Decision Analysis Chapter 12 Copyright © 2010 Pearson Education, Inc Publishing as Prentice Hall 12-1 Chapter Topics ■ Components of Decision Making ■ Decision Making without Probabilities ■ Decision Making with Probabilities ■ Decision Analysis with Additional Information ■ Utility Copyright © 2010 Pearson Education, Inc Publishing as Prentice Hall 12-2 Decision Analysis Components of Decision Making ■ A state of nature is an actual event that may occur in the future ■ A payoff table is a means of organizing a decision situation, presenting the payoffs from different decisions given the various states of nature Copyright © 2010 Pearson Education, Inc Publishing as Prentice Hall Table 12.1 Payoff Table 12-3 Decision Analysis Decision Making Without Probabilities Figure 12.1 Copyright © 2010 Pearson Education, Inc Publishing as Prentice Hall 12-4 Decision Analysis Decision Making without Probabilities Table 12.2 Decision-Making Criteria maximax minimax maximin minimax regret Hurwicz Copyright © 2010 Pearson Education, Inc Publishing as Prentice Hall equal 12-5 Decision Making without Probabilities In the maximax criterion the decision maker Maximax Criterion selects the decision that will result in the maximum of maximum payoffs; an optimistic criterion Table 12.3 Payoff Table Illustrating a Maximax Decision Copyright © 2010 Pearson Education, Inc Publishing as Prentice Hall 12-6 Decision Making without Probabilities Maximin Criterion In the maximin criterion the decision maker selects the decision that will reflect the maximum of the minimum payoffs; a pessimistic criterion Table 12.4 Payoff Table Illustrating a Copyright © 2010 Pearson Education, Inc Publishing as Maximin Decision Prentice Hall 12-7 Decision Making without Probabilities Minimax Regret Criterion Regret is the difference between the payoff from the best decision and all other decision payoffs The decision maker attempts to avoid regret by selecting the decision alternative that minimizes the maximum regret Table 12.6 Regret Table Illustrating the Minimax Regret Decision Copyright © 2010 Pearson Education, Inc Publishing as Prentice Hall 12-8 Decision Making without Probabilities Hurwicz Criterion The Hurwicz criterion is a compromise between the maximax and maximin criterion A coefficient of optimism,  , is a measure of the decision maker’s optimism The Hurwicz criterion multiplies the best payoff by  and the worst payoff by 1-  , for each decision, and the best result is selected Decision Apartment building 30,000(.6) = 38,000 Office building = 16,000 Copyright © 2010 Pearson Education, Inc Publishing as Prentice Hall Warehouse Values $50,000(.4) + $100,000(.4) - 40,000(.6) 12-9 $30,000(.4) + 10,000(.6) Decision Making without Probabilities Equal Likelihood Criterion The equal likelihood ( or Laplace) criterion multiplies the decision payoff for each state of nature by an equal weight, thus assuming that the states of nature are equally likely to occur Decision Apartment building 30,000(.5) = 40,000 Office building = 30,000 Warehouse = 20,000 Copyright © 2010 Pearson Education, Inc Publishing as Prentice Hall Values $50,000(.5) + $100,000(.5) - 40,000(.5) $30,000(.5) + 10,000(.5) 12- Decision Analysis with Additional Information Computing Posterior Probabilities with Tables Table 12.12 Computation of Posterior Copyright © 2010 Pearson Probabilities Education, Inc Publishing as Prentice Hall 12- Decision Analysis with Additional Information Computing Posterior Probabilities with Excel Exhibit 12.16 Copyright © 2010 Pearson Education, Inc Publishing as Prentice Hall 12- Decision Analysis with Additional Information Expected Value of Sample Information ■ The expected value of sample information (EVSI) is the difference between the expected value with and without information: For example problem, EVSI = $63,194 - 44,000 = $19,194 ■ The efficiency of sample information is the ratio of the expected value of sample information to the expected value of perfect information: efficiency = EVSI /EVPI = $19,194/ 28,000 = 68 Copyright © 2010 Pearson Education, Inc Publishing as Prentice Hall 12- Decision Analysis with Additional Information Utility (1 of 2) Table 12.13 Payoff Table for Auto Insurance Example Copyright © 2010 Pearson Education, Inc Publishing