数据、模型与决策(运筹学)课后习题和案例答案012(98页).doc

《数据、模型与决策(运筹学)课后习题和案例答案012(98页).doc》由会员分享，可在线阅读，更多相关《数据、模型与决策(运筹学)课后习题和案例答案012(98页).doc（98页珍藏版）》请在淘文阁 - 分享文档赚钱的网站上搜索。

1、-数据、模型与决策(运筹学)课后习题和案例答案012-第 98 页CHAPTER 12DECISION ANALYSISReview Questions12.1-1The decision alternatives are to drill for oil or to sell the land.12.1-2The consulting geologist believes that there is 1 chance in 4 of oil on the tract of land.12.1-3Max does not put much faith in the assessment.12.

2、1-4A detailed seismic survey of the land could be done to obtain more information.12.1-5The possible states of nature are the possible outcomes of the random factors that affect the payoff that would be obtained from a decision alternative.12.1-6Prior probabilities are the estimated probabilities of

3、 the states of nature prior to obtaining additional information through a test or survey.12.1-7The payoffs are quantitative measures of the outcomes from a decision alternative and a state of nature. Payoffs are generally expressed in monetary terms.12.2-1The maximax criterion identifies the maximum

4、 payoff for each decision alternative and chooses the decision alternative with the maximum of these maximum payoffs. The maximax criterion is for the eternal optimist.12.2-2The maximax citerion completely ignores the prior probabilities and ignores all payoffs except for the largest one.12.2-3The m

5、aximin criterion identifies the minimum payoff for each decision alternative and chooses the decision alternative with the maximum of these minimum payoffs. The maximin criterion is for the total pessimist.12.2-4The maximin criterion ignores the prior probabilities and ignores all payoffs except the

6、 maximin payoff.12.2-5The maximum likelihood criterion focuses on the most likely state of nature, the one with the largest prior probability.12.2-6Criticisms of the maximum likelihood criterion include: 1) this criterion chooses an alternative without considering its payoffs for states of nature ot

7、her than the most likely one, 2) for alternatives that are not chosen, this criterion ignores their payoffs for states of nature other than the most likely one, 3) if the differences in the payoffs for the most likely state of nature are much less than for another somewhat likely state of nature, th

8、en it might make sense to focus on this latter state of nature instead, and 4) if there are many states of nature and they are nearly equally likely, then the probability that the most likely state of nature will be the true one is fairly low.12.2-7Bayes decision rule says to choose the alternative

9、with the largest expected payoff.12.2-8The expected payoff is calculated by multiplying each payoff by the prior probability of the corresponding state of nature and then summing these products.12.2-9Criticisms of Bayes decision rule include: 1) there usually is considerable uncertainty involved in

10、assigning values to prior probabilities, 2) prior probabilities inherently are at least largely subjective in nature, whereas sound decision making should be based on objective data and procedures, and 3) by focusing on average outcomes, expected payoffs ignore the effect that the amount of variabil

11、ity in the possible outcomes should have on the decision making.12.3-1A decision tree is a graphical display of the progression of decisions and random events to be considered.12.3-2A decision node indicates that a decision needs to be made at that point in the process. An event node indicates that

12、a random event occurs at that point.12.3-3Decision nodes are represented by squares while circles represent event nodes.12.4-1Sensitivity analysis might be helpful to study the effect if some of the numbers included in the model are not correct.12.4-2It assures that each piece of data is in only one

13、 place and it makes it easy for anyone to interpret the model, even if they dont understand TreePlan or decision trees.12.4-3A data table displays results of selected output cells for various trial values of a data cell.12.4-4If there is less than a 23.75% chance of oil, they should sell. If its mor

14、e, they should drill.12.5-1Perfect information means knowing for sure which state of nature is the true state of nature.12.5-2The expected payoff with perfect information is calculated by multiplying the maximum payoff for each alternative by the prior probability of the corresponding state of natur

15、e.12.5-3The decision tree should be started with a chance node whose branches are the various states of nature.12.5-4EVPI = EP (with perfect information) EP (without more information)12.5-5If the cost of obtaining more information is more than the expected value of perfect information then it is not

