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Copyright 2009 John Wiley & Sons, Inc. Beni Asllani University of Tennessee at Chattanooga Operations Management - 6 th Edition Chapter 1 Supplement Roberta Russell & Bernard W. Taylor, III Decision Analysis

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Copyright 2009 John Wiley & Sons, Inc.Supplement 1-2 Lecture Outline Decision Analysis Decision Making without Probabilities Decision Making with Probabilities Expected Value of Perfect Information Sequential Decision Tree

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Copyright 2009 John Wiley & Sons, Inc.Supplement 1-3 Decision Analysis Quantitative methods a set of tools for operations manager a set of tools for operations manager Decision analysis a set of quantitative decision-making techniques for decision situations in which uncertainty exists a set of quantitative decision-making techniques for decision situations in which uncertainty exists Example of an uncertain situation Example of an uncertain situation demand for a product may vary between 0 and 200 units, depending on the state of market demand for a product may vary between 0 and 200 units, depending on the state of market

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Copyright 2009 John Wiley & Sons, Inc.Supplement 1-4 Decision Making Without Probabilities States of nature Events that may occur in the future Events that may occur in the future Examples of states of nature: Examples of states of nature: high or low demand for a product high or low demand for a product good or bad economic conditions good or bad economic conditions Decision making under risk probabilities can be assigned to the occurrence of states of nature in the future probabilities can be assigned to the occurrence of states of nature in the future Decision making under uncertainty probabilities can NOT be assigned to the occurrence of states of nature in the future probabilities can NOT be assigned to the occurrence of states of nature in the future

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Copyright 2009 John Wiley & Sons, Inc.Supplement 1-5 Payoff Table Payoff table method for organizing and illustrating payoffs from different decisions given various states of nature method for organizing and illustrating payoffs from different decisions given various states of nature Payoff outcome of a decision outcome of a decision States Of Nature Decisionab 1Payoff 1aPayoff 1b 2Payoff 2aPayoff 2b

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Copyright 2009 John Wiley & Sons, Inc.Supplement 1-6 Decision Making Criteria Under Uncertainty Maximax choose decision with the maximum of the maximum payoffs choose decision with the maximum of the maximum payoffs Maximin choose decision with the maximum of the minimum payoffs choose decision with the maximum of the minimum payoffs Minimax regret choose decision with the minimum of the maximum regrets for each alternative choose decision with the minimum of the maximum regrets for each alternative

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Copyright 2009 John Wiley & Sons, Inc.Supplement 1-7 Decision Making Criteria Under Uncertainty (cont.) Hurwicz choose decision in which decision payoffs are weighted by a coefficient of optimism, alpha choose decision in which decision payoffs are weighted by a coefficient of optimism, alpha coefficient of optimism is a measure of a decision maker’s optimism, from 0 (completely pessimistic) to 1 (completely optimistic) coefficient of optimism is a measure of a decision maker’s optimism, from 0 (completely pessimistic) to 1 (completely optimistic) Equal likelihood (La Place) choose decision in which each state of nature is weighted equally choose decision in which each state of nature is weighted equally

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Copyright 2009 John Wiley & Sons, Inc.Supplement 1-8 Southern Textile Company STATES OF NATURE Good ForeignPoor Foreign DECISION Competitive ConditionsCompetitive Conditions Expand$ 800,000$ 500,000 Maintain status quo1,300, ,000 Sell now320,000320,000

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Copyright 2009 John Wiley & Sons, Inc.Supplement 1-9 Maximax Solution STATES OF NATURE Good ForeignPoor Foreign DECISION Competitive ConditionsCompetitive Conditions Expand$ 800,000$ 500,000 Maintain status quo1,300, ,000 Sell now320,000320,000 Expand:$800,000 Status quo:1,300,000 Maximum Sell: 320,000 Decision: Maintain status quo

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Copyright 2009 John Wiley & Sons, Inc.Supplement 1-10 Maximin Solution STATES OF NATURE Good ForeignPoor Foreign DECISION Competitive ConditionsCompetitive Conditions Expand$ 800,000$ 500,000 Maintain status quo1,300, ,000 Sell now320,000320,000 Expand:$500,000 Maximum Status quo:-150,000 Sell: 320,000 Decision: Expand

