数据模型与决策运筹学课后习题和案例答案.docx
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1、Review 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.12.1-4A detailed seismic survey of the land could be done to ob
2、tain 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 the states of nature prior to obtaining additional informat
3、ion 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 payoff for each decision alternative and chooses the decisi
4、on 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 maximin criterion identifies the minimum payoff for each deci
5、sion 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 maximin payoff.12.2-5The maximum likelihood criterion focus
6、es 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 other than the most likely one, 2) for alternatives that are n
7、ot 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, then it might make sense to focus on this latter state of natu
8、re 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 with the largest expected payoff.12.2-8The expected payoff i
9、s 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 assigning values to prior probabilities, 2) prior probabilit
10、ies 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 variability in the possible outcomes should have on the decision mak
11、ing.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 a random event occurs at that point.12.3-3Decision nodes are
12、 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 place and it makes it easy for anyone to interpret the mode
13、l, 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 more, they should drill.12.5-1Perfect information means knowing
14、 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 nature.12.5-3The decision tree should be started with a chance no
15、de 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 worthwhile to obtain more information.12.5-6If the cost of
16、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.12.6-1Posterior probabilities are revised probabilities of the states
17、 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 estimated.12.6-4The five kinds of probabilities considered are pr
18、ior, 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).12.6-8Bayes theorem is used to calculate posterior probabilities
19、.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 of random events and the payoffs need to be inserted before
20、 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 probability of that branch and then summing these products.
21、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 sensitivity analysis on a piece of data should require changi
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