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A Decision-Making Tools

PowerPoint presentation to accompany PowerPoint presentation to accompany Heizer and Render Heizer and Render Operations Management, 10e Operations Management, 10e Principles of Operations Management, 8ePrinciples of Operations Management, 8e

PowerPoint slides by Jeff Heyl

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ExampleExample

Table A.1

State of NatureAlternatives Favorable Market Unfavorable Market

Construct large plant $200,000 –$180,000Construct small plant $100,000 –$ 20,000Do nothing $ 0 $ 0

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DM under UncertaintyDM under Uncertainty

1. If Optimistic (F), choice is a large plant2. If Pessimistic (UF), choice is to do nothing

Maximax Maximin Equally likely

States of NatureFavorable Unfavorable Maximum Minimum Row

Alternatives Market Market in Row in Row AverageConstruct

large plant $200,000 -$180,000 $200,000 -$180,000 $10,000Construct

small plant $100,000 -$20,000 $100,000 -$20,000 $40,000Do nothing $0 $0 $0 $0 $0

Not a sound business decision!

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DM Under Risk (Probability)?DM Under Risk (Probability)?

Each possible state of nature has an assumed probability

Probabilities must sum to 1 Determine the expected monetary value

(EMV) for each alternative

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DM Under RiskDM Under Risk

1. EMV(A1) = (.5)($200,000) + (.5)(-$180,000) = $10,000

Table A.3

States of NatureFavorable Unfavorable

Alternatives Market MarketConstruct large plant (A1) $200,000 -$180,000

Construct small plant (A2) $100,000 -$20,000

Do nothing (A3) $0 $0

Probabilities .50 .50

Best Option

2. EMV(A2) = (.5)($100,000) + (.5)(-$20,000) = $40,0003. EMV(A3) = (.5)($0) + (.5)($0) = $0

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EVwPI ExampleEVwPI Example

1. The best outcome for the state of nature “favorable market” is “build a large facility” with a payoff of $200,000. The best outcome for “unfavorable” is “do nothing” with a payoff of $0.

Expected value with perfect information

= ($200,000)(.50) + ($0)(.50) = $100,000

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DM under CertaintyDM under Certainty More certain about the payoff for each

market Is the cost of perfect information worth it? Determine the expected value of perfect

information (EVPI)

EVPI is the difference between the payoff under certainty and the payoff under risk

EVPI = –Expected value

with perfect information

Maximum EMV

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Expected Value of Expected Value of Perfect InformationPerfect Information

Expected value with perfect information (EVwPI)

= (Best outcome or consequence for 1st state of nature) x (Probability of 1st state of nature)

+ Best outcome for 2nd state of nature) x (Probability of 2nd state of nature)

+ … + Best outcome for last state of nature) x (Probability of last state of nature)

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EVPI ExampleEVPI Example

2. The maximum EMV is $40,000, which is the expected outcome without perfect information. Thus:

= $100,000 – $40,000 = $60,000

EVPI = EVwPI – Maximum EMV

The most the company should pay for perfect information is $60,000

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Decision Tree ExampleDecision Tree Example

Favorable market

Unfavorable market

Favorable market

Unfavorable market

Construct small plant

Do nothing

A decision node A state of nature node

Construct

large plant

Figure A.1

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Decision Tree ExampleDecision Tree Example= (.5)($200,000) + (.5)(-$180,000)EMV for node 1

= $10,000

EMV for node 2= $40,000 = (.5)($100,000) + (.5)(-$20,000)

Payoffs

$200,000

-$180,000

$100,000

-$20,000

$0

Construct large plant

Construct small plant

Do nothing

Favorable market (.5)

Unfavorable market (.5)1

Favorable market (.5)

Unfavorable market (.5)2

Figure A.2

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Complex Decision Tree Complex Decision Tree Example (Example 7)Example (Example 7)

Figure A.3

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Complex ExampleComplex Example

1. Given favorable survey results

EMV(2) = (.78)($190,000) + (.22)(-$190,000) = $106,400EMV(3) = (.78)($90,000) + (.22)(-$30,000) = $63,600

The EMV for no plant = -$10,000 so, if the survey results are favorable, build the large plant

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Complex ExampleComplex Example

2. Given negative survey results

EMV(4) = (.27)($190,000) + (.73)(-$190,000) = -$87,400EMV(5) = (.27)($90,000) + (.73)(-$30,000) = $2,400

The EMV for no plant = -$10,000 so, if the survey results are negative, build the small plant

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Complex ExampleComplex Example3. Compute the expected value of the

market survey

EMV(1) = (.45)($106,400) + (.55)($2,400) = $49,200

The EMV for no plant = $0 so, given no survey, build the small plant

4. If the market survey is not conducted

EMV(6) = (.5)($200,000) + (.5)(-$180,000) = $10,000EMV(7) = (.5)($100,000) + (.5)(-$20,000) = $40,000

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Decision TreesDecision Trees Information in decision tables can be

displayed as decision trees A decision tree is a graphic display of the

decision process that indicates decision alternatives, states of nature and their respective probabilities, and payoffs for each combination of decision alternative and state of nature

Appropriate for showing sequential decisions

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