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2000 by Prentice-Hall, Inc1 Supplement 2 – Decision Analysis A set of quantitative decision-making techniques for decision situations where uncertainty exists

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2000 by Prentice-Hall, Inc2 Decision Making States of nature Events that may occur in the future Events that may occur in the future Decision maker is uncertain which state of nature will occur Decision maker is uncertain which state of nature will occur Decision maker has no control over the states of nature Decision maker has no control over the states of nature

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2000 by Prentice-Hall, Inc3 Payoff Table A method of organizing & illustrating the payoffs from different decisions given various states of nature A method of organizing & illustrating the payoffs from different decisions given various states of nature A payoff is the outcome of the decision A payoff is the outcome of the decision

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2000 by Prentice-Hall, Inc4 Payoff Table States Of Nature Decisionab 1Payoff 1aPayoff 1b 2Payoff 2aPayoff 2b Table S2.1

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2000 by Prentice-Hall, Inc5 Decision Making Criteria Under Uncertainty Maximax criterion Choose decision with the maximum of the maximum payoffs Choose decision with the maximum of the maximum payoffs Maximin criterion Choose decision with the maximum of the minimum payoffs Choose decision with the maximum of the minimum payoffs Minimax regret criterion 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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2000 by Prentice-Hall, Inc6 Hurwicz criterion Choose decision in which decision payoffs are weighted by a coefficient of optimism, Choose decision in which decision payoffs are weighted by a coefficient of optimism, 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) criterion 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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2000 by Prentice-Hall, Inc7 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 Example S2.1

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2000 by Prentice-Hall, Inc8 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 Example S2.1 Maximax Solution Expand:$800,000 Status quo:1,300,000 Maximum Sell: 320,000 Decision: Maintain status quo

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2000 by Prentice-Hall, Inc9 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 Example S2.1 Maximin Solution Expand:$500,000 Maximum Status quo:-150,000 Sell: 320,000 Decision: Expand

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2000 by Prentice-Hall, Inc10 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 Example S2.1 Minimax Regret Solution $1,300, ,000= 500,000 $500, ,000= 0 1,300, ,300,000= 0500,000 - (-150,000)= 650,000 1,300, ,000= 980,000500, ,000= 180,000 GOOD CONDITIONSPOOR CONDITIONS Expand:$500,000 Minimum Status quo:650,000 Sell: 980,000 Decision: Expand

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2000 by Prentice-Hall, Inc11 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 Example S2.1 Hurwicz Criteria = = 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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2000 by Prentice-Hall, Inc12 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 Example S2.1 Equal Likelihood Criteria 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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2000 by Prentice-Hall, Inc13 Real Estate Investing Example STATES OF NATURE GoodFair Poor DECISION EconomicEconomic Economic ConditionsConditions Conditions Apartment $50,000 $25,000$10,000 Office 100,000 30, ,000 Warehouse 30,00015, ,000

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2000 by Prentice-Hall, Inc14 Decision Making with Probabilities Risk involves assigning probabilities to states of nature Risk involves assigning probabilities to states of nature Expected value is a weighted average of decision outcomes in which each future state of nature is assigned a probability of occurrence Expected value is a weighted average of decision outcomes in which each future state of nature is assigned a probability of occurrence

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2000 by Prentice-Hall, Inc15 Expected Value EV ( x ) = p ( x i ) x i n i =1 where x i = outcome i p ( x i )= probability of outcome i

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2000 by Prentice-Hall, Inc16 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 Example S2.2 Expected Value 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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2000 by Prentice-Hall, Inc17 Expected Value of Perfect Information The maximum value of perfect information to the decision maker The maximum value of perfect information to the decision maker EVPI = (expected value given perfect information) - (expected value without perfect information) EVPI = (expected value given perfect information) - (expected value without perfect information)

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2000 by Prentice-Hall, Inc18 Sequential Decision Trees A graphical method for analyzing decision situations that require a sequence of decisions over time A graphical method for analyzing decision situations that require a sequence of decisions over time Decision tree consists of Decision tree consists of Square nodes - indicating decision points Square nodes - indicating decision points Circles nodes - indicating states of nature Circles nodes - indicating states of nature Arcs - connecting nodes Arcs - connecting nodes

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2000 by Prentice-Hall, Inc19 Southern Textile Decision Tree Warehouse(-$600,000) Sell land Marketgrowth 0.70 Marketgrowth Expand(-$800,000) Purchase Land (-$200,000) Expand(-$800,000) No market growth $225,000 Market growth $2,000,000$3,000,000 $700,000 $2,300,000 $1,000,000 $210,000 No market growth growth 0.30 growth (3 years, $0 payoff) Market growth (3 years, $0 payoff) Example S2.3

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2000 by Prentice-Hall, Inc20 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 Expected values written above nodes 6 & 7 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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2000 by Prentice-Hall, Inc21 Decision Tree Solution Expand(-$800,000) Purchase Land (-$200,000) 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 Marketgrowth Marketgrowth No market growth growth Sell land No market growth (3 years, $0 payoff) Market growth (3 years, $0 payoff) Example S2.3

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2000 by Prentice-Hall, Inc22 Decision Tree Solution 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 Marketgrowth Marketgrowth No market growth growth Sell land No market growth (3 years, $0 payoff) Market growth (3 years, $0 payoff) $1,290, Example S2.3

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