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WelcomeWelcomeUnit 4 SeminarUnit 4 Seminar
WelcomeWelcomeUnit 4 SeminarUnit 4 Seminar
MM305 Wednesday 8:00 PM ETQuantitative Analysis for Management
Delfina Isaac
Six Steps in Decision MakingSix Steps in Decision Making
Identifying the Problem
Selecting the Best Alternatives
Analyzing the Alternatives
Following Up Determining AlternativeCourses of Action
Implementingthe Decision
Decision theory modelsDecision theory models
• Decision alternatives – this is a course of
action that may be chosen by the decision maker.
• States of nature – an occurrence that affects
the outcome of the decision; decision maker has no control over the states of nature
• Payoff – benefit that occurs when a specific
decision is made and a specific state of nature occurs.
ABC Land Development Corp.ABC Land Development Corp.ABC Land owns 5000 acres that are zoned to be developed as recreational home sites. Three development decision alternatives are being considered:
A1: Develop a small amount of acreage (500 acres)
A2: Develop a medium amount of acreage (2500 acres)
A3: Develop a large amount of acreage (5000 acres)
ABC Land Development Corp.ABC Land Development Corp.
Three possible states of nature that ABC anticipates as possibilities:
S1: Low customer demand
S2: Medium customer demand
S3: High customer demand
Decision TableDecision Table
Projected profit depends on the decision alternative and the state of nature that occurs.
S1 S2 S3
A1 35003500 30003000 27002700
A2 10001000 1250012500 1240012400
A3 -500-500 -250-250 2500025000
Which decision alternative would you choose?
Types of Decision-Making EnvironmentsTypes of Decision-Making Environments
Type 1Type 1:: Decision making under certainty
Decision maker knows with certaintyknows with certainty the consequences of every alternative or decision choice
Type 2Type 2:: Decision making under uncertainty
The decision maker does not knowdoes not know the probabilities of the various outcomes
Type 3Type 3:: Decision making under risk
The decision maker knowsknows the probabilities the probabilities of the various outcomes
Decision Making Under UncertaintyDecision Making Under Uncertainty
1. Maximax (optimistic)
2. Maximin (pessimistic)
3. Criterion of realism (Hurwicz)
4. Equally likely (Laplace)
5. Minimax regret
There are several criteria for making decisions under uncertainty
Maximax (optimistic) approachMaximax (optimistic) approach
S1 S2 S3
A1 35003500 30003000 27002700
A2 10001000 1250012500 1240012400
A3 -500-500 -250-250 2500025000
Max of row
3500
12500
25000
Max of maximums 25000
Find the maximum payoff for each decision alternative (row). Select the decision alternative with the maximum maximum – MAXIMAX.
Determines the best possible outcome for ABC
S1 S2 S3
A1 35003500 30003000 27002700
A2 10001000 1250012500 1240012400
A3 -500-500 -250-250 2500025000
Min of row
2700
1000
-500
Max of minimums 2700
Find the minimum payoff for each decision alternative (row). Select the decision alternative with the maximum minimum - MAXIMIN
Determines the best of the worst possible outcome for ABC
Maximin (pessimistic) approachMaximin (pessimistic) approach
S1 S2 S3
A1 35003500 30003000 27002700
A2 10001000 1250012500 1240012400
A3 -500-500 -250-250 2500025000
Criteria of Realism
(α=0.8)
3340
10200
19900
Max of realism 19900
Weighted average = (α) (maximum in row) + (1 – α)(minimum in row)
Determines compromise between optimistic and pessimistic
Criterion of Realism (Hurwicz)Criterion of Realism (Hurwicz)
Equally likely (Laplace) approachEqually likely (Laplace) approach
S1 S2 S3
A1 35003500 30003000 27002700
A2 10001000 1250012500 1240012400
A3 -500-500 -250-250 2500025000
Average
3067
8083
8633
Max of average 8633
Find the average payoff for each decision alternative (row). Select the decision alternative with the maximum average.
