数据、模型与决策(运筹学)课后习题和案例答案.pdf

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1、CHAPTER 12DECISION ANALYSISReview Questions12.1-1 The decision alternatives are to drill for oil or to sell the land.12.1-2 The consulting geologist believes that there is 1 chance in 4 of oil on the tract of land.12.1-3 Max does not put much faith in the assessment.12.1-4 A detailed seismic survey

2、of the land could be clone to obtain more information.12.1-5 The possible states of nature are the possible outcomes of the random factors that affect thepayoff that would be obtained from a decision alternative.12.1-6 Prior probabilities are the estimated probabilities of the states of nature prior

3、 to obtainingadditional information through a test or survey.12.1-7 The payoffs are quantitative measures of the outcomes from a decision alternative and a stateof nature.Payoffs are generally expressed in monetary terms.12.2-1 The maximax criterion identifies the maximum payoff for each decision al

4、ternative andchooses the decision alternative with the maximum of these maximum payoffs.The maximaxcriterion is for the eternal optimist.12.2-2 The maximax citerion completely ignores the prior probabilities and ignores all payoffs exceptfor the largest one.12.2-3 The maximin criterion identifies th

5、e minimum payoff fbr each decision alternative and choosesthe decision alternative with the maximum of these minimum payoffs.The maximin criterionis for the total pessimist.12.2-4 The maximin criterion ignores the prior probabilities and ignores all payoffs except themaximin payoff.12.2-5 The maximu

6、m likelihood criterion focuses on the most likely state of nature,the one with thelargest prior probability.12.2-6 Criticisms of the maximum likelihood criterion include:1)this criterion chooses an alternativewithout considering its payoffs fbr states of nature other than the most likely one,2)foral

7、ternatives that are not chosen,this criterion ignores their payoffs fbr states of nature otherthan the most likely one,3)if the differences in the payoffs for the most likely state of natureare much less than fbr another somewhat likely state of nature,then it might make sense tofbcus on this latter

8、 state of nature instead,and 4)if there are many states of nature and they arenearly equally likely,then the probability that the most likely state of nature will be the trueone is fairly low.12.2-7 Bayes decision rule says to choose the alternative with the largest expected payoff.12-112.2-8 The ex

9、pected payoff is calculated by multiplying each payoff by the prior probability of thecorresponding state of nature and then summing these products.12.2-9 Criticisms of Bayes decision rule include:1)there usually is considerable uncertaintyinvolved in assigning values to prior probabilities,2)prior

10、probabilities inherently are at leastlargely subjective in nature,whereas sound decision making should be based on objective dataand procedures,and 3)by focusing on average outcomes,expected payoffs ignore the effectthat the amount of variability in the possible outcomes should have on the decision

11、making.12.3-1 A decision tree is a graphical display of the progression of decisions and random events to beconsidered.12.3-2 A decision node indicates that a decision needs to be made at that point in the process.Anevent node indicates that a random event occurs at that point.12.3-3 Decision nodes

12、are represented by squares while circles represent event nodes.12.4-1 Sensitivity analysis might be helpful to study the effect if some of the numbers included in themodel are not correct.12.4-2 It assures that each piece of data is in only one place and it makes it easy for anyone tointerpret the m

13、odel,even if they dont understand TreePlan or decision trees.12.4-3 A data table displays results of selected output cells for various trial values of a data cell.12.4-4 If there is less than a 23.75%chance of oil,they should sell.If its more,they should drill.12.5-1 Perfect information means knowin

14、g for sure which state of nature is the true state of nature.12.5-2 The expected payoff with perfect information is calculated by multiplying the maximumpayoff for each alternative by the prior probability of the corresponding state of nature.12.5-3 The decision tree should be started with a chance

15、node whose branches are the various statesof nature.12.5-4 EVPI=EP(with perfect information)-EP(without more information)12.5-5 If the cost of obtaining more information is more than the expected value of perfectinformation then it is not worthwhile to obtain more information.12.5-6 If the cost of o

