ch02_sup Operation Management Roberta Russell & Bernard W. Taylor

Copyright 2006 John Wiley & Sons, Inc.Copyright 2006 John Wiley & Sons, Inc.Beni AsllaniBeni Asllani

University of Tennessee at ChattanoogaUniversity of Tennessee at Chattanooga

Operations Management - 5th EditionOperations Management - 5th Edition

Chapter 2 SupplementChapter 2 Supplement

Roberta Russell & Bernard W. Taylor, III

Decision AnalysisDecision Analysis

Copyright 2006 John Wiley & Sons, Inc.Copyright 2006 John Wiley & Sons, Inc. Supplement 2-Supplement 2-22

Lecture OutlineLecture Outline

Decision AnalysisDecision Analysis Decision Making without Probabilities Decision Making without Probabilities Decision Analysis with ExcelDecision Analysis with Excel Decision Making with ProbabilitiesDecision Making with Probabilities Expected Value of Perfect InformationExpected Value of Perfect Information Sequential Decision TreeSequential Decision Tree


Decision AnalysisDecision Analysis

Quantitative methodsQuantitative methods A set of tools for operations managerA set of tools for operations manager

Decision analysisDecision analysis a set of quantitative decision-making a set of quantitative decision-making

techniques for decision situations in which techniques for decision situations in which uncertainty existsuncertainty exists

Example of an uncertain situationExample of an uncertain situation demand for a product may vary between 0 and 200 demand for a product may vary between 0 and 200

units, depending on the state of marketunits, depending on the state of market


Decision Making Decision Making Without ProbabilitiesWithout Probabilities

States of natureStates of nature Events that may occur in the futureEvents that may occur in the future Examples of states of nature:Examples of states of nature:

high or low demand for a producthigh or low demand for a product good or bad economic conditionsgood or bad economic conditions

Decision making under riskDecision making under risk probabilities can be assigned to the occurrence of probabilities can be assigned to the occurrence of

states of nature in the futurestates of nature in the future

Decision making under uncertaintyDecision making under uncertainty probabilities can NOT be assigned to the probabilities can NOT be assigned to the

occurrence of states of nature in the futureoccurrence of states of nature in the future


Payoff: Payoff: outcome of a decisionoutcome of a decision

States Of NatureStates Of Nature

DecisionDecision aa bb

11 Payoff 1aPayoff 1a Payoff 1bPayoff 1b

22 Payoff 2aPayoff 2a Payoff 2bPayoff 2b

Payoff TablePayoff Table


Decision Making Criteria Under Decision Making Criteria Under UncertaintyUncertainty

MaximaxMaximax Choose decision with the maximum of the Choose decision with the maximum of the

maximum payoffsmaximum payoffs

MaximinMaximin Choose decision with the maximum of the Choose decision with the maximum of the

minimum payoffsminimum payoffs

Minimax regretMinimax regret Choose decision with the minimum of the Choose decision with the minimum of the

maximum regrets for each alternativemaximum regrets for each alternative


Decision Making Criteria Under Decision Making Criteria Under Uncertainty (cont.)Uncertainty (cont.)

Hurwicz Hurwicz Choose decision in which decision payoffs are Choose decision in which decision payoffs are

weighted by a coefficient of optimism, alphaweighted by a coefficient of optimism, alpha Coefficient of optimism is a measure of a Coefficient of optimism is a measure of a

decision maker’s optimism, from decision maker’s optimism, from 00 (completely (completely pessimistic) to pessimistic) to 11 (completely optimistic) (completely optimistic)

Equal likelihood (La Place)Equal likelihood (La Place) Choose decision in which each state of nature is Choose decision in which each state of nature is

weighted equallyweighted equally


Southern Textile Southern Textile CompanyCompany

STATES OF NATURESTATES OF NATURE

Good ForeignGood Foreign Poor ForeignPoor Foreign

DECISIONDECISION Competitive ConditionsCompetitive Conditions Competitive ConditionsCompetitive Conditions

ExpandExpand $ 800,000$ 800,000 $ 500,000$ 500,000Maintain status quoMaintain status quo 1,300,0001,300,000 -150,000-150,000Sell nowSell now 320,000320,000 320,000320,000


Maximax Solution Maximax Solution





Expand: $800,000Status quo: 1,300,000 MaximumSell: 320,000

Decision: Maintain status quo


Maximin Solution Maximin Solution





Expand: $500,000 Maximum

Status quo: -150,000Sell: 320,000

Decision: Expand


Minimax Regret SolutionMinimax Regret SolutionGood Foreign Poor ForeignCompetitive Conditions Competitive Conditions

$1,300,000 - 800,000 = 500,000 $500,000 - 500,000 = 01,300,000 - 1,300,000 = 0 500,000 - (-150,000)= 650,0001,300,000 - 320,000 = 980,000 500,000 - 320,000= 180,000

Expand: $500,000 MinimumStatus quo: 650,000Sell: 980,000

Decision: Expand


Hurwicz CriteriaHurwicz Criteria





= 0.3 1 - = 0.7

Expand: $800,000(0.3) + 500,000(0.7) = $590,000 MaximumStatus quo: 1,300,000(0.3) -150,000(0.7) = 285,000Sell: 320,000(0.3) + 320,000(0.7) = 320,000

Decision: Expand


Equal Likelihood CriteriaEqual Likelihood Criteria





Two states of nature each weighted 0.50Expand: $800,000(0.5) + 500,000(0.5) = $650,000 MaximumStatus quo: 1,300,000(0.5) -150,000(0.5) = 575,000Sell: 320,000(0.5) + 320,000(0.5) = 320,000

