Decision Analysis

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Decision Analysis

• A. A. Elimam
• College of Business
• San Francisco State University

2
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
3
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

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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

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Decision Table Example
State of Nature (Market)
Favorable()
Unfavorable()
Alternatives
-180,000
200,000
Large Plant
-20,000
100,000
Small Plant
Do Nothing
0
0
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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)

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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

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Thompson Lumber
State of Nature (Market)
Alternatives
Favorable ()
Unfavorable ()
EMV ()
200,000
Large Plant
-180,000
10,000
100,000
-20,000
Small Plant
40,000
0
0
Do Nothing
Probabilities
0.5
0.5
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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)

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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

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Thompson LumberExpected 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

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Decision Table Example
Possible Future Demand
Low ()
High ()
Alternative
270
200
Small Facility
800
160
Large Facility
Do Nothing
0
0
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Example A.5
Demand
Alternatives
Low ()
High ()
EMV ()
270
200
Small
242
160
800
Large
544
0
0
Do Nothing
Probabilities
0.4
0.6
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Example A.8Expected 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

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Opportunity Loss Thompson Lumber
State of Nature (Market)
Favorable ()
Unfavorable()
0-(-180,000)
200,000-200,000
0-(-20,000)
200,000-100,000
200,000-0
0 - 0
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Opportunity Loss Thompson Lumber
State of Nature (Market)
Alternatives
Favorable ()
Unfavorable ()
EOL ()
0
Large Plant
180,000
90,000
100,000
20,000
Small Plant
60,000
200,000
0
Do Nothing
100,000
Probabilities
0.5
0.5
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Sensitivity Analysis
EMV,
Point 2, p0.62
EMV(LF)
Point 1 p0.167
200,000
EMV(SF)
100,000
EMV(DN)
0
1
-100,000
Values of P
-200,000
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One Time Decision
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Decision Trees

• Decision Table Only Columns-Rows
• Columns State of Nature
• Rows Alternatives- 1 Decision ONLY
• For more than one Decision Trees
• Decision Trees can handle a sequence of one or
  more decision(s)

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Decision Trees

• Two Types of Nodes
• Selection Among Alternatives
• State of Nature
• Branches of the Decision Tree

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Decision Tree Example
Favorable (0.5)
Large
Unfavorable (0.5)
F. (0.5)
Small
U. (0.5)
Do Nothing
F. (0.5)
U. (0.5)
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A Decision Tree for Capacity Expansion(Payoff in
thousands of dollars)
Low demand 0.40
70
Dont expand
90
Small expansion
High demand 0.60
(109)
2
Expand
(135)
1
135
Low demand 0.40
Large expansion
40
(148)
High demand 0.60
(148)
220
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Decision Tree for Retailer
Low demand 0.4
200
High demand 0.6
Dont expand
Small facility
(242)
223
2
Expand
270
(270)
1
Do nothing
40
Modest response 0.3
3
(544)
20
Advertise
Low demand 0.4
Large facility
(160)
Sizable response 0.7
(160)
220
High demand 0.6
(544)
800