16、 worthwhile to obtain more information.12.5-6If the cost of obtaining more information is less than the expected value of perfect information then it might be worthwhile to obtain more information.12.5-7In the Goferbroke problem the EVPI C so it might be worthwhile to do the seismic survey.12.6-1Pos

17、terior probabilities are revised probabilities of the states of nature after doing a test or survey to improve the prior probabilities.12.6-2The possible findings are favorable with oil being fairly likely, or unfavorable with oil being quite unlikely.12.6-3Conditional probabilities need to be estim

18、ated.12.6-4The five kinds of probabilities considered are prior, conditional, joint, unconditional, and posterior.12.6-5P(state and finding) = P(state) * P(finding | state).12.6-6P(finding) = sum of P(state and finding) for each state.12.6-7P(state | finding) = P(state and finding) / P(finding).12.6

19、-8Bayes theorem is used to calculate posterior probabilities.12.7-1A decision tree provides a graphical display of the progression of decisions and random events for a problem.12.7-2A decision needs to be made at a decision node.12.7-3A random event will occur at a event node.12.7-4The probabilities

20、 of random events and the payoffs need to be inserted before beginning analysis.12.7-5When performing the analysis, start at the right side of the decision tree and move left one column at a time.12.7-6For each event node, calculate its expected payoff by multiplying the payoff of each branch by the

21、 probability of that branch and then summing these products.12.7-7For each decision node, compare the expected payoffs of its branches and choose the alternative whose branch has the largest expected payoff.12.8-1Consolidate the data and results into one section of the spreadsheet.12.8-2Performing s

22、ensitivity analysis on a piece of data should require changing a value in only one place on the spreadsheet.12.8-3A data table can consider changes in only one or two data cells.12.8-4One.12.8-5Yes. The spider graph can consider changes in many data cells at a time.12.8-6SensIts spider graph assumes

23、 that each data value varies by the same amount. Sensits tornado diagram overcomes this limitation.12.9-1Utilities are intended to reflect the true value of an outcome to the decision-maker.12.9-212.9-3Under the assumptions of utility theory, the decision-makers utility function for money has the pr

24、operty that the decision-maker is indifferent between two alternative courses of action if the two alternatives have the same expected utility.12.9-4The decision-maker is offered two hypothetical alternatives and asked to identify the point of indifference between the two.12.9-5The point of indiffer

25、ence is the value of p where the decision-maker is indifferent between the two hypothetical alternatives.12.9-6The value obtained to evaluate each node of the tree is the expected utility.12.9-7Max decided to do the seismic survey and to sell if the result is unfavorable or drill if the result is fa

26、vorable.12.10-1The Goferbroke problem contained the same elements as typical applications of decision analysis but is oversimplified.12.10-2An influence diagram complements the decision tree for representing and analyzing decision analysis problems.12.10-3Typical participants include management, an

27、analyst, and a group facilitator.12.10-4A manager can go to a management consulting firm that specializes in decision analysis.12.10-5Decision analysis is widely used around the world.Problems12.1a)Max(A1) = 6, Max(A2) = 4, Max(A3) = 8. Maximax = 8 with alternative A3.b)Min(A1) = 2, Min(A2) = 3, Min

28、(A3) = 1. Maximin = 3 with alternative A2.12.2a)Max(A1) = 30, Max(A2) = 31, Max(A3) = 22, Max(A4) = 29. Maximax = 31 with A2.b)Min(A1) = 20, Min(A2) = 14, Min(A3) = 22, Min(A4) = 21. Maximin = 22 with A3.12.3a)State of NatureAlternativeSell 10 casesSell 11 casesSell 12 casesSell 13 casesBuy 10 cases

29、$50$50$50$50Buy 11 cases$47$55$55$55Buy 12 cases$44$52$60$60Buy 13 cases$41$49$57$65Prior Probabilityb)Max(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 =

30、$50 with buying 10 cases.d)The most likely state of nature is to sell 11 cases. Under this state, she should buy 11 cases with a payoff of $55.e)Jean should buy 12 cases. The maximum expected payoff is $53.60.f)Jean should purchase 12 cases. The maximum expected payoff is $55.20.Jean should purchase

