Decision Analysis
A. A. Elimam
College of Business
San Francisco State University
Characteristics of a Good Decision
Based on Logic
 Considers all Possible Alternatives
 Uses all Available Data
 Applies Quantitative Approach

Decision Analysis Frequently
results in a favorable outcome
Decision Analysis (DA) Steps
 Clearly
define the problem
 List all possible alternatives
 Identify possible outcomes
 Determine payoff for each
alternative/outcome
 Select one of the DA models
 Apply model to make decision
Types of Decision Making (DM)
 DM
under Certainty: Select the
alternative with the Maximum
payoff
 DM under Uncertainty: Know
nothing about probability
 DM under Risk: Only know the
probability of occurrence of each
outcome
Decision Table Example
State of Nature (Market)
Alternatives Favorable($) Unfavorable($)
Large Plant
200,000
-180,000
Small Plant
100,000
-20,000
Do Nothing
0
0
Decision Making Under Risk

Expected Monetary Value (EMV)
EMV (Alternative i) =
(Payoff of first State of Nature-SN) x
(Prob. of first SN) + (Payoff of second
SN) x (Prob. of Second SN) + (Payoff
of third State of Nature-SN) x (Prob.
of third SN) + . . . + (Payoff of last
SN) x (Prob. of last SN)
Thompson Lumber Example

EMV(Large F.) =
(0.50)($200,000)+(0.5)(-180,000)= $10,000
 EMV(Small F.) =
(0.50)($100,000)+(0.5)(-20,000)= $40,000
 EMV(Do Nothing) =
(0.50)($0)+(0.5)(0)= $0
Thompson Lumber
State of Nature (Market)
Alternatives
Favorable ($) Unfavorable ($) EMV ($)
Large Plant
200,000
-180,000
10,000
Small Plant
100,000
-20,000
40,000
Do Nothing
0
0
Probabilities
0.5
0.5
Expected Value of Perfect
Information (EVPI)
 Expected
Value with Perfect
Information =
(Best Outcome for first SN) x (Prob. of
first SN) + (Best Outcome for
second SN) x (Prob. of Second SN) +
. . . + (Best Outcome for last SN) x
(Prob. of last SN)
Expected Value of Perfect
Information (EVPI)

EVPI = Expected Outcome with
Perfect Information - Expected
Outcome without Perfect
Information

EVPI = Expected Value with
Perfect Information - Maximum
EMV
Thompson Lumber
Expected Value of Perfect Information

Best Outcome For Each SN
• Favorable: Large plant, Payoff = $200,000
• Unfavorable: Do Nothing, Payoff = $0
So Expected Value with Perfect Info.
= (0.50)($200,000)+(0.5)(0)= $100,000
 The Max. EMV = $ 40,000
 EVPI = $100,000 - $40,000 = $ 60,000

Decision Table Example
Possible Future Demand
Alternative
Low ($)
High ($)
Small Facility
200
270
Large Facility
160
800
0
0
Do Nothing
Example A.5
Demand
Alternatives
Low ($)
High ($)
EMV ($)
Small
200
270
242
Large
160
800
544
0
0
0.4
0.6
Do Nothing
Probabilities
Example A.8
Expected Value of Perfect Information

Best Outcome For Each SN
• High Demand: Large , Payoff = $800
• Low Demand : Small , Payoff = $200
So Expected Value with Perfect Info.
= (0.60)($800)+(0.4)(200)= $560
 The Max. EMV = $ 544
 EVPI = $ 560 - $ 544 = $ 16

Opportunity Loss : Thompson Lumber
State of Nature (Market)
Favorable ($)
Unfavorable($)
200,000-200,000
0-(-180,000)
200,000-100,000
0-(-20,000)
200,000-0
0-0
Opportunity Loss : Thompson Lumber
State of Nature (Market)
Alternatives Favorable ($) Unfavorable ($) EOL ($)
Large Plant
0
180,000
90,000
Small Plant
100,000
20,000
60,000
Do Nothing
200,000
0
100,000
Probabilities
0.5
0.5
Sensitivity Analysis
EMV, $
200,000
Point 1
p=0.167
Point 2,
p=0.62
EMV(LF)
EMV(SF)
100,000
EMV(DN)
0
1
-100,000
-200,000
Values of P
One Time Decision
Fruit Baskets: Given
Demand and Associated Probabilities
Cost = $ 10/ unit Selling Price = $ 15/unit
Find the Quantity yielding Maximum EMV
Probability
0.3
0.5
0.2
EMV
Demand, D
10
25
40
Quantity,Q
10
$50
$50
$50 $50
25
-$100 $125 $125 $57.50
40
-$250 -$25
$200 -$47.5
Decision Trees

Decision Table: Only Columns-Rows

Columns: State of Nature

Rows: Alternatives- 1 Decision ONLY

For more than one Decision

Decision Trees can handle a sequence
of one or more decision(s)
Trees
Decision Trees

Two Types of Nodes

Selection Among Alternatives

State of Nature

Branches of the Decision Tree
Decision Tree: Example
A Decision Tree for Capacity Expansion
(Payoff in thousands of dollars)
Low demand [0.40]
$70
Don’t expand
($109)
1
($148)
($148)
$90
High demand [0.60]
2
($135)
Low demand [0.40]
$40
High demand [0.60]
$220
Expand
$135
Decision Tree for Retailer
Low demand [0.4]
Don’t expand
($242)
2
($270)
1
($544)
Do nothing
$223
$270
$40 Modest response [0.3]
$20
Advertise
($160)
Sizable response [0.7]
($160)
$220
High demand [0.6]
$800
3
($544)
Expand
$200