管理科学12决策分析课件

1、管理科学12决策分析课件1Chapter 12Decision AnalysisIntroduction to Management Science8th EditionbyBernard W. Taylor III管理科学12决策分析课件2 Components of Decision Making Decision Making without Probabilities Decision Making with Probabilities Decision Analysis with Additional Information UtilityChapter Topics管理科学12决策

2、分析课件3Table 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管理科学12决策分析课件4D

3、ecision situation: Decision-Making Criteria: maximax, maximin, minimax, minimax regret, Hurwicz, and equal likelihood Table 12.2Payoff Table for the Real Estate InvestmentsDecision AnalysisDecision Making without Probabilities管理科学12决策分析课件5Table 12.3Payoff Table Illustrating a Maximax Decision In the

4、 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管理科学12决策分析课件6Table 12.4Payoff Table Illustrating a Maximin Decision In the maximin criterion the decision maker

5、 selects the decision that will reflect the maximum of the minimum payoffs; a pessimistic criterion.Decision Making without ProbabilitiesMaximin Criterion管理科学12决策分析课件7Table 12.6 Regret Table Illustrating the Minimax Regret Decision Regret is the difference between the payoff from the best decision a

6、nd 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管理科学12决策分析课件8 The Hurwicz criterion is a compromise between the maximax and maximin criterio

7、n. 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 $100,0

8、00(.4) - 40,000(.6) = 16,000Warehouse $30,000(.4) + 10,000(.6) = 18,000Decision Making without ProbabilitiesHurwicz Criterion管理科学12决策分析课件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

9、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) = 20,000Decision Making without ProbabilitiesEqual Likelihood Criterion管理科学12决策分析课件10 A dominant decision is one that h

10、as 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 bui

11、ldingEqual likelihoodApartment buildingDecision Making without ProbabilitiesSummary of Criteria Results管理科学12决策分析课件11Exhibit 12.1Decision Making without ProbabilitiesSolution with QM for Windows (1 of 3)管理科学12决策分析课件12Exhibit 12.2Decision Making without ProbabilitiesSolution with QM for Windows (2 of

12、 3)管理科学12决策分析课件13Exhibit 12.3Decision Making without ProbabilitiesSolution with QM for Windows (3 of 3)管理科学12决策分析课件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(Of

13、fice) = $100,000(.6) - 40,000(.4) = 44,000EV(Warehouse) = $30,000(.6) + 10,000(.4) = 22,000Table 12.7Payoff table with Probabilities for States of NatureDecision Making with ProbabilitiesExpected Value管理科学12决策分析课件15 The expected opportunity loss is the expected value of the regret for each decision.

14、 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) = 50,000Table 12.8Regret (Opportunity Loss) Table with Probabilities for States of

15、NatureDecision Making with ProbabilitiesExpected Opportunity Loss管理科学12决策分析课件16Exhibit 12.4Expected Value ProblemsSolution with QM for Windows管理科学12决策分析课件17Exhibit 12.5Expected Value ProblemsSolution with Excel and Excel QM (1 of 2)管理科学12决策分析课件18Exhibit 12.6Expected Value ProblemsSolution with Excel

16、 and Excel QM (2 of 2)管理科学12决策分析课件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 o

17、pportunity loss (EOL) for the best decision.Decision Making with ProbabilitiesExpected Value of Perfect Information管理科学12决策分析课件20Table 12.9Payoff Table with Decisions, Given Perfect Information Decision Making with ProbabilitiesEVPI Example (1 of 2)管理科学12决策分析课件21 Decision with perfect information:$1

18、00,000(.60) + 30,000(.40) = $72,000 Decision 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) = $28,000Decision Making with ProbabilitiesEVPI Example (2 of 2)管理科学12决策分析课件22Exhibit 12.7Decision Making wit

19、h ProbabilitiesEVPI with QM for Windows管理科学12决策分析课件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 ExampleDecision Making with ProbabilitiesDeci

20、sion Trees (1 of 4)管理科学12决策分析课件24Figure 12.1Decision Tree for Real Estate Investment ExampleDecision Making with ProbabilitiesDecision Trees (2 of 4)管理科学12决策分析课件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) + .