Decision: Expand


Decision Analysis with Decision Analysis with ExcelExcel


Decision Analysis with Decision Analysis with Excel: FormulasExcel: Formulas


Decision Making with Decision Making with ProbabilitiesProbabilities

Risk involves assigning probabilities to Risk involves assigning probabilities to states of naturestates of nature

Expected valueExpected value a weighted average of decision outcomes in a weighted average of decision outcomes in

which each future state of nature is which each future state of nature is assigned a probability of occurrence assigned a probability of occurrence


Expected valueExpected value

EV (EV (xx) = ) = pp((xxii))xxiinn

i i =1=1

xxii = outcome = outcome ii

pp((xxii)) = probability of outcome = probability of outcome ii

wherewhere


Decision Making with Decision Making with Probabilities: ExampleProbabilities: Example





p(good) = 0.70 p(poor) = 0.30EV(expand): $800,000(0.7) + 500,000(0.3) = $710,000 EV(status quo): 1,300,000(0.7) -150,000(0.3) = 865,000 Maximum EV(sell): 320,000(0.7) + 320,000(0.3) = 320,000

Decision: Status quo


Decision Making with Decision Making with Probabilities: ExcelProbabilities: Excel


Expected Value of Expected Value of Perfect InformationPerfect Information

EVPIEVPI maximum value of perfect information to maximum value of perfect information to

the decision makerthe decision maker

Maximum amount that an investor Maximum amount that an investor would pay to purchase perfect would pay to purchase perfect informationinformation


EVPI ExampleEVPI Example

Good conditions will exist Good conditions will exist 70%70% of the time of the time choose maintain status quo with payoff of choose maintain status quo with payoff of $1,300,000$1,300,000

Poor conditions will exist Poor conditions will exist 30%30% of the time of the time choose expand with payoff of choose expand with payoff of $500,000$500,000

Expected value given perfect informationExpected value given perfect information= $1,300,000 (0.70) + 500,000 (0.30)= $1,300,000 (0.70) + 500,000 (0.30)= $1,060,000= $1,060,000

Recall that expected value without perfect Recall that expected value without perfect information was $865,000 (maintain status quo)information was $865,000 (maintain status quo)

EVPIEVPI== $1,060,000 - 865,000 = $195,000$1,060,000 - 865,000 = $195,000


Sequential Sequential Decision TreesDecision Trees

A graphical method for analyzing A graphical method for analyzing decision situations that require a decision situations that require a sequence of decisions over timesequence of decisions over time

Decision tree consists ofDecision tree consists of Square nodes - indicating decision pointsSquare nodes - indicating decision points Circles nodes - indicating states of natureCircles nodes - indicating states of nature Arcs - connecting nodesArcs - connecting nodes


Evaluations at NodesEvaluations at Nodes

Compute EV at nodes 6 & 7Compute EV at nodes 6 & 7EVEV((node 6node 6)= 0.80($3,000,000) + 0.20($700,000) = $2,540,000)= 0.80($3,000,000) + 0.20($700,000) = $2,540,000EVEV((node 7node 7)= 0.30($2,300,000) + 0.70($1,000,000)= $1,390,000)= 0.30($2,300,000) + 0.70($1,000,000)= $1,390,000

Decision at node 4 is betweenDecision at node 4 is between$2,540,000$2,540,000 for Expand and for Expand and$450,000$450,000 for Sell land for Sell land

Choose ExpandChoose ExpandRepeat expected value calculations and decisions at Repeat expected value calculations and decisions at remaining nodesremaining nodes


6

7

2

1

3

4

5

Expan

d

(-$80

0,00

0)

Purchase Land

(-$200,000)

$1,160,000

$1,360,000$790,000

$1,390,000

$1,740,000

$2,540,000

Expand

(-$800,000)

Warehouse

(-$600,000)

0.60

0.40No marketgrowth$225,000

Market growth$2,000,000

$3,000,000

$700,000

$2,300,000

$1,000,000

$210,000

Market

growth

Market

growth

No marketgrowth

No marketgrowthSell land

Sell land

0.80

0.40

0.70

0.30

No market

growth (3 years,

$0 payoff)

Mar

ket

growth

(3 y

ears

,

$0 p

ayoff)

$1,290,000

0.20

0.60

$450,000

Decision Tree AnalysisDecision Tree Analysis


Copyright 2006 John Wiley & Sons, Inc.Copyright 2006 John Wiley & Sons, Inc.All rights reserved. Reproduction or translation All rights reserved. Reproduction or translation of this work beyond that permitted in section 117 of this work beyond that permitted in section 117 of the 1976 United States Copyright Act without of the 1976 United States Copyright Act without express permission of the copyright owner is express permission of the copyright owner is unlawful. Request for further information should unlawful. Request for further information should be addressed to the Permission Department, be addressed to the Permission Department, John Wiley & Sons, Inc. The purchaser may John Wiley & Sons, Inc. The purchaser may make back-up copies for his/her own use only make back-up copies for his/her own use only and not for distribution or resale. The Publisher and not for distribution or resale. The Publisher assumes no responsibility for errors, omissions, assumes no responsibility for errors, omissions, or damages caused by the use of these or damages caused by the use of these programs or from the use of the information programs or from the use of the information herein. herein.

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ch02_sup Operation Management Roberta Russell & Bernard W. Taylor