as Prentice Hall 12- Decision Analysis with Additional Information Utility (2 of 2) Expected Cost (insurance) = 992($500) + 008(500) = $500 Expected Cost (no insurance) = 992($0) + 008(10,000) = $80 Decision should be not purchase insurance, but people almost always purchase insurance ■ Utility is a measure of personal satisfaction derived from money ■ Utiles are units of subjective measures of utility ■ Risk averters forgo a high expected value to Copyright © 2010 Pearson Education, Inc Publishing as avoid a low-probability disaster Prentice Hall 12- Decision Analysis Example Problem Solution (1 of 9) Copyright © 2010 Pearson Education, Inc Publishing as Prentice Hall 12- Decision Analysis Example Problem Solution (2 of 9) a Determine the best decision without probabilities using the criteria of the chapter b Determine best decision with probabilities assuming 70 probability of good conditions, 30 of poor conditions Use expected value and expected opportunity loss criteria c Compute expected value of perfect information d Develop a decision tree with expected value at the nodes e Given following, P(Pg) = 70, P(Ng) = 30, P(Pp) = 20, P(Np) = 80, determine posterior Copyright © 2010 Pearson Education, Inc Publishing as Prenticeprobabilities Hall using Bayes’ rule 12- Decision Analysis Example Problem Solution (3 of 9) Step (part a): Determine decisions without probabilities Maximax Decision: Maintain status quo Decisions Expand Status quo Sell Maximum Payoffs $800,000 1,300,000 (maximum) 320,000 Maximin Decision: Expand Decisions Minimum Payoffs Expand $500,000 (maximum) Status quo -150,000 Sell 320,000 Copyright © 2010 Pearson Education, Inc Publishing as Prentice Hall 12- Decision Analysis Example Problem Solution (4 of 9) Minimax Regret Decision: Expand Decisions Expand Status quo Sell Maximum Regrets $500,000 (minimum) 650,000 980,000 Hurwicz ( = 3) Decision: Expand Expand $590,000 Status quo = $285,000 $800,000(.3) + 500,000(.7) = $1,300,000(.3) - 150,000(.7) Sell $320,000(.3) + 320,000(.7) = Copyright © 2010 Pearson Education, Inc Publishing as Prentice$320,000 Hall 12- Decision Analysis Example Problem Solution (5 of 9) Equal Likelihood Decision: Expand Expand $650,000 Status quo $575,000 Sell $320,000 $800,000(.5) + 500,000(.5) = $1,300,000(.5) - 150,000(.5) = $320,000(.5) + 320,000(.5) = Step (part b): Determine Decisions with EV and EOL Expected value decision: Maintain status quo Expand $800,000(.7) + 500,000(.3) = $710,000 Copyright © 2010 Pearson Education, Inc Publishing as Prentice Hall 12- Decision Analysis Example Problem Solution (6 of 9) Expected opportunity loss decision: Maintain status quo Expand Status quo $195,000 Sell $740,000 $500,000(.7) + 0(.3) = $350,000 0(.7) + 650,000(.3) = $980,000(.7) + 180,000(.3) = Step (part c): Compute EVPI EV given perfect information = 1,300,000(.7) + 500,000(.3) = $1,060,000 EV without perfect information = $1,300,000(.7) - 150,000(.3) = $865,000 Copyright © 2010 Pearson Education, Inc Publishing as Prentice Hall 12- Decision Analysis Example Problem Solution (7 of 9) Step (part d): Develop a decision tree Copyright © 2010 Pearson Education, Inc Publishing as Prentice Hall 12- Decision Analysis Example Problem Solution (8 of 9) Step (part e): Determine posterior probabilities P(gP) = P(Pg)P(g)/[P(Pg)P(g) + P(Pp)P(p)] = (.70)(.70)/[(.70)(.70) + (.20)(.30)] = 891 P(pP) = 109 P(gN) = P(Ng)P(g)/[P(Ng)P(g) + P(Np)P(p)] = (.30)(.70)/[(.30)(.70) + (.80)(.30)] = 467 Copyright © 2010 Pearson Education, Inc Publishing as Prentice Hall 12- Decision Analysis Example Problem Solution (9 of 9) Step (part f): Decision tree analysis Copyright © 2010 Pearson Education, Inc Publishing as Prentice Hall 12- Copyright © 2010 Pearson Education, Inc Publishing as Prentice Hall 12- .. .Chapter Topics ■ Components of Decision Making ■ Decision Making without Probabilities ■ Decision Making... payoff from the best decision and all other decision payoffs The decision maker attempts to avoid regret by selecting the decision alternative that minimizes the maximum regret Table 12.6 Regret... of the decision maker’s optimism The Hurwicz criterion multiplies the best payoff by  and the worst payoff by 1-  , for each decision, and the best result is selected Decision Apartment building