Decision Analysis

Introduction Chapter 6

What kinds of problems ?

• Decision Alternatives (“what ifs”) are known

• States of Nature and their probabilities are known (ex. rainy 20%, partly cloudy 50%, sunny 20%)

• Outcomes, (referred to as “Payoffs”) are computable under different possible scenarios –each is a combination of a decision alternative and a state of nature

Decision Analysis Basic Terms

• Decision Alternatives

• States of Nature (eg. Condition of economy or weather)

• Payoffs ($ outcome of a choice assuming a state of nature)

• Criteria (i.e. Expected Value)

Decision Analysis Conditions

• Certainty– Decision Maker knows with certainty what the state of

nature will be - only one possible state of nature

• Ignorance– Decision Maker knows all possible states of nature,

but does not know probability of occurrence

• Risk– Decision Maker knows all possible states of nature,

and can assign probability of occurrence for each state –this will be our focus

Decision Making Under Certainty

Decision VariableUnits to build 150

Parameter EstimatesCost to build (/unit) 6,000$ Revenue (/unit) 14,000$ Demand (units) 250

Consequence VariablesTotal Revenue 2,100,000$ Total Cost 900,000$

Performance MeasureNet Revenue 1,200,000$

Decision Making Under Ignorance – Payoff Table

Kelly Construction Payoff Table (Prob. 8-17)

Low (50 units) Medium (100 units) High (150 units)

Build 50 400,000 400,000 400,000

Build 100 100,000 800,000 800,000

Build 150 (200,000) 500,000 1,200,000

State of Nature

DemandAlternative Actions

Decision Making Under Ignorance

Which alternative will we choose?

• Maximax– Select the strategy with the highest possible

return• Maximin

– Select the strategy with the smallest possible loss

Maximax: The Optimistic Point of View

• Select the “best of the best” strategy– Evaluates each decision by the maximum possible

return associated with that decision (Note: if cost data is used, the minimum return is “best”)

– The decision that yields the maximum of these maximum returns (maximax) is then selected

• For “risk takers”– Doesn’t consider the “down side” risk– Ignores the possible losses from the selected

alternative

Maximax Example

Low (50 units) Medium (100 units) High (150 units) Max

Build 50 400,000 400,000 400,000 400,000

Build 100 100,000 800,000 800,000 800,000

Build 150 (200,000) 500,000 1,200,000 1,200,000

State of NatureMaximax CriterionDemand

Alternative Actions

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Maximin: The Pessimistic Point of View

• Select the “best of the worst” strategy– Evaluates each decision by the minimum

possible return associated with the decision– The decision that yields the maximum value of

the minimum returns (maximin) is selected

• For “risk averse” decision makers– A “protect” strategy– Worst case scenario the focus

Maximin

Low (50 units) Medium (100 units) High (150 units) Min

Build 50 400,000 400,000 400,000 400,000

Build 100 100,000 800,000 800,000 100,000

Build 150 (200,000) 500,000 1,200,000 (200,000)

State of NatureMaximin CriterionDemand

Alternative Actions

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Decision Making Under Risk

• Expected Return (ER)*– Select the alternative with the highest

expected return

– Use a weighted average of the possible returns for each alternative, with probabilities used as weights

* Also referred to as Expected Value (EV) or Expected Monetary Value (EMV)

Expected Return

Low (50 units) Medium (100 units) High (150 units) ER

Build 50 400,000 400,000 400,000 400,000

Build 100 100,000 800,000 800,000 660,000

Build 150 (200,000) 500,000 1,200,000 570,000

Probability 0.2 0.5 0.3 1.0

State of NatureExpected

ReturnDemandAlternative

Actions

Note that we now have probabilities for each state of nature

Expected Value of Perfect Information• EVPI measures how much better you could do on this decision if

you could always know when each state of nature would occur, where:

– EVUPI = Expected Value Under Perfect Information (also called EVwPI, the EV with perfect information, or EVC, the EV “under

certainty”)

– EVUII = Expected Value of the best action with imperfect information (also called EVBest )

– EVPI = EVUPI – EVUII• EVPI tells you how much you are willing to pay for perfect

information (or is the upper limit for what you would pay for additional “imperfect” information!)

Expected Value of Perfect Information

Low (50 units) Medium (100 units) High (150 units) ER

Build 50 400,000 400,000 400,000 400,000

Build 100 100,000 800,000 800,000 660,000

Build 150 (200,000) 500,000 1,200,000 570,000

Probability 0.2 0.5 0.3 1.0

Best Decision 400,000 800,000 1,200,000 840,000

EVPI 180,000

State of NatureExpected

ReturnDemandAlternative

Actions

Using Excel to Calculate EVPI: Formulas View

A B C D E123 Payoffs States of Nature Expected Return4 Alternatives Low (50 units) Medium (100 units) High (150 units) ER5 Build 50 400000 400000 400000 =SUMPRODUCT(B5:D5,B$8:D$8)6 Build 100 100000 800000 800000 =SUMPRODUCT(B6:D6,B$8:D$8)7 Build 150 -200000 500000 1200000 =SUMPRODUCT(B7:D7,B$8:D$8)8 Probability 0.2 0.5 0.39 Best Decision =MAX(B5:B7) =MAX(C5:C7) =MAX(D5:D7)1011 EVwPI = =SUMPRODUCT(B9:D9,B8:D8)12 EVBest = =MAX(E5:E7)13 EVPI = =E11-E1214

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