1、Chapter 12 - Decision Analysis 1Chapter 12Decision AnalysisIntroduction to Management Science8th EditionbyBernard W. Taylor IIIChapter 12 - Decision Analysis 2Components of Decision MakingDecision Making without ProbabilitiesDecision Making with ProbabilitiesDecision Analysis with Additional Informa
2、tionUtilityChapter TopicsChapter 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 A
3、nalysisComponents of Decision MakingChapter 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 ProbabilitiesChapt
4、er 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 CriterionChapter 12 - Decision An
5、alysis 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 ProbabilitiesMaximin CriterionChapter 12 - Decision Analysis 7Table 12.
6、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 selecting the decision alternative that minimizes the maximum regret.Decision Making without Probabi
7、litiesMinimax Regret CriterionChapter 12 - Decision Analysis 8The 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- ., fo
8、r 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) = 18,000Decision Making without ProbabilitiesHurwicz CriterionChapter 12 - Decision Analysis 9The e
9、qual 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) = 30,0
10、00Warehouse $30,000(.5) + 10,000(.5) = 20,000Decision Making without ProbabilitiesEqual Likelihood CriterionChapter 12 - 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” perso
11、nality and philosophy of the decision maker. Criterion Decision (Purchase)MaximaxOffice buildingMaximinApartment buildingMinimax regretApartment buildingHurwiczApartment buildingEqual likelihoodApartment buildingDecision Making without ProbabilitiesSummary of Criteria ResultsChapter 12 - Decision An
12、alysis 11Exhibit 12.1Decision Making without ProbabilitiesSolution with QM for Windows (1 of 3)Chapter 12 - Decision Analysis 12Exhibit 12.2Decision Making without ProbabilitiesSolution with QM for Windows (2 of 3)Chapter 12 - Decision Analysis 13Exhibit 12.3Decision Making without ProbabilitiesSolu
13、tion with QM for Windows (3 of 3)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(Warehou
14、se) = $30,000(.6) + 10,000(.4) = 22,000Table 12.7Payoff table with Probabilities for States of NatureDecision Making with ProbabilitiesExpected ValueChapter 12 - Decision Analysis 15The expected opportunity loss is the expected value of the regret for each decision.The expected value and expected op
15、portunity 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 NatureDecision Making with Probabil
16、itiesExpected Opportunity LossChapter 12 - Decision Analysis 16Exhibit 12.4Expected Value ProblemsSolution with QM for WindowsChapter 12 - Decision Analysis 17Exhibit 12.5Expected Value ProblemsSolution with Excel and Excel QM (1 of 2)Chapter 12 - Decision Analysis 18Exhibit 12.6Expected Value Probl
17、emsSolution with Excel and Excel QM (2 of 2)Chapter 12 - Decision Analysis 19The 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
18、information.EVPI equals the expected opportunity loss (EOL) for the best decision.Decision Making with ProbabilitiesExpected Value of Perfect InformationChapter 12 - Decision Analysis 20Table 12.9Payoff Table with Decisions, Given Perfect Information Decision Making with ProbabilitiesEVPI Example (1
19、 of 2)Chapter 12 - Decision Analysis 21Decision 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) = $28,000Decision Making with Proba
20、bilitiesEVPI Example (2 of 2)Chapter 12 - Decision Analysis 22Exhibit 12.7Decision Making with ProbabilitiesEVPI with QM for WindowsChapter 12 - Decision Analysis 23A decision tree is a diagram consisting of decision nodes (represented as squares), probability nodes (circles), and decision alternati
21、ves (branches).Table 12.10Payoff Table for Real Estate Investment ExampleDecision Making with ProbabilitiesDecision Trees (1 of 4)Chapter 12 - Decision Analysis 24Figure 12.1Decision Tree for Real Estate Investment ExampleDecision Making with ProbabilitiesDecision Trees (2 of 4)Chapter 12 - Decision
22、 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 value are selected.Decision Making with Probab
23、ilitiesDecision Trees (3 of 4)Chapter 12 - Decision Analysis 26Figure 12.2Decision Tree with Expected Value at Probability NodesDecision Making with ProbabilitiesDecision Trees (4 of 4)Chapter 12 - Decision Analysis 27Exhibit 12.8Decision Making with ProbabilitiesDecision Trees with QM for WindowsCh
24、apter 12 - Decision Analysis 28Exhibit 12.9Decision Making with ProbabilitiesDecision Trees with Excel and TreePlan (1 of 4)Chapter 12 - Decision Analysis 29Exhibit 12.10Decision Making with ProbabilitiesDecision Trees with Excel and TreePlan (2 of 4)Chapter 12 - Decision Analysis 30Exhibit 12.11Dec
