
.7
$60
Low .3
$20
Expand
$62
High .7
$80
High .7
$80
$61
Low .3
$40
High .7
$70
- Branches leaving square nodes represent alternatives.
- Branches leaving circular nodes represent outcomes.
Saba Bahouth – UCO
Low .3
$40
High .7
$70
10

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
$20
$40
$60
$80
$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
Saba Bahouth – UCO 11

Saba Bahouth – UCO 12

Probabilities associated with each outcome are estimates. What happens if they were different?
50
40
Do N.
Sub.
Exp.
20
80
70
60
Equations:
Do nothing:
Expand:
Subcontract:
50 + 10P
20 + 60P
40 + 30P
After solving pairs of equations with two unknown:
Do nothing for:
Subcontract for:
Expand for:
0.00 < P < 0.50
0.50 < P < 0.67
0.67 < P < 1.00
0 .50
.67
Probability of high demand
1.0
Saba Bahouth – UCO 13