Decision Analysis
Introduction
Chapter 6
What kinds of problems ?
• Decision Alternatives (“what ifs”) are
known
• States of Nature and their probabilities are
known (ex. rainy 20%, partly cloudy 50%,
sunny 20%)
• Outcomes, (referred to as “Payoffs”) are
computable under different possible
scenarios –each is a combination of a
decision alternative and a state of nature
Decision Analysis Basic Terms
• Decision Alternatives
• States of Nature (eg. Condition of
economy or weather)
• Payoffs ($ outcome of a choice assuming
a state of nature)
• Criteria (i.e. Expected Value)
Decision Analysis Conditions
• Certainty
– Decision Maker knows with certainty what the state of
nature will be - only one possible state of nature
• Ignorance
– Decision Maker knows all possible states of nature,
but does not know probability of occurrence
• Risk
– Decision Maker knows all possible states of nature,
and can assign probability of occurrence for each
state –this will be our focus
Decision Making Under Certainty
Decision Variable
Units to build
Parameter Estimates
Cost to build (/unit)
Revenue (/unit)
Demand (units)
150
$
$
6,000
14,000
250
Consequence Variables
Total Revenue
Total Cost
$ 2,100,000
$ 900,000
Performance Measure
Net Revenue
$ 1,200,000
Decision Making Under Ignorance
– Payoff Table
Kelly Construction Payoff Table (Prob. 8-17)
State of Nature
Demand
Alternative
Actions Low (50 units) Medium (100 units) High (150 units)
Build 50
400,000
400,000
400,000
Build 100
100,000
800,000
800,000
Build 150
(200,000)
500,000
1,200,000
Decision Making Under Ignorance
Which alternative will we choose?
• Maximax
– Select the strategy with the highest possible
return
• Maximin
– Select the strategy with the smallest possible
loss
Maximax:
The Optimistic Point of View
• Select the “best of the best” strategy
– Evaluates each decision by the maximum possible
return associated with that decision (Note: if cost data
is used, the minimum return is “best”)
– The decision that yields the maximum of these
maximum returns (maximax) is then selected
• For “risk takers”
– Doesn’t consider the “down side” risk
– Ignores the possible losses from the selected
alternative
Maximax Example
Kelly Construction
State of Nature
Alternative
Actions
Demand
Maximax
Criterion
Low (50 units) Medium (100 units) High (150 units)
Max
Build 50
400,000
400,000
400,000
400,000
Build 100
100,000
800,000
800,000
800,000
Build 150
(200,000)
500,000
1,200,000
1,200,000
Maximin:
The Pessimistic Point of View
• Select the “best of the worst” strategy
– Evaluates each decision by the minimum
possible return associated with the decision
– The decision that yields the maximum value
of the minimum returns (maximin) is selected
• For “risk averse” decision makers
– A “protect” strategy
– Worst case scenario the focus
Maximin
Kelly Construction
State of Nature
Alternative
Actions
Demand
Maximin
Criterion
Low (50 units) Medium (100 units) High (150 units)
Min
Build 50
400,000
400,000
400,000
400,000
Build 100
100,000
800,000
800,000
100,000
Build 150
(200,000)
500,000
1,200,000
(200,000)
Decision Making Under Risk
• Expected Return (ER)*
– Select the alternative with the highest
expected return
– Use a weighted average of the possible
returns for each alternative, with probabilities
used as weights
* Also referred to as Expected Value (EV) or
Expected Monetary Value (EMV)
Expected Return
State of Nature
Alternative
Actions
Demand
Expected
Return
Low (50 units) Medium (100 units) High (150 units)
ER
Build 50
400,000
400,000
400,000
400,000
Build 100
100,000
800,000
800,000
660,000
Build 150
(200,000)
500,000
1,200,000
570,000
0.5
0.3
1.0
Probability
0.2
Note that we now have probabilities for each state of nature
Expected Value of Perfect Information
• EVPI measures how much better you could do on
this decision if you could always know when each
state of nature would occur, where:
– EVUPI = Expected Value Under Perfect Information
(also called EVwPI, the EV with perfect information, or
EVC, the EV “under certainty”)
– EVUII = Expected Value of the best action with
imperfect information (also called EVBest )
– EVPI = EVUPI – EVUII
• EVPI tells you how much you are willing to pay for
perfect information (or is the upper limit for what you
would pay for additional “imperfect” information!)
Expected Value of Perfect Information
State of Nature
Alternative
Actions
Demand
Expected
Return
Low (50 units) Medium (100 units) High (150 units)
ER
Build 50
400,000
400,000
400,000
400,000
Build 100
100,000
800,000
800,000
660,000
Build 150
(200,000)
500,000
1,200,000
570,000
0.2
0.5
0.3
1.0
400,000
800,000
1,200,000
840,000
EVPI
180,000
Probability
Best Decision
Using Excel to Calculate EVPI:
Formulas View
Kelly Construction
A
1
2
3
4
5
6
7
8
9
10
11
12
13
14
Payoffs
Alternatives
Build 50
Build 100
Build 150
Probability
Best Decision
B
C
States of Nature
Low (50 units) Medium (100 units)
400000
400000
100000
800000
-200000
500000
0.2
0.5
=MAX(B5:B7)
=MAX(C5:C7)
D
E
Expected Return
High (150 units)
ER
400000
=SUMPRODUCT(B5:D5,B$8:D$8)
800000
=SUMPRODUCT(B6:D6,B$8:D$8)
1200000
=SUMPRODUCT(B7:D7,B$8:D$8)
0.3
=MAX(D5:D7)
EVwPI = =SUMPRODUCT(B9:D9,B8:D8)
EVBest = =MAX(E5:E7)
EVPI = =E11-E12