管理科學決策分析

1、管理科學決策分析 Chapter 12 - Decision Analysis1第1頁，共57頁，2022年，5月20日，7點56分，星期二Chapter 12 - Decision Analysis 2Components of Decision MakingDecision Making without ProbabilitiesDecision Making with ProbabilitiesDecision Analysis with Additional InformationUtilityChapter Topics第2頁，共57頁，2022年，5月20日，7點56分，星期二Ch

2、apter 12 - Decision Analysis 3Table 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 Decisi

3、on Making第3頁，共57頁，2022年，5月20日，7點56分，星期二Chapter 12 - Decision Analysis 4Decision 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第4頁

4、，共57頁，2022年，5月20日，7點56分，星期二Chapter 12 - Decision Analysis 5Table 12.3Payoff Table Illustrating 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 C

5、riterion第5頁，共57頁，2022年，5月20日，7點56分，星期二Chapter 12 - Decision Analysis 6Table 12.4Payoff Table Illustrating a Maximin DecisionIn the maximin criterion the decision maker selects the decision that will reflect the maximum of the minimum payoffs; a pessimistic criterion.Decision Making without Probabili

6、tiesMaximin Criterion第6頁，共57頁，2022年，5月20日，7點56分，星期二Chapter 12 - Decision Analysis 7Table 12.6 Regret Table Illustrating the Minimax Regret DecisionRegret is the difference between the payoff from the best decision and all other decision payoffs.The decision maker attempts to avoid regret by selectin

7、g the decision alternative that minimizes the maximum regret.Decision Making without ProbabilitiesMinimax Regret Criterion第7頁，共57頁，2022年，5月20日，7點56分，星期二Chapter 12 - Decision Analysis 8The Hurwicz criterion is a compromise between the maximax and maximin criterion.A coefficient of optimism, , is a me

8、asure 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 $3

9、0,000(.4) + 10,000(.6) = 18,000Decision Making without ProbabilitiesHurwicz Criterion第8頁，共57頁，2022年，5月20日，7點56分，星期二Chapter 12 - Decision Analysis 9The equal likelihood ( or Laplace) criterion multiplies the decision payoff for each state of nature by an equal weight, thus assuming that the states of

10、 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第9頁，共57頁，2022年，5月20日，7點56分，星期二Chapter 12

11、 - Decision Analysis 10A 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 build

12、ingMinimax regretApartment buildingHurwiczApartment buildingEqual likelihoodApartment buildingDecision Making without ProbabilitiesSummary of Criteria Results第10頁，共57頁，2022年，5月20日，7點56分，星期二Chapter 12 - Decision Analysis 11Exhibit 12.1Decision Making without ProbabilitiesSolution with QM for Windows

13、(1 of 3)第11頁，共57頁，2022年，5月20日，7點56分，星期二Chapter 12 - Decision Analysis 12Exhibit 12.2Decision Making without ProbabilitiesSolution with QM for Windows (2 of 3)第12頁，共57頁，2022年，5月20日，7點56分，星期二Chapter 12 - Decision Analysis 13Exhibit 12.3Decision Making without ProbabilitiesSolution with QM for Windows

14、(3 of 3)第13頁，共57頁，2022年，5月20日，7點56分，星期二Chapter 12 - Decision Analysis 14Expected 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(W

15、arehouse) = $30,000(.6) + 10,000(.4) = 22,000Table 12.7Payoff table with Probabilities for States of NatureDecision Making with ProbabilitiesExpected Value第14頁，共57頁，2022年，5月20日，7點56分，星期二Chapter 12 - Decision Analysis 15The expected opportunity loss is the expected value of the regret for each decisi

16、on.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 o

17、f NatureDecision Making with ProbabilitiesExpected Opportunity Loss第15頁，共57頁，2022年，5月20日，7點56分，星期二Chapter 12 - Decision Analysis 16Exhibit 12.4Expected Value ProblemsSolution with QM for Windows第16頁，共57頁，2022年，5月20日，7點56分，星期二Chapter 12 - Decision Analysis 17Exhibit 12.5Expected Value ProblemsSolutio

