管理科学12 决策分析解析课件.ppt

Chapter 12 - Decision Analysis,1,Chapter 12Decision Analysis,Introduction to Management Science8th EditionbyBernard W. Taylor III,Chapter 12 - Decision Analysis,2,Components of Decision MakingDecision Making without ProbabilitiesDecision Making with ProbabilitiesDecision Analysis with Additional InformationUtility,Chapter Topics,Chapter 12 - Decision Analysis,3,Table 12.1Payoff Table,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.,Decision AnalysisComponents of Decision Making,Chapter 12 - Decision Analysis,4,Decision situation:Decision-Making Criteria: maximax, maximin, minimax, minimax regret, Hurwicz, and equal likelihood,Table 12.2Payoff Table for the Real Estate Investments,Decision AnalysisDecision Making without Probabilities,Chapter 12 - Decision Analysis,5,Table 12.3Payoff Table Illustrating a Maximax Decision,In the maximax criterion the decision maker selects the decision that will result in the maximum of maximum payoffs; an optimistic criterion.,Decision Making without ProbabilitiesMaximax Criterion,Chapter 12 - Decision Analysis,6,Table 12.4Payoff Table Illustrating a Maximin Decision,In the maximin criterion the decision maker selects the decision that will reflect the maximum of the minimum payoffs; a pessimistic criterion.,Decision Making without ProbabilitiesMaximin Criterion,Chapter 12 - Decision Analysis,7,Table 12.6 Regret Table Illustrating the Minimax Regret Decision,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.,Decision Making without ProbabilitiesMinimax Regret Criterion,Chapter 12 - Decision Analysis,8,The Hurwicz criterion is a compromise between the maximax and maximin criterion.A coefficient of optimism, , is a measure of the decision makers 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 ValuesApartment building $50,000(.4) + 30,000(.6) = 38,000Office building $100,000(.4) - 40,000(.6) = 16,000Warehouse $30,000(.4) + 10,000(.6) = 18,000,Decision Making without ProbabilitiesHurwicz Criterion,Chapter 12 - Decision Analysis,9,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 ValuesApartment building $50,000(.5) + 30,000(.5) = 40,000Office building $100,000(.5) - 40,000(.5) = 30,000Warehouse $30,000(.5) + 10,000(.5) = 20,000,Decision Making without ProbabilitiesEqual Likelihood Criterion,Chapter 12 - Decision Analysis,10,A dominant decision is one that has a better payoff than another decision under each state of nature.The appropriate criterion is dependent on the “risk” personality and philosophy of the decision maker. Criterion Decision (Purchase)MaximaxOffice buildingMaximinApartment buildingMinimax regretApartment buildingHurwiczApartment buildingEqual likelihoodApartment building,Decision Making without ProbabilitiesSummary of Criteria Results,Chapter 12 - Decision Analysis,11,Exhibit 12.1,Decision Making without ProbabilitiesSolution with QM for Windows (1 of 3),Chapter 12 - Decision Analysis,12,Exhibit 12.2,Decision Making without ProbabilitiesSolution with QM for Windows (2 of 3),Chapter 12 - Decision Analysis,13,Exhibit 12.3,Decision Making without ProbabilitiesSolution with QM for Windows (3 of 3),Chapter 12 - Decision Analysis,14,Expected value is computed by multiplying each decision outcome under each state of nature by the probability of its occurrence.EV(Apartment) = $50,000(.6) + 30,000(.4) = 42,000EV(Office) = $100,000(.6) - 40,000(.4) = 44,000EV(Warehouse) = $30,000(.6) + 10,000(.4) = 22,000,Table 12.7Payoff table with Probabilities for States of Nature,Decision Making with ProbabilitiesExpected Value,Chapter 12 - Decision Analysis,15,The expected opportunity loss is the expected value of the regret for each decision.The expected value and expected opportunity loss criterion result in the same decision.EOL(Apartment) = $50,000(.6) + 0(.4) = 30,000EOL(Office) = $0(.6) + 70,000(.4) = 28,000EOL(Warehouse) = $70,000(.6) + 20,000(.4) = 50,000,Table 12.8Regret (Opportunity Loss) Table with Probabilities for States of Nature,Decision Making with ProbabilitiesExpected Opportunity Loss,Chapter 12 - Decision Analysis,16,Exhibit 12.4,Expected Value ProblemsSolution with QM for Windows,Chapter 12 - Decision Analysis,17,Exhibit 12.5,Expected Value ProblemsSolution with Excel and Excel QM (1 of 2),Chapter 12 - Decision Analysis,18,Exhibit 12.6,Expected Value ProblemsSolution with Excel and Excel QM (2 of 2),Chapter 12 - Decision Analysis,19,The expected value of perfect information (EVPI) is the maximum amount a decision maker would pay for additional information.EVPI equals the expected value given perfect information minus the expected value without perfect information.EVPI equals the expected opportunity loss (EOL) for the best