wk2 decision analysis

7/31/2019 WK2 Decision Analysis

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OperationsOperations

ManagementManagement

Decision-Making ToolsDecision-Making Tools



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OutlineOutline

♦Decision Making & Models.

♦Decision Tables.

♦ Decision making under uncertainty.♦ Decision making under risk.

♦ Expected value of perfect

information (EVPI).

♦Decision Trees.



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The Decision-MakingThe Decision-Making

ProcessProcess

Problem Decision

QuantitativeAnalysis

LogicHistorical Data

Marketing ResearchScientific AnalysisModeling

Qualitative Analysis

EmotionsIntuitionPersonal Experienceand Motivation

Rumors



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Models and ScientificModels and Scientific

ManagementManagement

♦ Can Help Managers toCan Help Managers to:

♦Gain deeper insights into the

business.♦Make better decisions!

♦Better assess alternative plans

and actions.

♦Quantify, reduce andunderstand the uncertainty

surrounding business plansand actions.



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Steps to GoodSteps to Good

DecisionsDecisions♦Define problem and influencing

factors.

♦ Establish decision criteria.

♦Select decision-making tool(model).

♦ Identify and evaluatealternatives using decision-making tool (model).

♦Select best alternative.

♦ Implement decision.



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Benefits of ModelsBenefits of Models

♦Allow better and fasterdecisions.

♦ Less expensive and disruptive

than experimenting with the realworld system.

♦Allow managers to ask “What

if…?” questions.♦ Force a consistent and

systematic approach to the

analysis of problems.♦



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Limitations of ModelsLimitations of Models

♦May be expensive and time-consuming to develop and test.

♦May be unused, misused ormisunderstood (and feared!).

♦ Due to mathematical and logicalcomplexity.

♦May downplay the value of qualitative information.

♦May use assumptions that

oversimplify the real world.



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Decision TheoryDecision Theory

Terms:

Alternative: Course of action orchoice.

Decision-maker chooses amongalternatives.

State of nature: An occurrenceover which the decision maker

has no control .



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Decision TableDecision Table

States of Nature

State 1 State 2

Alternative 1

Outcome 1 Outcome 2

Alternative 2

Outcome 3 Outcome 4



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A firm has two options for expanding production of a product: (1) construct a large plant; or (2)construct a small plant. Whether or not the firmexpands, the future market for the product will be

either favorable or unfavorable.

If a large plant is constructed and the market isfavorable, then the result is a profit of $200,000. If a large plant is constructed and the market is

unfavorable, then the result is a loss of $180,000.

If a small plant is constructed and the market isfavorable, then the result is a profit of $100,000. If a small plant is constructed and the market isunfavorable, then the result is a loss of $20,000. Of course the irm ma also choose to “do nothin ”

xamp e - ec s onxamp e - ec s onMaking UnderMaking UnderUncertaintyUncertainty

xamp e ec s onxamp e ec s on



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xamp e - ec s onxamp e - ec s onMaking UnderMaking UnderUncertaintyUncertainty

States of NatureAlternativesFavorable

MarketUnfavorable

Market

Constructlarge plant $200,000-$180,000

Constructsmall plant

$100,000 -$20,000

$0 $0Donothing



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Decision Making UnderDecision Making Under

Uncertainty - CriteriaUncertainty - Criteria♦Maximax - Choose alternative

that maximizes the maximumoutcome for every alternative

(Optimistic criterion).

♦Maximin - Choose alternativethat maximizes the minimum

outcome for every alternative(Pessimistic criterion).

♦Expected Value - Choose

alternative with the highest



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Example - MaximaxExample - Maximax


MarketUnfavorable

Market

Constructlarge plant

$200,000-$180,000


$100,000 -$20,000

$0 $0Donothing

Maximax decision is to constructlarge plant.



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Example - MaximinExample - Maximin

Minimumin Row

-$180,000

-$20,000

$0

Maximin decision is to do nothing.

(Maximum of minimums for eachalternative)


MarketUnfavorable

Market


$200,000-$180,000


$100,000 -$20,000

$0 $0Donothing

i i ki d



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♦Probabilistic decisionsituation.

♦States of nature have

probabilities of occurrence.

♦Select alternative with largestexpected value (EV).

♦ EV = Average return for alternativeif decision were repeated manytimes.