21、40(-40,000) = $44,000EV(node 4) = .60($30,000) + .40(10,000) = $22,000 Branches with the greatest expected value are selected.Decision Making with ProbabilitiesDecision Trees (3 of 4)管理科学12决策分析课件26Figure 12.2Decision Tree with Expected Value at Probability NodesDecision Making with ProbabilitiesDeci

22、sion Trees (4 of 4)管理科学12决策分析课件27Exhibit 12.8Decision Making with ProbabilitiesDecision Trees with QM for Windows管理科学12决策分析课件28Exhibit 12.9Decision Making with ProbabilitiesDecision Trees with Excel and TreePlan (1 of 4)管理科学12决策分析课件29Exhibit 12.10Decision Making with ProbabilitiesDecision Trees with

23、 Excel and TreePlan (2 of 4)管理科学12决策分析课件30Exhibit 12.11Decision Making with ProbabilitiesDecision Trees with Excel and TreePlan (3 of 4)管理科学12决策分析课件31Exhibit 12.12Decision Making with ProbabilitiesDecision Trees with Excel and TreePlan (4 of 4)管理科学12决策分析课件32Decision Making with ProbabilitiesSequenti

24、al 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

25、made: 管理科学12决策分析课件33Figure 12.3Sequential Decision TreeDecision Making with ProbabilitiesSequential Decision Trees (2 of 4)管理科学12决策分析课件34Decision Making with ProbabilitiesSequential Decision Trees (3 of 4) Decision is to purchase land; highest net expected value ($1,160,000). Payoff of the decision

26、is $1,160,000. 管理科学12决策分析课件35Figure 12.4Sequential Decision Tree with Nodal Expected ValuesDecision Making with ProbabilitiesSequential Decision Trees (4 of 4)管理科学12决策分析课件36Exhibit 12.13Sequential Decision Tree AnalysisSolution with QM for Windows管理科学12决策分析课件37Exhibit 12.14Sequential Decision Tree A

27、nalysisSolution with Excel and TreePlan管理科学12决策分析课件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

28、 $444,000, and EVPI of $28,000. Table 12.11Payoff Table for the Real Estate Investment ExampleDecision Analysis with Additional InformationBayesian Analysis (1 of 3)管理科学12决策分析课件39 A conditional probability is the probability that an event will occur given that another event has already occurred. Eco

29、nomic 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 Add

30、itional InformationBayesian Analysis (2 of 3)管理科学12决策分析课件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) = .40 Posteria probabilities by Bayes

31、rule:(gP) = P(PG)P(g)/P(Pg)P(g) + P(Pp)P(p) = (.80)(.60)/(.80)(.60) + (.10)(.40) = .923 Posteria (revised) probabilities for decision:P(gN) = .250P(pP) = .077P(pN) = .750Decision Analysis with Additional InformationBayesian Analysis (3 of 3)管理科学12决策分析课件41Decision Analysis with Additional Information

32、Decision 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.管理科学12决策分析课件42Figur

33、e 12.5Decision Tree with Posterior Probabilities Decision Analysis with Additional InformationDecision Trees with Posterior Probabilities (2 of 4)管理科学12决策分析课件43Decision Analysis with Additional InformationDecision Trees with Posterior Probabilities (3 of 4)EV (apartment building) = $50,000(.923) + 3

34、0,000(.077) = $48,460EV (strategy) = $89,220(.52) + 35,000(.48) = $63,194管理科学12决策分析课件44Figure 12.6Decision Tree AnalysisDecision Analysis with Additional InformationDecision Trees with Posterior Probabilities (4 of 4)管理科学12决策分析课件45Table 12.12Computation of Posterior ProbabilitiesDecision Analysis wi

35、th Additional InformationComputing Posterior Probabilities with Tables管理科学12决策分析课件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 = $19,194 The efficiency of sample information

36、is the ratio of the expected value of sample information to the expected value of perfect information: efficiency = EVSI /EVPI = $19,194/ 28,000 = .68Decision Analysis with Additional InformationExpected Value of Sample Information管理科学12决策分析课件47Table 12.13Payoff Table for Auto Insurance ExampleDecis

37、ion Analysis with Additional InformationUtility (1 of 2)管理科学12决策分析课件48Expected Cost (insurance) = .992($500) + .008(500) = $500Expected Cost (no insurance) = .992($0) + .008(10,000) = $80 Decision should be do not purchase insurance, but people almost always do purchase insurance. Utility is a measu

38、re 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 Add

39、itional InformationUtility (2 of 2)管理科学12决策分析课件49 States of Nature Decision Good Foreign Competitive Conditions Poor Foreign Competitive Conditions Expand Maintain Status Quo Sell now $ 800,000 1,300,000 320,000 $ 500,000 -150,000 320,000 Decision Analysis Example Problem Solution (1 of 9)管理科学12决策分析

40、课件50Decision 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 los

41、s 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 obt

42、ained in part e.管理科学12决策分析课件51Step 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 -150,000Sel

43、l 320,000Decision Analysis Example Problem Solution (3 of 9)管理科学12决策分析课件52Minimax 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) = $320,000Decision Analysis Example Problem Solution (4 of 9)管理科学1