管理科学决策分析.pptx
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1、 1Table 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 Making第1页/共56页 2Decision s
2、ituation: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2页/共56页 3Table 12.3Payoff Table Illustrating a Maximax DecisionIn the maximax criterion t
3、he decision maker selects the decision that will result in the maximum of maximum payoffs;an optimistic criterion.Decision Making without ProbabilitiesMaximax Criterion第3页/共56页 4Table 12.4Payoff Table Illustrating a Maximin DecisionIn the maximin criterion the decision maker selects the decision tha
4、t will reflect the maximum of the minimum payoffs;a pessimistic criterion.Decision Making without ProbabilitiesMaximin Criterion第4页/共56页 5Table 12.6 Regret Table Illustrating the Minimax Regret DecisionRegret is the difference between the payoff from the best decision and all other decision payoffs.
5、The decision maker attempts to avoid regret by selecting the decision alternative that minimizes the maximum regret.Decision Making without ProbabilitiesMinimax Regret Criterion第5页/共56页 6The Hurwicz criterion is a compromise between the maximax and maximin criterion.A coefficient of optimism,is a me
6、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$30,000(.4)+10,0
7、00(.6)=18,000Decision Making without ProbabilitiesHurwicz Criterion第6页/共56页 7The 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$50,0
8、00(.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7页/共56页 8A dominant decision is one that has a better payoff than another decision under each state of nature.The appropriate cri
9、terion is dependent on the“risk”personality and philosophy of the decision maker.Criterion Decision(Purchase)MaximaxOffice buildingMaximinApartment buildingMinimax regretApartment buildingHurwiczApartment buildingEqual likelihoodApartment buildingDecision Making without ProbabilitiesSummary of Crite
10、ria Results第8页/共56页 9Exhibit 12.1Decision Making without ProbabilitiesSolution with QM for Windows(1 of 3)第9页/共56页 10Exhibit 12.2Decision Making without ProbabilitiesSolution with QM for Windows(2 of 3)第10页/共56页 11Exhibit 12.3Decision Making without ProbabilitiesSolution with QM for Windows(3 of 3)第
11、11页/共56页 12Expected 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)=22,000Table 12.7Payoff table with Probab
12、ilities for States of NatureDecision Making with ProbabilitiesExpected Value第12页/共56页 13The 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)=30,000EO
13、L(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 ProbabilitiesExpected Opportunity Loss第13页/共56页 14Exhibit 12.4Expected Value ProblemsSolution with QM for Windows第14页/共56页
14、 15Exhibit 12.5Expected Value ProblemsSolution with Excel and Excel QM(1 of 2)第15页/共56页 16Exhibit 12.6Expected Value ProblemsSolution with Excel and Excel QM(2 of 2)第16页/共56页 17The expected value of perfect information(EVPI)is the maximum amount a decision maker would pay for additional information.
15、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第17页/共56页 18Table 12.9Payoff Table with Decisions,G
16、iven Perfect Information Decision Making with ProbabilitiesEVPI Example(1 of 2)第18页/共56页 19Decision 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
17、,000Decision Making with ProbabilitiesEVPI Example(2 of 2)第19页/共56页 20Exhibit 12.7Decision Making with ProbabilitiesEVPI with QM for Windows第20页/共56页 21A decision tree is a diagram consisting of decision nodes(represented as squares),probability nodes(circles),and decision alternatives(branches).Tab
18、le 12.10Payoff Table for Real Estate Investment ExampleDecision Making with ProbabilitiesDecision Trees(1 of 4)第21页/共56页 22Figure 12.1Decision Tree for Real Estate Investment ExampleDecision Making with ProbabilitiesDecision Trees(2 of 4)第22页/共56页 23The expected value is computed at each probability
19、 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)第23页/共56页 24Figure 12.2Decision Tree with Expected V
20、alue at Probability NodesDecision Making with ProbabilitiesDecision Trees(4 of 4)第24页/共56页 25Exhibit 12.8Decision Making with ProbabilitiesDecision Trees with QM for Windows第25页/共56页 26Exhibit 12.9Decision Making with ProbabilitiesDecision Trees with Excel and TreePlan(1 of 4)第26页/共56页 27Exhibit 12.
21、10Decision Making with ProbabilitiesDecision Trees with Excel and TreePlan(2 of 4)第27页/共56页 28Exhibit 12.11Decision Making with ProbabilitiesDecision Trees with Excel and TreePlan(3 of 4)第28页/共56页 29Exhibit 12.12Decision Making with ProbabilitiesDecision Trees with Excel and TreePlan(4 of 4)第29页/共56
22、页 30Decision 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 pe
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