25、ision Making with ProbabilitiesDecision Trees with Excel and TreePlan (3 of 4)Chapter 12 - Decision Analysis 31Exhibit 12.12Decision Making with ProbabilitiesDecision Trees with Excel and TreePlan (4 of 4)Chapter 12 - Decision Analysis 32Decision Making with ProbabilitiesSequential Decision Trees (1
26、 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 - Deci
27、sion Analysis 33Figure 12.3Sequential Decision TreeDecision Making with ProbabilitiesSequential Decision Trees (2 of 4)Chapter 12 - Decision Analysis 34Decision Making with ProbabilitiesSequential Decision Trees (3 of 4)Decision is to purchase land; highest net expected value ($1,160,000).Payoff of
28、the decision is $1,160,000. Chapter 12 - Decision Analysis 35Figure 12.4Sequential Decision Tree with Nodal Expected ValuesDecision Making with ProbabilitiesSequential Decision Trees (4 of 4)Chapter 12 - Decision Analysis 36Exhibit 12.13Sequential Decision Tree AnalysisSolution with QM for WindowsCh
29、apter 12 - Decision Analysis 37Exhibit 12.14Sequential Decision Tree AnalysisSolution with Excel and TreePlanChapter 12 - Decision Analysis 38Bayesian analysis uses additional information to alter the marginal probability of the occurrence of an event.In real estate investment example, using expecte
30、d 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 ExampleDecision Analysis with Additional InformationBayesian Analysis (1 of 3)Chapter 12 - Decision Analysis 39A conditional p
31、robability 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 r
32、eportN = negative economic reportP(Pg) = .80P(NG) = .20P(Pp) = .10P(Np) = .90 Decision Analysis with Additional InformationBayesian Analysis (2 of 3)Chapter 12 - Decision Analysis 40A posteria probability is the altered marginal probability of an event based on additional information.Prior probabili
33、ties 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) = .750Decision An
34、alysis with Additional InformationBayesian Analysis (3 of 3)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
35、 of tree represent report outcomes. Probabilities of each state of nature are posterior probabilities from Bayes rule.Chapter 12 - Decision Analysis 42Figure 12.5Decision Tree with Posterior Probabilities Decision Analysis with Additional InformationDecision Trees with Posterior Probabilities (2 of
36、4)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) = $63,194Chapter 12 - Decision Analysis 44Figure 12.6Decision
37、 Tree AnalysisDecision Analysis with Additional InformationDecision Trees with Posterior Probabilities (4 of 4)Chapter 12 - Decision Analysis 45Table 12.12Computation of Posterior ProbabilitiesDecision Analysis with Additional InformationComputing Posterior Probabilities with TablesChapter 12 - Deci
38、sion 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 efficiency of sample information is the ratio of the expected value of sample information to the expecte
39、d value of perfect information:efficiency = EVSI /EVPI = $19,194/ 28,000 = .68Decision Analysis with Additional InformationExpected Value of Sample InformationChapter 12 - Decision Analysis 47Table 12.13Payoff Table for Auto Insurance ExampleDecision Analysis with Additional InformationUtility (1 of
40、 2)Chapter 12 - Decision Analysis 48Expected 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
41、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)Cha
42、pter 12 - Decision Analysis 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)Chapter 12 - Decision Analysi
43、s 50Decision Analysis Example Problem Solution (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 opportuni
44、ty loss criteria.c. Compute expected value of perfect 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 posterio
45、r probability obtained in part e.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 Decision: ExpandDecisionsMinimum PayoffsExpand$500
46、,000 (maximum)Status quo -150,000Sell 320,000Decision Analysis Example Problem Solution (3 of 9)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(
47、.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)Chapter 12 - Decision Analysis 53Equal Likelihood Decision: ExpandExpand $800,000(.5) + 500,000(.5) = $650,000Status quo $1,300,000(.5) - 150,00
48、0(.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) = $320,000Decision
49、Analysis Example Problem Solution (5 of 9)Chapter 12 - Decision Analysis 54Expected 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 in
50、formation = 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 Example Problem Solution (6 of 9)Chapter 12 - Decision Analysis 55 Step 4 (part d): Develop a decision tree.Decision Ana