16、btaining more information is less than the expected value of perfect informationthen it might be worthwhile to obtain more information.12.5-7 In the Goferbroke problem the EVPI C so it might be worthwhile to do the seismic survey.12.6-1 Posterior probabilities are revised probabilities of the states

17、 of nature after doing a test orsurvey to improve the prior probabilities.12.6-2 The possible findings are favorable with oil being fairly likely,or unfavorable with oil beingquite unlikely.12.6-3 Conditional probabilities need to be estimated.12.6-4 The five kinds of probabilities considered are pr

18、ior,conditional,joint,unconditional,andposterior.12.6-5 P(state and finding)=P(state)*P(finding I state).12-212.6-6 P(finding)=sum of P(state and finding)for each state.12.6-7 P(state I finding)=P(state and finding)/P(finding).12.6-8 Bayes theorem is used to calculate posterior probabilities.12.7-1

19、A decision tree provides a graphical display of the progression of decisions and random eventsfor a problem.12.7-2 A decision needs to be made at a decision node.12.7-3 A random event will occur at a event node.12.7-4 The probabilities of random events and the payoffs need to be inserted before begi

20、nninganalysis.12.7-5 When performing the analysis,start at the right side of the decision tree and move left onecolumn at a time.12.7-6 For each event node,calculate its expected payoff by multiplying the payoff of each branch bythe probability of that branch and then summing these products.12.7-7 F

21、or each decision node,compare the expected payoffs of its branches and choose thealternative whose branch has the largest expected payoff.12.8-1 Consolidate the data and results into one section of the spreadsheet.12.8-2 Performing sensitivity analysis on a piece of data should require changing a va

22、lue in only oneplace on the spreadsheet.12.8-3 A data table can consider changes in only one or two data cells.12.8-4 One.12.8-5 Yes.The spider graph can consider changes in many data cells at a time.12.8-6 Senslts spider graph assumes that each data value varies by the same amount.Sensitstornado di

23、agram overcomes this limitation.12.9-1 Utilities are intended to reflect the true value of an outcome to the decision-maker.12.9-3 Under the assumptions of utility theory,the decision-maker utility function fbr money hasthe property that the decision-maker is indifferent between two alternative cour

24、ses of action ifthe two alternatives have the same expected utility.12-312.9-4 The decision-maker is offered two hypothetical alternatives and asked to identify the point ofindifference between the two.12.9-5 The point of indifference is the value of p where the decision-maker is indifferent between

25、 thetwo hypothetical alternatives.12.9-6 The value obtained to evaluate each node of the tree is the expected utility.12.9-7 Max decided to do the seismic survey and to sell if the result is unfavorable or drill if the resultis favorable.12.10-1 The Goferbroke problem contained the same elements as

26、typical applications of decisionanalysis but is oversimplified.12.10-2 An influence diagram complements the decision tree for representing and analyzing decisionanalysis problems.12.10-3 Typical participants include management,an analyst,and a group facilitator.12.10-4 A manager can go to a manageme

27、nt consulting firm that specializes in decision analysis.12.10-5 Decision analysis is widely used around the world.Problems12.1 a)Max(4)=6,Max(A2)=4,Max(A3)=8.Maximax=8 with alternative A3.b)Min(A)=2,Min(A2)=3,Min(A3)=1.Maximin=3 with alternative A2.12.2 a)Max(Aj)=30,Max(A2)=31,Max(A3)=22,Max(A4)=29

28、.Maximax=31 with A?-b)Min(Aj)=20,Min(A2)=14,Min(4)=22,Min(A4)=21.Maximin=22 with A3.12.3 a)AlternativeState of NatureSell 1()casesSell 11 casesSell 12 casesSell 13 casesBuy 10 cases$50$50$50$50Buy 11 cases$47$55$55$55Buy 12 cases$44$52$60$60Buy 13 cases$41$49$57$65Prior Probability0.20.40.30.1b)Max(

29、Buy 10)=$50,Max(Buy 11)=$55,Max(Buy 12)=$60,Max(Buy 13)=$65.Maximax=$65 with buying 13 cases.c)Min(Buy 10)=$50,Min(Buy 11)=$47,Min(Buy 12)=$44,Min(Buy 13)=$41.Maximin=$50 with buying 10 cases.d)The most likely state of nature is to sell 11 cases.Under this state,she should buy 11 caseswith a payoff

