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