管理科学12-决策分析解析课件.ppt

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1、Chapter 12Decision AnalysisIntroduction to Management Science8th EditionbyBernard W.Taylor III1Chapter 12-Decision AnalysisComponents of Decision MakingDecision Making without ProbabilitiesDecision Making with ProbabilitiesDecision Analysis with Additional InformationUtilityChapter Topics2Chapter 12

2、-Decision AnalysisTable 12.1Payoff TableA 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 Making3Cha

3、pter 12-Decision AnalysisDecision 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 Probabilities4Chapter 12-Decision AnalysisTable 12.3Payoff Table Ill

4、ustrating a Maximax DecisionIn 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 Criterion5Chapter 12-Decision AnalysisTable 12.4Payoff Table Illustrating a Maximin Dec

5、isionIn 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 Criterion6Chapter 12-Decision AnalysisTable 12.6 Regret Table Illustrating the Minimax Regret DecisionRegret

6、 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 Criterion7Chapter 12-Decision AnalysisTh

7、e 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 ValuesApartm

8、ent building$50,000(.4)+30,000(.6)=38,000Office building$100,000(.4)-40,000(.6)=16,000Warehouse$30,000(.4)+10,000(.6)=18,000Decision Making without ProbabilitiesHurwicz Criterion8Chapter 12-Decision AnalysisThe equal likelihood(or Laplace)criterion multiplies the decision payoff for each state of na

9、ture 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)=20,000Decision Making without ProbabilitiesEqual Likelihood Criterion

10、9Chapter 12-Decision AnalysisA 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 bui

11、ldingMinimax regretApartment buildingHurwiczApartment buildingEqual likelihoodApartment buildingDecision Making without ProbabilitiesSummary of Criteria Results10Chapter 12-Decision AnalysisExhibit 12.1Decision Making without ProbabilitiesSolution with QM for Windows(1 of 3)11Chapter 12-Decision Ana

12、lysisExhibit 12.2Decision Making without ProbabilitiesSolution with QM for Windows(2 of 3)12Chapter 12-Decision AnalysisExhibit 12.3Decision Making without ProbabilitiesSolution with QM for Windows(3 of 3)13Chapter 12-Decision AnalysisExpected value is computed by multiplying each decision outcome u

13、nder 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)=22,000Table 12.7Payoff table with Probabilities for States of NatureDecision Making with ProbabilitiesExpected Value

14、14Chapter 12-Decision AnalysisThe 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(.

15、6)+20,000(.4)=50,000Table 12.8Regret(Opportunity Loss)Table with Probabilities for States of NatureDecision Making with ProbabilitiesExpected Opportunity Loss15Chapter 12-Decision AnalysisExhibit 12.4Expected Value ProblemsSolution with QM for Windows16Chapter 12-Decision AnalysisExhibit 12.5Expecte

16、d Value ProblemsSolution with Excel and Excel QM(1 of 2)17Chapter 12-Decision AnalysisExhibit 12.6Expected Value ProblemsSolution with Excel and Excel QM(2 of 2)18Chapter 12-Decision AnalysisThe expected value of perfect information(EVPI)is the maximum amount a decision maker would pay for additiona

17、l 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 Information19Chapter 12-Decision AnalysisTable 1

18、2.9Payoff Table with Decisions,Given Perfect Information Decision Making with ProbabilitiesEVPI Example(1 of 2)20Chapter 12-Decision AnalysisDecision with perfect information:$100,000(.60)+30,000(.40)=$72,000Decision without perfect information:EV(office)=$100,000(.60)-40,000(.40)=$44,000EVPI=$72,00

19、0-44,000=$28,000EOL(office)=$0(.60)+70,000(.4)=$28,000Decision Making with ProbabilitiesEVPI Example(2 of 2)21Chapter 12-Decision AnalysisExhibit 12.7Decision Making with ProbabilitiesEVPI with QM for Windows22Chapter 12-Decision AnalysisA decision tree is a diagram consisting of decision nodes(repr

20、esented as squares),probability nodes(circles),and decision alternatives(branches).Table 12.10Payoff Table for Real Estate Investment ExampleDecision Making with ProbabilitiesDecision Trees(1 of 4)23Chapter 12-Decision AnalysisFigure 12.1Decision Tree for Real Estate Investment ExampleDecision Makin

21、g with ProbabilitiesDecision Trees(2 of 4)24Chapter 12-Decision AnalysisThe 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

22、 are selected.Decision Making with ProbabilitiesDecision Trees(3 of 4)25Chapter 12-Decision AnalysisFigure 12.2Decision Tree with Expected Value at Probability NodesDecision Making with ProbabilitiesDecision Trees(4 of 4)26Chapter 12-Decision AnalysisExhibit 12.8Decision Making with ProbabilitiesDec

23、ision Trees with QM for Windows27Chapter 12-Decision AnalysisExhibit 12.9Decision Making with ProbabilitiesDecision Trees with Excel and TreePlan(1 of 4)28Chapter 12-Decision AnalysisExhibit 12.10Decision Making with ProbabilitiesDecision Trees with Excel and TreePlan(2 of 4)29Chapter 12-Decision An

