Decision AnalysisDecision Analysis

A. A. ElimamA. A. ElimamCollege of BusinessCollege of Business

San Francisco State UniversitySan Francisco State University

Characteristics of a Good Characteristics of a Good DecisionDecision

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) StepsDecision 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)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 ExampleDecision Table Example

200,000

100,000

0

-180,000

-20,000

0

Favorable($) Unfavorable($)Alternatives

Large Plant

Small Plant

Do Nothing

State of Nature (Market)

Decision Making Under RiskDecision 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 ExampleThompson 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 LumberThompson Lumber

200,000

100,000

0

-180,000

-20,000

0

Favorable ($) Unfavorable ($)Alternatives

Large Plant

Small Plant

Do Nothing

State of Nature (Market)

EMV ($)

Probabilities 0.5 0.5

10,000

40,000

Expected Value of PerfectExpected Value of Perfect Information (EVPI) 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 Expected Value of Perfect Information (EVPI)Information (EVPI)

EVPI = Expected Outcome with Perfect Information - Expected Outcome without Perfect Information

EVPI = Expected Value with Perfect Information - Maximum EMV

Thompson LumberThompson 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

Decision Table ExampleDecision Table Example

200

160

0

270

800

0

Low ($) High ($)Alternative

Small Facility

Large Facility

Do Nothing

Possible Future Demand

Example A.5Example A.5

200

160

0

270

800

0

Low ($) High ($)Alternatives

Small

Large

Do Nothing

Demand

EMV ($)

Probabilities 0.4 0.6

242

544

Example A.8Example 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

Opportunity Loss : Thompson LumberOpportunity Loss : Thompson Lumber

200,000-200,000

200,000-100,000

200,000-0

0-(-180,000)

0-(-20,000)

0 - 0

Favorable ($) Unfavorable($)

State of Nature (Market)

Opportunity Loss : Thompson LumberOpportunity Loss : Thompson Lumber

0

100,000

200,000

180,000

20,000

0

Favorable ($) Unfavorable ($)Alternatives

Large Plant

Small Plant

Do Nothing

State of Nature (Market)

EOL ($)

Probabilities 0.5 0.5

90,000

60,000

100,000

Sensitivity AnalysisSensitivity AnalysisEMV, $

0

-100,000

1

Values of P

-200,000

100,000

200,000

EMV(LF)

EMV(DN)

EMV(SF)

Point 2, p=0.62 Point 1

p=0.167

One Time DecisionOne Time Decision

Fruit Baskets: GivenDemand and Associated ProbabilitiesCost = $ 10/ unit Selling Price = $ 15/unitFind the Quantity yielding Maximum EMV

Probability 0.3 0.5 0.2Demand, DQuantity,Q

10 25 40 EMV

10 $50 $50 $50 $5025 -$100 $125 $125 $57.5040 -$250 -$25 $200 -$47.5

Decision TreesDecision 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)

Decision TreesDecision Trees

Two Types of Nodes

Selection Among Alternatives

State of Nature

Branches of the Decision Tree

Decision Tree: ExampleDecision Tree: Example

SmallLarge

Do Nothing

Unfavorable (0.5)

F. (0.5)

Favorable (0.5)

U. (0.5)

U. (0.5)

F. (0.5)

A Decision Tree for Capacity ExpansionA Decision Tree for Capacity Expansion(Payoff in thousands of dollars)(Payoff in thousands of dollars)

Low demand [0.40]$70

High demand [0.60]

($135)

2

Low demand [0.40]$40

High demand [0.60]$220

($109)

($148)

($148)

1

Don’t expand$90

Expand$135

Small expansion

Large expansion

Decision Tree for RetailerDecision Tree for Retailer

3

2

1

Low demand [0.4]$200

Don’t expand$223

Expand$270

Do nothing$40

AdvertiseModest response [0.3]

$20

Sizable response [0.7]

$220

High demand [0.6]$800

($544)

($544)

($160)

($160)

($270)

($242)

Large facility Low demand

[0.4]

Small facil

ityHigh demand

[0.6]