Decision Making UnderDecision Making Under

Risk Risk



E l E t dExample Expected



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Example - ExpectedExample - ExpectedValueValue

Suppose: Probability of favorable

market = 0.5Probability of unfavorable

market = 0.5States of Nature

AlternativesFavorableMarketUnfavorableMarket


$200,000-$180,000

Constructsmall plant $100,000 -$20,000

$0 $0Donothing

ExpectedValue$10,000

$40,000

$0

Decision is to “Construct small

plant”.

Example ExpectedExample Expected



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Suppose: Probability of favorable

market = 0.7Probability of unfavorable

market = 0.3States of Nature



$200,000-$180,000


$0 $0Donothing

ExpectedValue$86,000

$64,000

$0

Now, decision is to “Construct largeplant”.




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Over what range of values for probability

of favorable market is “Construct largeplant” preferred?

Solve for x: 380000x-180000 >

120000x-20000

States of Nature



$200,000-$180,000


$0 $0Donothing

ExpectedValue

380,000x - 180,000

120,000x - 20,000




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Solve for x: 380000x - 180000 >

120000x - 20000

x > 0.6154

So, as long as probability of a favorablemarket exceeds 0.6154, then “Constructlarge plant”.


Over what range of values for probability of favorable market is “Construct large plant”preferred?



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Expected Value of Expected Value of Perfect InformationPerfect Information

((EVPI))♦EVPIEVPI places an upper bound onwhat one would pay foradditional information.♦ EVPI is the maximum you should

pay to learn the future.

♦EVPIEVPI is the expected valueunder certainty (EVUC) minusthe maximum EV.

EVPI = EVUC - maximum EV



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Expected Value UnderExpected Value UnderCertainty (EVUC)Certainty (EVUC)

)P(S* j∑==

EVUC

n

j 1

where:

P(S j ) = The probability of state of nature

j.

n = Number of states of nature.

( Best outcome for the state of nature j)



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Example - EVUCExample - EVUC

Best outcome for Favorable Market= $200,000

Best outcome for Unfavorable=

States of NatureAlternativesFavorableMarket

UnfavorableMarket

Construct

large plant

$200,000-$180,000


$100,000 -$20,000

$0 $0Do

nothing

d l f



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EVPIEVPI = EVUC - max(EV EV )= ($200,000*0.50 +

0*0.50) - $40,000

= $60,000

Thus, you should be willing to pay

up to $60,000 to learn whetherthe market will be favorable or

Suppose: Probability of favorablemarket = 0.5

Probability of unfavorable

market = 0.5

d l fE d V l f



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EVPIEVPI = EVUC - max(EV EV )= ($200,000*0.70 +

0*0.30) - $86,000

= $54,000

Now, you should be willing to pay

up to $54,000 to learn whetherthe market will be favorable or

Now suppose: Probability of favorablemarket = 0.7

Probability of unfavorable

market = 0.3



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♦Graphical display of decisionprocess.

♦Used for solving problems withseveral sets of alternatives andstates of nature (sequential

decisions).♦ Decision tables can not be used for

more than one decision.

♦ Expected Value criterion is used.

Decision TreesDecision Trees



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Using Decision TreesUsing Decision Trees

♦Define the problem.♦Draw the decision tree.

♦Assign probabilities to all statesof nature.

♦Estimate payoffs for eachcombination of alternatives and

states of nature.

♦Solve the problem:

♦ Compute expected values for each

state-of-nature node moving right



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Decision TheoryDecision Theory

Terms:♦ Alternative: Course of action or

choice.

♦ State of nature: An occurrence overwhich the decision maker has nocontrol.

Symbols used in decision tree:A decision node from which one of

several alternatives may be

selected.A state of nature node out of which



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Decision TreeDecision Tree

1

2

State 1

State 2

State 1

State 2

A l t e r n a t i v

e 1

A l t e r n a t i v e 2

DecisionDecision

NodeNode

OutcomeOutcome

11OutcomeOutcome

11

OutcomeOutcome22OutcomeOutcome22

OutcomeOutcome

33OutcomeOutcome

33

OutcomeOutcome44OutcomeOutcome44

State of NatureState of Nature

NodeNode

Decision Tree forDecision Tree for



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ExampleExample

Favorable Mkt (0.7)

B u i l d

L a r g e

B u i l d S m a l l

Unfavorable Mkt (0.3)

$200,000

Favorable Mkt (0.7)


-$180,000

$100,000

-$20,000

$0

D o n o t h i n g




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Example - SolutionExample - Solution

Favorable Mkt (0.7)

B u i l d

L a r g e

B u i l d S m a l l


$200,000

Favorable Mkt (0.7)


-$180,000

$100,000

-$20,000

$0

D o n o t h i n g

$86,000

$64,000

$0



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Decision Tree ExampleDecision Tree ExampleA firm can build a large plant or small plant initially

(for a new product). Demand for the new productwill be high or low initially. The probability of highdemand is 0.6. (The probability of low demand is0.4.)