24、alysisExhibit 12.11Decision Making with ProbabilitiesDecision Trees with Excel and TreePlan(3 of 4)30Chapter 12-Decision AnalysisExhibit 12.12Decision Making with ProbabilitiesDecision Trees with Excel and TreePlan(4 of 4)31Chapter 12-Decision AnalysisDecision Making with ProbabilitiesSequential Dec

25、ision 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:32Chapt

26、er 12-Decision AnalysisFigure 12.3Sequential Decision TreeDecision Making with ProbabilitiesSequential Decision Trees(2 of 4)33Chapter 12-Decision AnalysisDecision Making with ProbabilitiesSequential Decision Trees(3 of 4)Decision is to purchase land;highest net expected value($1,160,000).Payoff of

27、the decision is$1,160,000.34Chapter 12-Decision AnalysisFigure 12.4Sequential Decision Tree with Nodal Expected ValuesDecision Making with ProbabilitiesSequential Decision Trees(4 of 4)35Chapter 12-Decision AnalysisExhibit 12.13Sequential Decision Tree AnalysisSolution with QM for Windows36Chapter 1

28、2-Decision AnalysisExhibit 12.14Sequential Decision Tree AnalysisSolution with Excel and TreePlan37Chapter 12-Decision AnalysisBayesian analysis uses additional information to alter the marginal probability of the occurrence of an event.In real estate investment example,using expected value criterio

29、n,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 ExampleDecision Analysis with Additional InformationBayesian Analysis(1 of 3)38Chapter 12-Decision AnalysisA conditional probability is the probabi

30、lity 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

31、(Pg)=.80P(NG)=.20P(Pp)=.10P(Np)=.90 Decision Analysis with Additional InformationBayesian Analysis(2 of 3)39Chapter 12-Decision AnalysisA posteria probability is the altered marginal probability of an event based on additional information.Prior probabilities for good or poor economic conditions in r

32、eal 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)=.750Decision Analysis with Additional InformationBayesian Analysis(3 of 3)40Chapter

33、12-Decision AnalysisDecision 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 ar

34、e posterior probabilities from Bayes rule.41Chapter 12-Decision AnalysisFigure 12.5Decision Tree with Posterior Probabilities Decision Analysis with Additional InformationDecision Trees with Posterior Probabilities(2 of 4)42Chapter 12-Decision AnalysisDecision Analysis with Additional InformationDec

35、ision 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)=$63,19443Chapter 12-Decision AnalysisFigure 12.6Decision Tree AnalysisDecision Analysis with Additional InformationDecision Trees with Posterior Probabilitie

36、s(4 of 4)44Chapter 12-Decision AnalysisTable 12.12Computation of Posterior ProbabilitiesDecision Analysis with Additional InformationComputing Posterior Probabilities with Tables45Chapter 12-Decision AnalysisThe expected value of sample information(EVSI)is the difference between the expected value w

37、ith 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=.68Decision Analysis with Additional InformationEx

38、pected Value of Sample Information46Chapter 12-Decision AnalysisTable 12.13Payoff Table for Auto Insurance ExampleDecision Analysis with Additional InformationUtility(1 of 2)47Chapter 12-Decision AnalysisExpected Cost(insurance)=.992($500)+.008(500)=$500Expected Cost(no insurance)=.992($0)+.008(10,0

39、00)=$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 ta

40、kers 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)48Chapter 12-Decision AnalysisDecision Analysis Example Problem Solution(1 of 9)49Chapter 12-Decision AnalysisDecision Analysis Example Problem Solutio

41、n(2 of 9)a.Determine the best decision without probabilities using the 5 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 perfec

42、t information.d.Develop a decision tree with expected value at the nodes.e.Given following,P(Pg)=.70,P(Ng)=.30,P(Pp)=20,P(Np)=.80,determine posteria probabilities using Bayes rule.f.Perform a decision tree analysis using the posterior probability obtained in part e.50Chapter 12-Decision AnalysisStep

43、 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 320,000Decision Analysis Example Problem

44、 Solution(3 of 9)51Chapter 12-Decision AnalysisMinimax 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)=$320,0

45、00Decision Analysis Example Problem Solution(4 of 9)52Chapter 12-Decision AnalysisEqual 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

46、 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)=$320,000Decision Analysis Example Problem Solution(5 of 9)53Chapter 12-Decision AnalysisExpected opportunity loss decision:Maintain status quoExpand$500,000(.

47、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=$195,000Decision Analysis

48、Example Problem Solution(6 of 9)54Chapter 12-Decision Analysis Step 4(part d):Develop a decision tree.Decision Analysis Example Problem Solution(7 of 9)55Chapter 12-Decision AnalysisStep 5(part e):Determine posterior probabilities.P(gP)=P(PG)P(g)/P(Pg)P(g)+P(Pp)P(p)=(.70)(.70)/(.70)(.70)+(.20)(.30)=.891 P(pP)=.109 P(gN)=P(NG)P(g)/P(Ng)P(g)+P(Np)P(p)=(.30)(.70)/(.30)(.70)+(.80)(.30)=.467P(pN)=.533Decision Analysis Example Problem Solution(8 of 9)56Chapter 12-Decision AnalysisStep 6(part f):Decision tree analysis.Decision Analysis Example Problem Solution(9 of 9)57Chapter 12-Decision Analysis