18、n with Excel and Excel QM (1 of 2)第17頁，共57頁，2022年，5月20日，7點56分，星期二Chapter 12 - Decision Analysis 18Exhibit 12.6Expected Value ProblemsSolution with Excel and Excel QM (2 of 2)第18頁，共57頁，2022年，5月20日，7點56分，星期二Chapter 12 - Decision Analysis 19The expected value of perfect information (EVPI) is the maximu

19、m 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 Perfe

20、ct Information第19頁，共57頁，2022年，5月20日，7點56分，星期二Chapter 12 - Decision Analysis 20Table 12.9Payoff Table with Decisions, Given Perfect Information Decision Making with ProbabilitiesEVPI Example (1 of 2)第20頁，共57頁，2022年，5月20日，7點56分，星期二Chapter 12 - Decision Analysis 21Decision with perfect information:$100

21、,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) = $28,000Decision Making with ProbabilitiesEVPI Example (2 of 2)第21頁，共57頁，2022年，5月20日，7點56分，星期二Chapter 12 - Deci

22、sion Analysis 22Exhibit 12.7Decision Making with ProbabilitiesEVPI with QM for Windows第22頁，共57頁，2022年，5月20日，7點56分，星期二Chapter 12 - Decision Analysis 23A decision tree is a diagram consisting of decision nodes (represented as squares), probability nodes (circles), and decision alternatives (branches).

23、Table 12.10Payoff Table for Real Estate Investment ExampleDecision Making with ProbabilitiesDecision Trees (1 of 4)第23頁，共57頁，2022年，5月20日，7點56分，星期二Chapter 12 - Decision Analysis 24Figure 12.1Decision Tree for Real Estate Investment ExampleDecision Making with ProbabilitiesDecision Trees (2 of 4)第24頁，

24、共57頁，2022年，5月20日，7點56分，星期二Chapter 12 - Decision Analysis 25The 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

25、 value are selected.Decision Making with ProbabilitiesDecision Trees (3 of 4)第25頁，共57頁，2022年，5月20日，7點56分，星期二Chapter 12 - Decision Analysis 26Figure 12.2Decision Tree with Expected Value at Probability NodesDecision Making with ProbabilitiesDecision Trees (4 of 4)第26頁，共57頁，2022年，5月20日，7點56分，星期二Chapte

26、r 12 - Decision Analysis 27Exhibit 12.8Decision Making with ProbabilitiesDecision Trees with QM for Windows第27頁，共57頁，2022年，5月20日，7點56分，星期二Chapter 12 - Decision Analysis 28Exhibit 12.9Decision Making with ProbabilitiesDecision Trees with Excel and TreePlan (1 of 4)第28頁，共57頁，2022年，5月20日，7點56分，星期二Chapt

27、er 12 - Decision Analysis 29Exhibit 12.10Decision Making with ProbabilitiesDecision Trees with Excel and TreePlan (2 of 4)第29頁，共57頁，2022年，5月20日，7點56分，星期二Chapter 12 - Decision Analysis 30Exhibit 12.11Decision Making with ProbabilitiesDecision Trees with Excel and TreePlan (3 of 4)第30頁，共57頁，2022年，5月20

28、日，7點56分，星期二Chapter 12 - Decision Analysis 31Exhibit 12.12Decision Making with ProbabilitiesDecision Trees with Excel and TreePlan (4 of 4)第31頁，共57頁，2022年，5月20日，7點56分，星期二Chapter 12 - Decision Analysis 32Decision Making with ProbabilitiesSequential Decision Trees (1 of 4)A sequential decision tree is

29、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: 第32頁，共57頁，2022年，5月20日，7點56分，星期二Chapter 12 - Decision

30、Analysis 33Figure 12.3Sequential Decision TreeDecision Making with ProbabilitiesSequential Decision Trees (2 of 4)第33頁，共57頁，2022年，5月20日，7點56分，星期二Chapter 12 - Decision Analysis 34Decision Making with ProbabilitiesSequential Decision Trees (3 of 4)Decision is to purchase land; highest net expected val

