系統(tǒng)工程第六章ppt課件-資料下載頁(yè)
2025-08-23 04:14本頁(yè)面
【正文】 ore people can fly safely to Mars. Three 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 teamscall them 1,2, and 3will not succeed is , , and , respectively. 重慶大學(xué)制造工程研究所副所長(zhǎng) 鄢萍 教授 博士 ?2022SYSTEMS ENGINEERING Table 11,2 gives the estimated probability that the respective teams will fail when 0, 1, or 2 additional scientists are added to that team. Only integer numbers of scientists are considered because each new scientist will need to devote full attention to one team. The problem is to determine how to allocate the two additional scientists to minimize the probability that all three teams will fail. 重慶大學(xué)制造工程研究所副所長(zhǎng) 鄢萍 教授 博士 ?2022SYSTEMS ENGINEERING Because both Examples 2 and 3 are distribution of effort problems, their underlying structure is actually very similar, In this case, scientists replace medical teams as the kind of resource involved, and research teams replace countries as the activities. Therefore, instead of medical teams being allocated to countries, scientists are being allocated to research teams. The only basic difference between the two problems is in their objective functions. 重慶大學(xué)制造工程研究所副所長(zhǎng) 鄢萍 教授 博士 ?2022SYSTEMS ENGINEERING With so few scientists and teams involved, this problem could be solved very easily by a process of exhaustive enumeration. However, the dynamic programming solution is presented for illustrative purposes. In this case, stage n (n = 1, 2, 3) corresponds to research team n, and the state Sn is the number of new scientists still available for allocation to the remaining teams. The decision variables xn (n=1, 2, 3) are the number of additional scientists allocated to team n. 重慶大學(xué)制造工程研究所副所長(zhǎng) 鄢萍 教授 博士 ?2022SYSTEMS ENGINEERING Let pi(xi) denote the probability of failure for team i if it is assigned xi additional scientists, as given by Table . If we let Il denote multiplication, the government39。s objective is to choose x1, x2, x3 so as to 重慶大學(xué)制造工程研究所副所長(zhǎng) 鄢萍 教授 博士 ?2022SYSTEMS ENGINEERING 2201 0012IIIIII重慶大學(xué)制造工程研究所副所長(zhǎng) 鄢萍 教授 博士 ?2022SYSTEMS ENGINEERING Case study 3: A pany which is consisted of 3 factories has $50,000,000 as investment. The president of the pany wants to use the money to increase the productivities of the factories. The alternative activities and the rewards of individual activity are shown as below table. Please use the Dynamic Programming Method to obtain the optimal solution. 重慶大學(xué)制造工程研究所副所長(zhǎng) 鄢萍 教授 博士 ?2022SYSTEMS ENGINEERING Investment Revenue Unit 1 Unit 2 Unit 3 0 0 0 0 1000 1500 － 1300 2022 2600 2800 2500 3000 3500 3900 － 4000 － 4200 － 重慶大學(xué)制造工程研究所副所長(zhǎng) 鄢萍 教授 博士 ?2022SYSTEMS ENGINEERING Solution: ABCDEFGHIⅠ Ⅱ Ⅲ(3500)(2600)(1500)(0)(2800)(3900)(3900)(2800)(4200)(3900)(2800)(4200)(3900)(0)(1300)(2500)680028004100530064000130025000
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