大硕文化教育事业91年度线上模拟考(试题).doc

大碩文化教育事業91年度線上模擬考(試題)科目：作業研究老師：楊文生範圍：專案管理、決策理論、對局理論、整數規劃、動態規劃、目標規劃作答時間：80分鐘 頁數： 1 /8題目1：（配分）The promoter of a rock concert in Indianapolis must perform the tasks shown in The following table before the concert can be held (all durations are in days).ActivityDescriptionImmediatePredecessorsOptimistic EstimateMost Likely EstimatePessimistic Estimate AFind engineers- 6 9 18 BSet up ticker agents - 1 2 3 CPrepare electronics A 3 9 9 DPrint advertising B 5 8 17 ESet up transportation A,B 4 4 10 F Rehearsals C,D 1 2 3 GLast-minute details F 4 4 4Please (一)draw the network diagram and identify the critical path. (二)compute the expected value and standard deviation of this concert project.答案1：(1) A(10) C(8) F(2) B(2) D(2) G(4) E(9) Critical path：ACFG 完工時間為24天 (2) expected value=24 standard deviation= 頁數： 2 /8詳解1： (1) A(10) C(8) F(2) B(2) D(2) G(4) E(9) Critical path：ACFG 完工時間為24天 (2) ActivityteA104B21/9C81D24E91F21/9G40 Critical path：ACFGexpected value=10+8+2+4=24standard deviation=題目2：（配分）Use dynamic programming to solve the following integer programming. max Z = 3x1 + 4x2 + 8x3 2x1 + 2x2 +2x3 8 x1 + x2 + x3 4 x1,x2,x3 1, integers.答案2： Z=23 頁數： 3 /8詳解2：Let 、 Max s.t n=3 S000181N=2 S010001840N=1 S011830 Z=8+15=23題目3：（配分） A government space project is conducting research on a certain engineering problem that must be solved before people can fly safely to Mars. There research teams are currently trying three different approaches for solving this problem.The estimate has been made that , under present circumstances, the probability that the respective teams will not succeed is 0.40, 0.60, and 0.80, respectively.Because the objective is to minimize the probability of failure, two or more top scientists have been assigned to the project. Table gives the estimated probability that the respective teams will fail when 0,1,or 2 additional scientists are added to that team. The problem is to determine how to allocate the two additional scientists to minimize the probability that all three teams will fail. Please apply dynamic programming to solve this problem. 頁數： 4 /8Table Data for the government space project problemNew ScientistsProbability of failureTeam 1Team 2Team 300.400.600.8010.200.400.5020.150.200.30The estimate has been made that , under present circumstances, the probability that the respective teams will not succeed is 0.40, 0.60, and 0.80, respectively.Because the objective is to minimize the probability of failure, two or more top scientists have been assigned to the project. Table gives the estimated probability that the respective teams will fail when 0,1,or 2 additional scientists are added to that team. The problem is to determine how to allocate the two additional scientists to minimize the probability that all three teams will fail. Please apply dynamic programming to solve this problem.答案3： probability of failure=0.06詳解3：Xn=增加科學家至team n S=增加科學家所有狀態 Pn=失敗率n=3 S00.8010.5120.32 頁數： 5 /8n=2 S01200.480.48010.30.320.3020.180.20.160.162n=1 S01220.0640.060.0720.061 probability of failure=0.06題目4：（配分） Decision Making Under Uncertainty (EVPI and EVSI) Consider the following pay-off table (i.e., profit entry) which is to be used for the decision making in a future time period:DecisionD1D2D3State of Natures 1200180120s2120150190 In order to enhance the accuracy of decision making, some information indicator classified as I1 : Positive Indicator and I2 : Negative Indicator are adopted. Previous record of 100 cases show that 75 cases turned out to be s 1. (We would then assume the probability of occurrence of s 1 0.75.) Among these 75 cases, 84% of them had been flagged as I1. For the remaining 25 cases which turned out to be s2, 72% of them had been flagged as I2 . Use the decision tree on next page to assist your answering of the following questions.(一) What would be your decision if a positive indicator, I, appears before the decision is made? What about if the negative indicator, I, turns out? (Show your calculation to support the claim)(二) Assume that your would adopt the expected monetary value criterion to make the decision under situation where no indicator is available. Now that with the indicator available, what is 頁數： 6 /8the maximum amount that you would be willing to pay for the service provided by the information indicator? (i.e. what is the Expected Value of Sample Information?) S1 2004 120 S2 d1 S1 18052 d2 S2 1506 I1 d3 S1 120 S2 1 190 S1 2007 S2 d1 12038 I2 d2 S1 180 S2 d3 1509 S1 120 S2 190答案4：(1) I1：d1 、I2：d3 (2)EVSI=3詳解4：(1)P(S1)=0.75 、P(S2)=0.25 =0.9 頁數： 7 /8 192 0.9 2004 120 0.1 192 d1 177 0.9 18052 d2 0.1 1506 I1(0.7) d3 127 0.9 120 0.1 1 183 190 152 0.9 2007 0.1 162 d1 12038 I2(0.3) d2 152 0.4 180 0.6 d3 1509 162 0.4 120 0.6 190 I1：d1 、I2：d3 (2) 180 0.75 2004 120 0.25 180 d1 172.5 0.75 18052 d2 0.25 150 d3 137.5 0.75 1206 0.25 190 EVSI=183-180=3 頁數： 8 /8題目5：（配分） 利用 Branch-And-Bound Method 解決下列線性整數規劃問題(Linear Integer Programming