30、of$55.12-4ABCDEFGH1Purchase Price$32Selling Price$834Payoff TableState o Nature5SellSellSellSellExpected6Alternative10111213Payoff7Buy 10$50$50$50$50$50.008Buy 11$47$55$55$55$53.409Buy 12$44$52$60$60$53.6010Buy 13$41$49$57$65$51.401112Prior Probability0.20.40.30.1Jean should buy 12 cases.The maximum

31、 expected payoff is$53.60.f)(i)0.2 and 0.5ABCDEFGH1Purchase Price$32Selling Price$834Payoff TableState o Nature5SellSellSellSellExpected6Alternative10111213Payoff7Buy 10$50$50$50$50$50.008Buy 11$47$55$55$55$53.409Buy 12$44$52$60$60$55.2010Buy 13$41$49$57$65$53.001112Prior Probability0.20.20.50.1Jean

32、 should purchase 12 cases.The maximum expected payoff is$55.20.(ii)0.3 and 0.4ABCDEFGH1Purchase Price$32Selling Price$834Payoff TableState o Nature5SellSellSellSellExpected6Alternative10111213Payoff7Buy 10$50$50$50$50$50.008Buy 11$47$55$55$55$53.409Buy 12$44$52$60$60$54.4010Buy 13$41$49$57$65$52.201

33、112Prior Probability0.20.30.40.1Jean should purchase 12 cases.The maximum expected payoff is$54.40.12-5(iii)0.5 and 0.2ABcDEFGH1Purchase Price$32Selling Price$834Payoff TableState ol Nature5SellSellSellSellExpected6Alternative10111213Payoff7Buy 10$50$50$50$50$50.008Buy 11$47$55$55$55$53.409Buy 12$44

34、$52$60$60$52.8010Buy 13$41$49$57$65$50.601112Prior Probability0.20.50.20.1Jean should purchase 11 cases.The maximum expected payoff is$53.40.12.4 a)Max(Conservative)=$30 millionMax(Speculative)=$40 millionMax(Countercyclical)=$15 millionMaximax=$40 million with the speculative investmentb)Min(Conser

35、vative)=-$10 millionMin(Speculative)=-$30 millionMin(Countercyclical)=-$10 millionMaximin=-$1()million with either the conservative of countercyclical investment.c)The stable economy is the most likely state of nature.The speculative investment has the maximum payoff for this state($10 million).d)Th

36、e countercyclical investment has the maximum expected payoff of$5 minion.ABCDEF1Payoff Table($million)Expected2AlternativeState of Nature(Economy)Payoff3(Investment)ImprovingStableWorsening($million)4Conservative305-101.55Speculative4010-30-36Countercyclical-10015578Prior Probability0.10.50.412.5 a)

37、The countercyclical investmenl has ihe maximum expected payoff of$8 minion.12-6ABCDEF1Payoff Table($million)Expected2AlternativeState of Nature(Economy)Payoff3(Investment)ImprovingStableWorsening($million)4Conservative305-10-1.55Speculative4010-30-116Countercyclical-10015878Prior Probability0.10.30.

38、6b)The speculative investment has the maximum expected payoff of$5 miHion.ABCDEF1Payoff Table($million)Expected2AlternativeState of Nature(Economy)Payoff3(Investment)ImprovingStableWorsening($million)4Conservative305-104.55Speculative4010-3056Countercyclical-10015278Prior Probability0.10.70.212-7c&d

39、)12-8e)ADEF GHIJKLMN0p10.12ImprovincPayoff Table($million)330AlternativeState of Nature(Economy)43030(Investment)ImprovingStableWorsening5/Conservative305-106/0.5Speculative4010-307Conservative/StableCountercyclical1001585901.555Prior Probability0.10.50.410110.4InvestmentCountercyclical12Worsening13