31、 12 cases. The maximum expected payoff is $54.40.Jean should purchase 11 cases. The maximum expected payoff is $53.40.12.4a)Max(Conservative) = $30 millionMax(Speculative) = $40 millionMax(Countercyclical) = $15 millionMaximax = $40 million with the speculative investmentb)Min(Conservative) = $10 mi

32、llionMin(Speculative) = $30 millionMin(Countercyclical) = $10 millionMaximin = $10 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)The countercy

33、clical investment has the maximum expected payoff of $5 million.12.5a)The countercyclical investment has the maximum expected payoff of $8 million.b)The speculative investment has the maximum expected payoff of $5 million.c&d)e)f)Part a)Part b)g)h)Counter-cyclical and conservative cross at approxima

34、tely p=0.62.Conservative and speculative cross at approximately p = 0.68.i)Let p = prior probability of stable economyFor the conservative option:EP= (0.1)(30) + p(5) + (10.1p)(10) = 3 + 5p 9 +10p = 15p 6For the speculative option:EP= (0.1)(40) + p(10) + (10.1p)(30) = 4 + 10p 27 +30p = 40p 23For the

35、 counter-cyclical option:EP= (0.1)(10) + p(0) + (10.1p)(15) = 1 + 0 + 13.5 15p = 15p + 12.5Counter-cyclical and conservative cross when15p + 12.5 = 15p 6 or 30p = 18.5 or p = 0.617Conservative and speculative cross when15p 6 = 40p 23 or 25p = 17 or p = 0.68They should choose the counter-cyclical opt

36、ion when p 0.617, the conservative option when 0.617 p 0.433.h)Let p = prior probability of S1.For A1: EP= p(220) + (0.3)(170) + (1 0.3 p)(110) = 220p + 51 + 77 110p = 110p + 128For A2: EP= p(200) + (0.3)(180) + (1 0.3 p)(150) = 200p + 54 + 105 150p = 50p + 159A1 and A2 cross when 110p + 128 = 50p +

37、 159 or 60p = 31 or p = 0.517.They should choose A2 when p 0.517, A1 when p 0.517.i)Let p = prior probability of S2.For A1: EP= (0.6)(220) + p(170) + (1 0.6 p)(110) = 132 + 170p + 44 110p = 60p + 176For A2: EP= (0.6)(200) + p(180) + (1 0.6 p)(150) = 120 + 180p + 60 150p = 30p + 180A1 and A2 cross wh

38、en 60p + 176 = 30p + 180 or 30p = 4 or p = 0.133.They should choose A2 when p 0.133, A1 when p 0.133.j)Alternative A1 should be chosen.12.8a)State of Nature (Weather)AlternativeDryModerateDampCrop 1203540Crop 23045Crop 3302525Crop 4202020Prior Probabilityb)c)Crop 1 has the highest expected payoff of

39、 $31,500.d)When the prior probability of moderate weather is 0.2, Crop 2 has the highest expected payoff of $35,250. When the prior probability of moderate weather is 0.3, Crop 2 has the highest expected payoff of $33,750.When the prior probability of moderate weather is 0.4, Crop 2 has the highest

40、expected payoff of $32,250. When the prior probability of moderate weather is 0.6, Crop 1 has the highest expected payoff of $31,000.12.9When x = 50, alternative A3 has the highest expected payoff of $5,600.When x = 75, alternative A1 has the highest expected payoff of $7,400.Barbara Miller should p

41、ay a maximum of $1,800 to increase x to 75.12.10a)Alternative A2 has the highest expected payoff of $1,000.b)With perfect information, choose A1 for when the state is S1, A2 when the state is S2, and A3 when the state is S3.EP(with perfect information) = (0.2)(4) + (0.5)(2) + (0.3)(1) = $2,100EVPI = EP(with perfect information) EP (without more information)= $2,100 $1,000 = $1,100.c)EVPI = EP(with perfect information) EP (without more information)= $2,100 $1,000 = $1,100.d)Since the information will cost $1,000 and the value is no more than $1,100, it might be worthwhile to spen