decision analysis
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Copyright 2006 John Wiley & Sons, Inc.Copyright 2006 John Wiley & Sons, Inc.Beni AsllaniBeni Asllani
University of Tennessee at ChattanoogaUniversity of Tennessee at Chattanooga
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
Copyright 2006 John Wiley & Sons, Inc.Copyright 2006 John Wiley & Sons, Inc. Supplement 2-Supplement 2-33
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
Copyright 2006 John Wiley & Sons, Inc.Copyright 2006 John Wiley & Sons, Inc. Supplement 2-Supplement 2-44
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
Copyright 2006 John Wiley & Sons, Inc.Copyright 2006 John Wiley & Sons, Inc. Supplement 2-Supplement 2-55
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
Copyright 2006 John Wiley & Sons, Inc.Copyright 2006 John Wiley & Sons, Inc. Supplement 2-Supplement 2-66
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
Copyright 2006 John Wiley & Sons, Inc.Copyright 2006 John Wiley & Sons, Inc. Supplement 2-Supplement 2-77
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
Copyright 2006 John Wiley & Sons, Inc.Copyright 2006 John Wiley & Sons, Inc. Supplement 2-Supplement 2-88
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
Copyright 2006 John Wiley & Sons, Inc.Copyright 2006 John Wiley & Sons, Inc. Supplement 2-Supplement 2-99
Maximax Solution Maximax Solution
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
Expand: $800,000Status quo: 1,300,000 MaximumSell: 320,000
Decision: Maintain status quo
Copyright 2006 John Wiley & Sons, Inc.Copyright 2006 John Wiley & Sons, Inc. Supplement 2-Supplement 2-1010
Maximin Solution Maximin Solution
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
Expand: $500,000 Maximum
Status quo: -150,000Sell: 320,000
Decision: Expand
Copyright 2006 John Wiley & Sons, Inc.Copyright 2006 John Wiley & Sons, Inc. Supplement 2-Supplement 2-1111
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
Copyright 2006 John Wiley & Sons, Inc.Copyright 2006 John Wiley & Sons, Inc. Supplement 2-Supplement 2-1212
Hurwicz CriteriaHurwicz Criteria
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
= 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
Copyright 2006 John Wiley & Sons, Inc.Copyright 2006 John Wiley & Sons, Inc. Supplement 2-Supplement 2-1313
Equal Likelihood CriteriaEqual Likelihood Criteria
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
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
Copyright 2006 John Wiley & Sons, Inc.Copyright 2006 John Wiley & Sons, Inc. Supplement 2-Supplement 2-1414
Decision Analysis with Decision Analysis with ExcelExcel
Copyright 2006 John Wiley & Sons, Inc.Copyright 2006 John Wiley & Sons, Inc. Supplement 2-Supplement 2-1515
Decision Analysis with Decision Analysis with Excel: FormulasExcel: Formulas
Copyright 2006 John Wiley & Sons, Inc.Copyright 2006 John Wiley & Sons, Inc. Supplement 2-Supplement 2-1616
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
Copyright 2006 John Wiley & Sons, Inc.Copyright 2006 John Wiley & Sons, Inc. Supplement 2-Supplement 2-1717
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
Copyright 2006 John Wiley & Sons, Inc.Copyright 2006 John Wiley & Sons, Inc. Supplement 2-Supplement 2-1818
Decision Making with Decision Making with Probabilities: ExampleProbabilities: Example
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
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
Copyright 2006 John Wiley & Sons, Inc.Copyright 2006 John Wiley & Sons, Inc. Supplement 2-Supplement 2-1919
Decision Making with Decision Making with Probabilities: ExcelProbabilities: Excel
Copyright 2006 John Wiley & Sons, Inc.Copyright 2006 John Wiley & Sons, Inc. Supplement 2-Supplement 2-2020
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
Copyright 2006 John Wiley & Sons, Inc.Copyright 2006 John Wiley & Sons, Inc. Supplement 2-Supplement 2-2121
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
Copyright 2006 John Wiley & Sons, Inc.Copyright 2006 John Wiley & Sons, Inc. Supplement 2-Supplement 2-2222
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
Copyright 2006 John Wiley & Sons, Inc.Copyright 2006 John Wiley & Sons, Inc. Supplement 2-Supplement 2-2323
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
Copyright 2006 John Wiley & Sons, Inc.Copyright 2006 John Wiley & Sons, Inc. Supplement 2-Supplement 2-2424
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. Supplement 2-Supplement 2-2525
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.