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Chapter 1 SupplementDecision Analysis Support Tools and ProcessesSupplement 1-*

Copyright 2011 John Wiley & Sons, Inc.

Lecture OutlineDecision AnalysisDecision Making without Probabilities Decision Analysis with ExcelDecision Analysis with OM ToolsDecision Making with ProbabilitiesExpected Value of Perfect InformationSequential Decision TreeCopyright 2011 John Wiley & Sons, Inc.Supplement 1-*



Decision AnalysisQuantitative methodsa set of tools for operations managerDecision analysisa set of quantitative decision-making techniques for decision situations in which uncertainty existsExample of an uncertain situationdemand for a product may vary between 0 and 200 units, depending on the state of marketSupplement 1-*



Decision Making Without ProbabilitiesStates of natureEvents that may occur in the futureExamples of states of nature:high or low demand for a productgood or bad economic conditionsDecision making under riskprobabilities can be assigned to the occurrence of states of nature in the futureDecision making under uncertaintyprobabilities can NOT be assigned to the occurrence of states of nature in the futureSupplement 1-*


Payoff TablePayoff tablemethod for organizing and illustrating payoffs from different decisions given various states of naturePayoffoutcome of a decision

Supplement 1-*Copyright 2011 John Wiley & Sons, Inc.


Decision Making Criteria Under UncertaintyMaximaxchoose decision with the maximum of the maximum payoffsMaximinchoose decision with the maximum of the minimum payoffsMinimax regretchoose decision with the minimum of the maximum regrets for each alternativeCopyright 2011 John Wiley & Sons, Inc.Supplement 1-*


Decision Making Criteria Under UncertaintyHurwicz choose decision in which decision payoffs are weighted by a coefficient of optimism, alphacoefficient of optimism is a measure of a decision makers optimism, from 0 (completely pessimistic) to 1 (completely optimistic)Equal likelihood (La Place)choose decision in which each state of nature is weighted equallyCopyright 2011 John Wiley & Sons, Inc.Supplement 1-*


Maximax Solution Copyright 2011 John Wiley & Sons, Inc.Supplement 1-*

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

Decision: Maintain status quo

A very optimistic method


Maximin Solution Copyright 2011 John Wiley & Sons, Inc.Supplement 1-*

Expand:$500,000 MaximumStatus quo:-150,000Sell: 320,000Decision: ExpandA pessimistic method


Hurwicz CriteriaCopyright 2011 John Wiley & Sons, Inc.Supplement 1-* = 0.3 1 - = 0.7

Expand: $800,000(0.3) + 500,000(0.7) = $590,000 Maximum

Status quo: 1,300,000(0.3) -150,000(0.7) = 285,000

Sell: 320,000(0.3) + 320,000(0.7) = 320,000

Decision: Expand


Equal Likelihood CriteriaCopyright 2011 John Wiley & Sons, Inc.Supplement 1-*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) = 320,000Decision: Expand


Decision Analysis with OM ToolsCopyright 2011 John Wiley & Sons, Inc.Supplement 1-*



Decision Making with ProbabilitiesRisk involves assigning probabilities to states of nature

Expected valuea weighted average of decision outcomes in which each future state of nature is assigned a probability of occurrence Supplement 1-*



Expected ValueSupplement 1-*EV (x) = p(xi)xixi= outcome ip(xi)= probability of outcome iwhere


Decision Making with ProbabilitiesCopyright 2011 John Wiley & Sons, Inc.Supplement 1-*p(good) = 0.70 p(poor) = 0.30 EV(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


Expected Value of Perfect InformationEVPImaximum value of perfect information to the decision makermaximum amount that would be paid to gain information that would result in a decision better than the one made without perfect informationCopyright 2011 John Wiley & Sons, Inc.Supplement 1-*


EVPIGood conditions will exist 70% of the timechoose maintain status quo with payoff of $1,300,000Poor conditions will exist 30% of the timechoose expand with payoff of $500,000Expected value given perfect information = $1,300,000 (0.70) + 500,000 (0.30) = $1,060,000Recall that expected value without perfect information was $865,000 (maintain status quo)EVPI= $1,060,000 - 865,000 = $195,000Copyright 2011 John Wiley & Sons, Inc.Supplement 1-*


Sequential Decision TreesA graphical method for analyzing decision situations that require a sequence of decisions over timeDecision tree consists ofSquare nodes - indicating decision pointsCircles nodes - indicating states of natureArcs - connecting nodesCopyright 2011 John Wiley & Sons, Inc.Supplement 1-*


Evaluations at Nodes Compute EV at nodes 6 & 7EV(node 6)= 0.80($3,000,000) + 0.20($700,000) = $2,540,000EV(node 7)= 0.30($2,300,000) + 0.70($1,000,000)= $1,390,000 Decision at node 4 is between $2,540,000 for Expand and $450,000 for Sell land Choose Expand Repeat expected value calculations and decisions at remaining nodesCopyright 2011 John Wiley & Sons, Inc.Supplement 1-*


Copyright 2011 John Wiley & Sons, Inc.Supplement 1-*Copyright 2011 John Wiley & Sons, Inc. All rights reserved. Reproduction or translation of this work beyond that permitted in section 117 of the 1976 United States Copyright Act without express permission of the copyright owner is unlawful. Request for further information should be addressed to the Permission Department, John Wiley & Sons, Inc. The purchaser may make back-up copies for his/her own use only and not for distribution or resale. The Publisher assumes no responsibility for errors, omissions, or damages caused by the use of these programs or from the use of the information herein.


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