Determines the highest average outcome.
Minimax RegretMinimax Regret
S1 S2 S3
A13500-35003500-3500 12500-300012500-3000 25000-270025000-2700
A23500-10003500-1000 12500-1250012500-12500 25000-1240025000-12400
A33500-(-500)3500-(-500) 12500-(-250)12500-(-250) 25000-2500025000-25000
Create Opportunity Loss Tables.
S1 S2 S3
A100 95009500 2230022300
A225002500 00 1260012600
A340004000 1275012750 00
Minimax RegretMinimax Regret
S1 S2 S3
A1 00 95009500 2230022300
A2 25002500 00 1260012600
A3 40004000 1275012750 00
Max
22300
12750
12600
Minimax 12600
Determines the highest average outcome.
Which is the best decision?Which is the best decision?
ApproachApproach DecisionDecision
Maximax (optimistic) A3
Maximin (pessimistic) A1
Realism A3
Equally Likely A2
Minimax Regret A2
Decision Making Under RiskDecision Making Under Risk
• Decision making when there are several possible states of nature and we know the probabilities associated with each possible state
• Most popular method is to choose the alternative with the highest expected monetary value (EMV)
EMV (alternative i)
= (payoff of S1)*P(S1) +
(payoff of S2)*P(S2) +…..+
(payoff of Sn)*P(Sn)
Decision-making with probabilitiesDecision-making with probabilities
What if ABC estimates the likelihood of each state of nature occurring.
S1: Low customer demand P(S1) = 0.2
S2: Medium customer demandP(S2) = 0.5
S3: High customer demand P(S3) = 0.3
Would this change your decision previously made?
Expected Monetary Value ApproachExpected Monetary Value Approach
S1 S2 S3
A1 35003500 30003000 27002700
A2 10001000 1250012500 1240012400
A3 -500-500 -250-250 2500025000
Expected value
3010
10170
7275
Max of expected values – Max EV 10170
EMV (500 acres) = (0.2)(3500) + (0.5)(3000) + (0.3)(2700) = 3010
Represents the average best (with probabilities) outcome for ABC.
0.20.2 0.50.5 0.30.3
Expected Value of Perfect Information (EVPI)
Expected Value of Perfect Information (EVPI)
• EVPI places an upper bound on what you
should pay for additional information
EVPI = EVwPI – Maximum EMV
• EVwPI is the long run average return if we
have perfect information before a decision is
made
Expected Value with Perfect Information (EVwPI)Expected Value with Perfect Information (EVwPI)
S1 S2 S3
A1 35003500 30003000 27002700
A2 10001000 1250012500 1240012400
A3 -500-500 -250-250 2500025000
0.20.2 0.50.5 0.30.3
EVwPI = 0.2(3500) + 0.5(12500) + 0.3(25000) =14450
Expected Opportunity LossExpected Opportunity Loss
• Expected opportunity loss (EOL) is the cost of not
picking the best solution
1. First construct an opportunity loss table
2. For each alternative, multiply the opportunity loss
by the probability of that loss for each possible
outcome and add these together
• Minimum EOL will always result in the same
decision as maximum EMV
• Minimum EOL will always equal EVPI
Expected Opportunity LossExpected Opportunity Loss
S1 S2 S3
A1 00 95009500 2230022300
A2 25002500 00 1260012600
A3 40004000 1275012750 00
EOL
22300
12750
12600
Minimum EOL 12600
Construct opportunity loss table.
EOL (2500 acres) = (0.2)(2500) + (0.5)(0) + (0.3)(12600) = 4280
0.20.2 0.50.5 0.30.3
Sensitivity AnalysisSensitivity Analysis
Sensitivity analysis examines how our decision might change with different input data
Examines the effects of various probabilities for
the states of nature on the expected values for
the decision alternatives.
Using Excel QM to Solve Decision Theory ProblemsUsing Excel QM to Solve Decision Theory Problems
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