Decision Analysis (1)

7/28/2019 Decision Analysis (1)

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To accompany Quantitative Analysis

for Management, 8e

by Render/Stair/Hanna3-1

2003 by Prentice Hall, Inc.

Upper Saddle River, NJ 07458

Decision Analysis(Theory)


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Introduction

Decision theory is an analytical

and systematic way to tackle

problems

A good decision is based on

logic.


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The Six Steps inDecision Theory

1) Clearly define the problem at

hand

2) List the possible alternatives3) Identify the possible outcomes

4) List the payoff or profit of

each combination ofalternatives and outcomes

5) Select one of the mathematical

decision theory models6) Apply the model and make

your decision


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Decision Tablefor Thompson Lumber

State of Nature

Alternative FavorableMarket

UnfavorableMarket

Construct alarge plant

$200,000 -$180,000

Construct asmall plant

$100,000 -$20,000

Do nothing $0 0


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Types of Decision-Making Environments

Type 1: Decision-making under certainty

decision-makerknows with certainty the

consequences of every alternative or decision choice

Type 2: Decision-making under risk

The decision-makerdoes know the probabilities of

the various outcomes

Type 3: Decision-making under uncertainty

The decision-makerdoes not know the probabilities

of the various outcomes


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Decision-MakingCertainty

Knows with certainty the result

of every alternative


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Decision-MakingUnder Risk

Expected Monetary Value

nature.ofstagesofnumbernwhere

)(*SPayoffative)EMV(Altern1

j

j

n

j

SP


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Decision Table(Matrix)

for Thompson Lumber

Favorable

Market

Unfavorable

MarketAlternative State of Nature

Construct a

large plant

$200,000 -$180,000 $10,000


$100,000 -$20,000 $40,000

Do nothing $0 0

0.50 0.50


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Expected Value ofPerfect Information

(EVPI)

EVPIplaces an upper bound on

what one would pay for

additional information

EVPIis the expected value with

perfect information minus themaximum EMV


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Expected Value WithPerfect Information

(EV | PI)

nature.ofstatesofnumbern

)P(S*nature)ofstateforoutcome(BestPI|EVn

1j

j


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EVPI=EV|PI- maximumEMV


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State of Nature

Alternative Favorable

Market

Unfavorable

Market

EMV


$200,000

Construct a

small plant

$40,000

Do Nothing $0

0.50 0.50


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EVPI= expected value with perfect

information - max(EMV)

= $200,000*0.50 + $0*0.50 - $40,000

= $60,000


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Expected OpportunityLoss

EOL is the cost of not picking

the best solution

EOL = Expected Regret


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Computing EOL - TheOpportunity Loss Table

State of Nature

ternative Favorable Market

($)

Unfavorabl

Market ($)

Large Plant 200,000 - 200,000 0 - (-180,000

Small Plant 200,000 - 100,000 0 -(-20,000

Do Nothing 200,000 - 0 0-0

Probability 0.50 0.50


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The Opportunity LossTable continued

State of Nature

lternative FavorableMarket

UnfavorablMarket

Large Plant 0 $180,000

Small Plant $100,000 $20,000

Do Nothing $200,000 0



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The Opportunity LossTable - continued

lternative EOL

Large Plant (0.50)*$0 +(0.50)*($180,000)

$90,000

Small Plant (0.50)*($100,000)+ (0.50)(*$20,000)

$60,000

Do Nothing (0.50)*($200,000)

+ (0.50)*($0)

$100,000


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Sensitivity Analysis

EMV(Large Plant) = $200,000P- (1-

P)$180,000

EMV(Small Plant) = $100,000P-

$20,000(1-P)

EMV(Do Nothing) = $0P+ 0(1-P)


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Sensitivity Analysis -continued

-200000

-150000

-100000

-500000

50000

100000

150000

200000

250000

0 0.2 0.4 0.6 0.8

Values of P

EMV

Values

Point 1 Point 2Small Plant

Large Plant EMV


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Decision MakingUnder Uncertainty

Maximax

Maximin

Equally likely (Laplace)

Criterion of Realism

Minimax


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Maximax - Choose the alternativewith the maximum output

State of Nature


UnfavorableMarket


200,000 -180,000


100,000 -20,000

Do nothing 0 0



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Maximin - Choose the alternative withthe maximum minimum output

State of Nature


UnfavorableMarket

Construct a

large plant

200,000 -180,000

Construct a

small plant

100,000 -20,000

Do nothing 0 0

Probabilities


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Equally likely (Laplace) - Assume all

states of nature to be equally

likely, choose maximum Average

States of Nature


Market

Unfavorable

Market

Avg.

Construct

Large Plant

$200,000 -$180,000 10,000

Construct

mall plant

100,000 -20,000 40,000

Do nothing 0 0 0


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Criterion of Realism (Hurwicz):

CR = *(row max) + (1-)*(row min)

State of Nature


Market

Unfavorable

Market

CR

Constructarge plant $200,000 -180,000 124,000

Construct

small plant

$100,000 -20,000 76,000

Do nothing 0 0 0

0.80 0.20


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Minimax - choose the alternative withthe minimum maximum OpportunityLoss

States of Nature


Unfavorable

MarketMax

Construct a

arge plant

0$ $180,000 $180,000

Construct a

mall plant

$100,000 20,000 100,000

Do nothing 200,000 0 200,000

Regret Matrix


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Marginal Analysis -Discrete Distributions

Steps using Normal Distributions:

Determine the value forP.

Locate P on the normal distribution. For agiven area under the curve, we findZfrom

thestandard Normal table.

Using we can now

solve forX*

sm

*

XZ

MPML

ML

P +


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Joes NewsstandExample A

ML = 4

MP= 6

m= Average demand = 50

papers per day

s= Standard deviation of

demand = 10


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Joes Newsstand

Example A - continued

Step 1:

Step 2: Look in the Normal tableforP= 0.6 (i.e., 1 0.4)

.

40.064

4

+

+

MPML

MLp

newspapers53or52.5500.25*10X

or

10

50X0.25Z

*

*

+

-


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Joes Newsstand

Example A continued


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Joes NewsstandExample B

ML = 8

MP= 2

m= Average demand = 100

papers per day

s= Standard deviation ofdemand = 10


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Joes Newsstand

Example B - continued

Step 1:

Step 2:Z= -0.84 for an areaof 0.80

and

or:

80.028

8

+

+

MPML

MLp

10

1000X0.84

*-

-

newspapers92or91.6

1000.84(10)X*

+- 0


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Joes Newsstand

Example B continued


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Decision Analysis (1)