decision.,Decision Making with ProbabilitiesExpected Value of Perfect Information,Chapter 12 - Decision Analysis,20,Table 12.9Payoff Table with Decisions, Given Perfect Information,Decision Making with ProbabilitiesEVPI Example (1 of 2),Chapter 12 - Decision Analysis,21,Decision with perfect information:$100,000(.60) + 30,000(.40) = $72,000Decision without perfect information:EV(office) = $100,000(.60) - 40,000(.40) = $44,000EVPI = $72,000 - 44,000 = $28,000EOL(office) = $0(.60) + 70,000(.4) = $28,000,Decision Making with ProbabilitiesEVPI Example (2 of 2),Chapter 12 - Decision Analysis,22,Exhibit 12.7,Decision Making with ProbabilitiesEVPI with QM for Windows,Chapter 12 - Decision Analysis,23,A decision tree is a diagram consisting of decision nodes (represented as squares), probability nodes (circles), and decision alternatives (branches).,Table 12.10Payoff Table for Real Estate Investment Example,Decision Making with ProbabilitiesDecision Trees (1 of 4),Chapter 12 - Decision Analysis,24,Figure 12.1Decision Tree for Real Estate Investment Example,Decision Making with ProbabilitiesDecision Trees (2 of 4),Chapter 12 - Decision Analysis,25,The expected value is computed at each probability node: EV(node 2) = .60($50,000) + .40(30,000) = $42,000EV(node 3) = .60($100,000) + .40(-40,000) = $44,000EV(node 4) = .60($30,000) + .40(10,000) = $22,000Branches with the greatest expected value are selected.,Decision Making with ProbabilitiesDecision Trees (3 of 4),Chapter 12 - Decision Analysis,26,Figure 12.2Decision Tree with Expected Value at Probability Nodes,Decision Making with ProbabilitiesDecision Trees (4 of 4),Chapter 12 - Decision Analysis,27,Exhibit 12.8,Decision Making with ProbabilitiesDecision Trees with QM for Windows,Chapter 12 - Decision Analysis,28,Exhibit 12.9,Decision Making with ProbabilitiesDecision Trees with Excel and TreePlan (1 of 4),Chapter 12 - Decision Analysis,29,Exhibit 12.10,Decision Making with ProbabilitiesDecision Trees with Excel and TreePlan (2 of 4),Chapter 12 - Decision Analysis,30,Exhibit 12.11,Decision Making with ProbabilitiesDecision Trees with Excel and TreePlan (3 of 4),Chapter 12 - Decision Analysis,31,Exhibit 12.12,Decision Making with ProbabilitiesDecision Trees with Excel and TreePlan (4 of 4),Chapter 12 - Decision Analysis,32,Decision Making with ProbabilitiesSequential Decision Trees (1 of 4),A sequential decision tree is used to illustrate a situation requiring a series of decisions.Used where a payoff table, limited to a single decision, cannot be used.Real estate investment example modified to encompass a ten-year period in which several decisions must be made:,Chapter 12 - Decision Analysis,33,Figure 12.3Sequential Decision Tree,Decision Making with ProbabilitiesSequential Decision Trees (2 of 4),Chapter 12 - Decision Analysis,34,Decision Making with ProbabilitiesSequential Decision Trees (3 of 4),Decision is to purchase land; highest net expected value ($1,160,000).Payoff of the decision is $1,160,000.,Chapter 12 - Decision Analysis,35,Figure 12.4Sequential Decision Tree with Nodal Expected Values,Decision Making with ProbabilitiesSequential Decision Trees (4 of 4),Chapter 12 - Decision Analysis,36,Exhibit 12.13,Sequential Decision Tree AnalysisSolution with QM for Windows,Chapter 12 - Decision Analysis,37,Exhibit 12.14,Sequential Decision Tree AnalysisSolution with Excel and TreePlan,Chapter 12 - Decision Analysis,38,Bayesian analysis uses additional information to alter the marginal probability of the occurrence of an event.In real estate investment example, using expected value criterion, best decision was to purchase office building with expected value of $444,000, and EVPI of $28,000.,Table 12.11Payoff Table for the Real Estate Investment Example,Decision Analysis with Additional InformationBayesian Analysis (1 of 3),Chapter 12 - Decision Analysis,39,A conditional probability is the probability that an event will occur given that another event has already occurred.Economic analyst provides additional information for real estate investment decision, forming conditional probabilities:g = good economic conditionsp = poor economic conditionsP = positive economic reportN = negative economic reportP(Pg) = .80P(NG) = .20P(Pp) = .10P(Np) = .90,Decision Analysis with Additional InformationBayesian Analysis (2 of 3),Chapter 12 - Decision Analysis,40,A posteria probability is the altered marginal probability of an event based on additional information.Prior probabilities for good or poor economic conditions in real estate decision:P(g) = .60; P(p) = .40Posteria probabilities by Bayes rule:(gP) = P(PG)P(g)/P(Pg)P(g) + P(Pp)P(p) = (.80)(.60)/(.80)(.60) + (.10)(.40) = .923Posteria (revised) probabilities for decision:P(gN) = .250P(pP) = .077P(pN) = .750,Decision Analysis with Additional InformationBayesian Analysis (3 of 3),Chapter 12 - Decision Analysis,41,Decision Analysis with Additional InformationDecision Trees with Posterior Probabilities (1 of 4),Decision tree with posterior probabilities differ from earlier versions in that: Two new branches at beginning of tree represent report outcomes. Probabilities of each state of nature are posterior probabilities from Bayes rule.,Chapter 12 - Decision Analysis,42,Figure 12.5Decision Tree with Posterior Probabilities,Decision Analysis with Additional InformationDecision Trees with Posterior Probabilities (2 of 4),Chapter 12 - Decision Analysis,43,Decision Analysis with Additional InformationDecision Trees with Posterior Probabilities (3 of 4),EV (apartment building) = $50,000(.923) + 30,000(.077) = $48,460EV (strategy) = $89,220(.52) + 35,000(.48) = $63,194,Chapter 12 - Decision Analysis,44,Figure 12.6Decision Tree Analysis,Decision Analysis with Additional InformationDecision Trees with Posterior Probabilities (4 of 4),Chapter 12 - Decision Analysis,45,Table 12.12Computation of Posterior Probabilities,Decision Analysis with Additional InformationComputing Posterior Probabilities with Tables,Chapter 12 - Decision Analysis,46,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 = $19,194The 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,Decision Analysis with Additional InformationExpected Value of Sample Information,Chapter 12 - Decision Analysis,47,Table 12.13Payoff Table for Auto Insurance Example,Decision Analysis with Additional InformationUtility (1 of 2),Chapter 12 - Decision Analysis,48,Expected Cost (insurance) = .992($500) + .008(500) = $500Expected Cost (no insurance) = .992($0) + .008(10,000) = $80Decision should be do not purchase insurance, but people almost always do 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 avoid a low-probability disaster.Risk takers take a chance for a bonanza on a very low-probability event in lieu of a sure thing.,Decision Analysis with Additional InformationUtility (2 of 2),Chapter 12 - Decision Analysis,49,Decision Analysis Example Problem Solution (1 of 9),Chapter 12 - Decision Analysis,50,Decision Analysis Example Problem Solution (2 of 9),Determine the best decision without probabilities using the 5 criteria of the chapter.Determine best decision with probabilities assuming .70 probability of good conditions, .30 of poor conditions. Use expected value and expected opportunity loss criteria.Compute expected value of perfect information.Develop a decision tree with expected value at the nodes.Given following, P(Pg) = .70, P(Ng) = .30, P(Pp) = 20, P(Np) = .80, determine posteria probabilities using Bayes rule.Perform a decision tree analysis using the posterior probability obtained in part e.,Chapter 12 - Decision Analysis,51,Step 1 (part a): Determine decisions without probabilities.Maximax Decision: Maintain status quoDecisionsMaximum PayoffsExpand $800,000Status quo1,300,000 (maximum)Sell 320,000Maximin Decision: ExpandDecisionsMinimum PayoffsExpand$500,000 (maximum)Status quo -150,000Sell 320,000,Decision Analysis Example Problem Solution (3 of 9),Chapter 12 - Decision Analysis,52,Minimax Regret Decision: ExpandDecisionsMaximum RegretsExpand$500,000 (minimum)Status quo 650,000Sell 980,000Hurwicz ( = .3) Decision: ExpandExpand $800,000(.3) + 500,000(.7) = $590,000Status quo$1,300,000(.3) - 150,000(.7) = $285,000Sell $320,000(.3) + 320,000(.7) = $320,000,Decision Analysis Example Problem Solution (4 of 9),Chapter 12 - Decision Analysis,53,Equal Likelihood Decision: ExpandExpand $800,000(.5) + 500,000(.5) = $650,000Status quo $1,300,000(.5) - 150,000(.5) = $575,000Sell $320,000(.5) + 320,000(.5) = $320,000Step 2 (part b): Determine Decisions with EV and EOL.Expected value decision: Maintain status quoExpand $800,000(.7) + 500,000(.3) = $710,000Status quo $1,300,000(.7) - 150,000(.3) = $865,000Sell $320,000(.7) + 320,000(.3) = $320,000,Decision Analysis Example Problem Solution (5 of 9),Chapter 12 - Decision Analysis,54,Expected opportunity loss decision: Maintain status quoExpand $500,000(.7) + 0(.3) = $350,000Status quo 0(.7) + 650,000(.3) = $195,000Sell $980,000(.7) + 180,000(.3) = $740,000Step 3 (part c): Compute EVPI.EV given perfect information = 1,300,000(.7) + 500,000(.3) = $1,060,000EV without perfect information = $1,300,000(.7) - 150,000(.3) = $865,000EVPI = $1.060,000 - 865,000 = $195,000,Decision Analysis Example Problem Solution (6 of 9),Chapter 12 - Decision Analysis,55,Step 4 (part d): Develop a decision tree.,Decision Analysis Example Problem Solution (7 of 9),Chap