If they build “small” and demand is “low”, thepayoff is $40 million. If they build “small” anddemand is “high”, they can do nothing and payoff is$45 million, or they can expand. If they expand,

there is a 30% chance the demand drops off and thepayoff will be $35 million, and a 70% chance thedemand grows and the payoff is $48 million.

If they build “large” and demand is “high”, the

payoff is $60 million. If they build “large” anddemand is “low” the can do nothin and a off is -

i i l



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Decision Tree ExampleDecision Tree Example Three decisions:

1. Build “Large” or “Small” plant initially.

2. If build “Small” and demand is “High”,then “Expand” or “Do nothing”.

3. If build “Large” and demand is “Low”, thendecide to “Reduce prices” or “Do nothing”.

Two states of nature:

1. Demand is “High” (0.6) or “Low” (0.4)initially.

2. If build “Small”, demand is “High”, and

decision is “Expand”, then demand “Grows”(0.7) or demand “Drops” (0.3).

D i i T



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B u i l d s m a

l l

B u i l d l a r g e

H i g h ( 0. 6 )

L o w ( 0 .4 )

H i g h

( 0. 6 )

L o w ( 0 .4 )

E x p a n d

Do nothing

Do nothing

Reduce prices

Demand grows (0.7)

Demand drops (0.3)

$48

$35

$45

$40

$60

$20

-$10

1

3

2

i i S l iD i i T S l ti



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Decision Tree SolutionDecision Tree Solution

Work right to left (from end back tobeginning).

Start with Decision 3:“Reduce prices” or “Do nothing”.

Choose “Reduce prices” (20 >

-10).

D i i TD i i T



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B u i l d s m a

l l

B u i l d l a r g e

H i g h ( 0. 6 )

L o w ( 0 .4 )

H i g h

( 0. 6 )

L o w ( 0 .4 )

E x p a n d

Do nothing

Do nothing

Reduce prices

Demand grows (0.7)

Demand drops (0.3)

$48

$35

$45

$40

$60

$20

-$10

1

3

2

$20

D i i T S l tiD i i T S l ti



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Decision Tree SolutionDecision Tree Solution

Consider Decision 2: “Expand” or “Donothing”.

To compare outcomes we needexpected value if we “Expand”:(48*0.7) + (35*0.3) = 44.1

Choose “Do nothing” (45 > 44.1).

D i i TD i i T



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B u i l d s m a

l l

B u i l d l a r g e

H i g h ( 0. 6 )

L o w ( 0 .4 )

H i g h

( 0. 6 )

L o w ( 0 .4 )

E x p a n d

Do nothing

Do nothing

Reduce prices

Demand grows (0.7)

Demand drops (0.3)

$48

$35

$45

$40

$60

$20

-$10

1

3

2

$44.

1

$45

$20

$45

D i i TD i i T



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B u i l d s

m a l l

B u i l d l a r g e

H i g h ( 0. 6 )

L o w ( 0 .4 )

H i g h

( 0. 6 )

L o w ( 0 .4 )

E x p a n d

Do nothing

Do nothing

Reduce prices

Demand grows (0.7)

Demand drops (0.3)

$48

$35

$45

$40

$60

$20

-$10

1

3

2

$44.

1

$45

$20

$45

$44

$43

Decision Tree FinalDecision Tree Final



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SolutionSolution

Decisions:

1. Build “Large”.

2. If demand is “Low”, then “Reduceprices”.

Expected payoff = $44 million.

Larger Decision TreeLarger Decision Tree



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Larger Decision TreeLarger Decision Tree

0.4

$10

$ 8

$12

$11

$ 6

$ 8

$ 9

1

3

2

0.3

0.3

0.6

0.4

0.5

0.3

0.20.6

0.4

$ 9

$12

$ 8

Larger Decision Tree -Larger Decision Tree -



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gg

SolutionSolution

0.4

$10

$ 8

$12

$11

$ 6

$ 8

$ 9

1

3

2

0.3

0.3

0.6

0.4

0.5

0.3

0.20.6

0.4

$ 9

$12

$ 8

$10.28

$9.6

$9.6

$8.3

$10.4$10.4

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