31、ue ($1,160,000).Payoff of the decision is $1,160,000. 第34頁，共57頁，2022年，5月20日，7點56分，星期二Chapter 12 - Decision Analysis 35Figure 12.4Sequential Decision Tree with Nodal Expected ValuesDecision Making with ProbabilitiesSequential Decision Trees (4 of 4)第35頁，共57頁，2022年，5月20日，7點56分，星期二Chapter 12 - Decision

32、 Analysis 36Exhibit 12.13Sequential Decision Tree AnalysisSolution with QM for Windows第36頁，共57頁，2022年，5月20日，7點56分，星期二Chapter 12 - Decision Analysis 37Exhibit 12.14Sequential Decision Tree AnalysisSolution with Excel and TreePlan第37頁，共57頁，2022年，5月20日，7點56分，星期二Chapter 12 - Decision Analysis 38Bayesian

33、 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

34、 Real Estate Investment ExampleDecision Analysis with Additional InformationBayesian Analysis (1 of 3)第38頁，共57頁，2022年，5月20日，7點56分，星期二Chapter 12 - Decision Analysis 39A conditional probability is the probability that an event will occur given that another event has already occurred.Economic analyst p

35、rovides 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 Informa

36、tionBayesian Analysis (2 of 3)第39頁，共57頁，2022年，5月20日，7點56分，星期二Chapter 12 - Decision Analysis 40A 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

37、Posteria 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)第40頁，共57頁，2022年，5月20日，7點56分，

38、星期二Chapter 12 - Decision Analysis 41Decision 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

39、 state of nature are posterior probabilities from Bayes rule.第41頁，共57頁，2022年，5月20日，7點56分，星期二Chapter 12 - Decision Analysis 42Figure 12.5Decision Tree with Posterior Probabilities Decision Analysis with Additional InformationDecision Trees with Posterior Probabilities (2 of 4)第42頁，共57頁，2022年，5月20日，7點

40、56分，星期二Chapter 12 - Decision Analysis 43Decision 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第43頁，共57頁，2022年，5月20日，7點56分，星期二Chapter 12 - Dec

41、ision Analysis 44Figure 12.6Decision Tree AnalysisDecision Analysis with Additional InformationDecision Trees with Posterior Probabilities (4 of 4)第44頁，共57頁，2022年，5月20日，7點56分，星期二Chapter 12 - Decision Analysis 45Table 12.12Computation of Posterior ProbabilitiesDecision Analysis with Additional Inform

42、ationComputing Posterior Probabilities with Tables第45頁，共57頁，2022年，5月20日，7點56分，星期二Chapter 12 - Decision Analysis 46The 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 effici

43、ency 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 InformationExpected Value of Sample Information第46頁，共57頁，2022年，5月20日，7點56分，星期二Chapter 12 -

44、 Decision Analysis 47Table 12.13Payoff Table for Auto Insurance ExampleDecision Analysis with Additional InformationUtility (1 of 2)第47頁，共57頁，2022年，5月20日，7點56分，星期二Chapter 12 - Decision Analysis 48Expected Cost (insurance) = .992($500) + .008(500) = $500Expected Cost (no insurance) = .992($0) + .008(

45、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.

46、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)第48頁，共57頁，2022年，5月20日，7點56分，星期二Chapter 12 - Decision Analysis 49Decision Analysis Example Problem Solution (1 of 9)第49頁，共57頁，2022年，5月20日，7點56分，

47、星期二Chapter 12 - Decision Analysis 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 va

48、lue 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 usi

49、ng the posterior probability obtained in part e.第50頁，共57頁，2022年，5月20日，7點56分，星期二Chapter 12 - Decision Analysis 51Step 1 (part a): Determine decisions without probabilities.Maximax Decision: Maintain status quoDecisionsMaximum PayoffsExpand $800,000Status quo1,300,000 (maximum)Sell 320,000Maximin Deci

50、sion: ExpandDecisionsMinimum PayoffsExpand$500,000 (maximum)Status quo -150,000Sell 320,000Decision Analysis Example Problem Solution (3 of 9)第51頁，共57頁，2022年，5月20日，7點56分，星期二Chapter 12 - Decision Analysis 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)第52頁，共57頁，2022年，5月20日，7點