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Copyright 2009 John Wiley & Sons, Inc.Supplement 1-11 Minimax Regret Solution Good Foreign Poor ForeignCompetitive Conditions $1,300, ,000 = 500,000 $500, ,000 = 0 1,300, ,300,000 = 0 500,000 - (-150,000)= 650,000 1,300, ,000 = 980, , ,000= 180,000 Expand:$500,000 Minimum Status quo:650,000 Sell: 980,000 Decision: Expand

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Copyright 2009 John Wiley & Sons, Inc.Supplement 1-12 Hurwicz Criteria STATES OF NATURE Good ForeignPoor Foreign DECISION Competitive ConditionsCompetitive Conditions Expand$ 800,000$ 500,000 Maintain status quo1,300, ,000 Sell now320,000320,000 = = 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

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Copyright 2009 John Wiley & Sons, Inc.Supplement 1-13 Equal Likelihood Criteria STATES OF NATURE Good ForeignPoor Foreign DECISION Competitive ConditionsCompetitive Conditions Expand$ 800,000$ 500,000 Maintain status quo1,300, ,000 Sell now320,000320,000 Two states of nature each weighted 0.50 Expand: $800,000(0.5) + 500,000(0.5) = $650,000 Maximum Status quo: 1,300,000(0.5) -150,000(0.5) = 575,000 Sell: 320,000(0.5) + 320,000(0.5) = 320,000 Decision: Expand

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Copyright 2009 John Wiley & Sons, Inc.Supplement 1-14 Decision Making with Probabilities Risk involves assigning probabilities to states of nature Expected value a weighted average of decision outcomes in which each future state of nature is assigned a probability of occurrence a weighted average of decision outcomes in which each future state of nature is assigned a probability of occurrence

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Copyright 2009 John Wiley & Sons, Inc.Supplement 1-15 Expected value EV ( x ) = p ( x i ) x i n i =1 x i = outcome i p ( x i )= probability of outcome i where

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Copyright 2009 John Wiley & Sons, Inc.Supplement 1-16 Decision Making with Probabilities: Example STATES OF NATURE Good ForeignPoor Foreign DECISION Competitive ConditionsCompetitive Conditions Expand$ 800,000$ 500,000 Maintain status quo1,300, ,000 Sell now320,000320,000 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

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Copyright 2009 John Wiley & Sons, Inc.Supplement 1-17 Expected Value of Perfect Information EVPI maximum value of perfect information to the decision maker maximum value of perfect information to the decision maker maximum amount that would be paid to gain information that would result in a decision better than the one made without perfect information maximum amount that would be paid to gain information that would result in a decision better than the one made without perfect information

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Copyright 2009 John Wiley & Sons, Inc.Supplement 1-18 EVPI Example Good conditions will exist 70% of the time choose maintain status quo with payoff of $1,300,000 Poor conditions will exist 30% of the time choose expand with payoff of $500,000 Expected value given perfect information = $1,300,000 (0.70) + 500,000 (0.30) = $1,060,000 Recall that expected value without perfect information was $865,000 (maintain status quo) EVPI= $1,060, ,000 = $195,000

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Copyright 2009 John Wiley & Sons, Inc.Supplement 1-19 Sequential Decision Trees A graphical method for analyzing decision situations that require a sequence of decisions over time Decision tree consists of Square nodes - indicating decision points Circles nodes - indicating states of nature Arcs - connecting nodes

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Copyright 2009 John Wiley & Sons, Inc.Supplement 1-20 Evaluations at Nodes Compute EV at nodes 6 & 7 EV(node 6)= 0.80($3,000,000) ($700,000) = $2,540,000 EV(node 7)= 0.30($2,300,000) ($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 nodes

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Copyright 2009 John Wiley & Sons, Inc.Supplement Expand (-$800,000) 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) No market growth $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 market growth No market growth Sell land No market growth (3 years, $0 payoff) Market growth (3 years, $0 payoff) $1,290, $450,000 Decision Tree Analysis

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