40、-10Expected Payoff514-10-10(Smillion)15160.117Improvinc184019/404020/21/0.522Speculative/Stable233卜102450-3101025260.427Worsening28-3029-30-3030310.132Improvinc-103334/-10-103536/0.537Countercyclical/Stable38IL039050040410.442Worsening431544151512-9f)art a)MN0P2Payoff Table($million)3AlternativeStat

41、e of Nature(Economy)4(Investment)ImprovingStableWorsening5Conservative30 5-1040 10-30-10 0 156Speculative7Countercyclical89Prior Probability0.1 0.3 0.61011InvestmentCountercyclical1213Expected Payoff814($million)MN0P2Payoff Table($million)3AlternativeState of Nature(Economy)4(Investment)ImprovingSta

42、bleWorsening5Conservative30 5-1040 10-30-10 0 156Speculative7Countercyclical89Prior Probability0.1 0.7 0.21011InvestmentSpeculative1213Expected Payoff514($million)12-10MNO16Expected17Probability ofOptimalPayoff18Stable EconomyInvestment($million)19Speculative5200Countercyclical12.5210.1Countercyclic

43、al11220.2Countercyclical9.5230.3Countercyclical8240.4Countercyclical6.5250.5Countercyclical5260.6Countercyclical3.5270.7Speculative5280.8Speculative9290.9Speculative13h)Expected Payoff($million)15.ConservativeSpeculativeCountercyclicalCounter-cyclical and conservative cross at approximately p=0.62.C

44、onservative and speculative cross at approximately p=0.68.12-11i)Let p=prior probability of stable economyFor the conservative option:EP=(0.1)(30)+p +(1-O.l-pX-lO)=3+5/?-9 4-1 Op=15p-6For the speculative option:EP=(0.1)(40)+p(10)+(1-0.1-p)(-30)=4+10p-27+30=40 -23For the counter-cyclical option:EP=(0

45、.1)(-10)+p(0)+(l-0.1-p)(15)=-l+0+13.5-15p=-15p+12.5Counter-cyclical and conservative cross when一 15p+12.5=15p-6 or 30P=18.5 or p=0.617Conservative and speculative cross when15/?-6=40p-23 or 25P=17 or p=0.68They should choose the counter-cyclical option when p 0.617,the conservative optionwhen 0.617

46、p 0.68.12.6 a)Max(A)=80,Max(A2)=50,Max(A3)=60.Maximax=$80 thousand when choosing alternative A1.b)Min(A1)=25,Min(A2)=30,Min(A3)=40.Maximin=$40 thousand when choosing alternative A3.c)S2 is the most likely outcome.For this state,the maximum payoff of$50 thousand occurswith alternative A2-d)Alternativ

47、e A3 has the highest expected payoff of$48 thousand._12-12ABCDE1Payoff Table($thousand)Expected2State 0 NaturePayoff3AlternativeS,S2($thousand)48025475305042660404878Prior Probability0.40.6e)0.412-13f)When the prior probability of S)is 0.2,alternative A2 should be chosen,with an expected)ayoff of$46

48、 thousand.ABcDEF GHIJKLMNO10.22State 1Payoff Table(Sthousand)380State of Nature4Alternative 1/8080Alternatives,s25、JA,80 2530 5060 4060360.8A27State 2A38259/2525Prior Probability0.20.81011/0.2Best Alternative212State 113/30Expected Payoff4614Alternative 2/3030(Sthousand)152c16460460.817State 2185019

49、505020210.222State 1236024Alternative 3/6060251 t7260440.827State 22840294040When the prior probability of S)is 0.6,alternative A should be chosen,with an expectedpayoffof658 thousand.AB DEF GH1JKLMNO10.62State 1Payoff Table(Sthousand)380State of Nature4Alternative 1/8080AlternativeSis25、/A,80 2530

50、5060 406/0580.4Az7State 2A38I250.692525Prior Probability0.41011/0.6Best Alternative112State 11330Expected Payoff5814Alternative 2/3030(Sthousand)1b1-16580380.417State 2185019505020210.622State 123I/6024Alternative 3/606025260520.427State 2284029404012-14g)MN017PriorExpected18ProbabilityBestPayoff19o