《系統(tǒng)工程第六章》ppt課件(文件)
【正文】 ach to solving this problem is to use trial and error. However, the number of possible routes is large (18), and having to calculate the total cost for each route is not an appealing task. 重慶大學(xué)制造工程研究所副所長 鄢萍 教授 博士 ?2022SYSTEMS ENGINEERING Fortunately, dynamic programming provides a solution with much less effort than exhaustive（徹底的） enumeration（列舉） . (The putational savings are enormous（巨大的） for larger versions of this problem.) Dynamic programming starts with a small portion of the original problem and finds the optimal solution for this smaller problem. It then gradually enlarges the problem, finding the current optimal solution from the preceding one, until the original problem is solved in its entirety. 重慶大學(xué)制造工程研究所副所長 鄢萍 教授 博士 ?2022SYSTEMS ENGINEERING For the stagecoach problem, we start with the smaller problem where the fortune seeker has nearly pleted his journey and has only one more stage (stagecoach run) to go. The obvious optimal solution for this smaller problem is to go from his current state (whatever it is) to his ultimate destination (state J). 重慶大學(xué)制造工程研究所副所長 鄢萍 教授 博士 ?2022SYSTEMS ENGINEERING 1 2 3 4 重慶大學(xué)制造工程研究所副所長 鄢萍 教授 博士 ?2022SYSTEMS ENGINEERING CHARACTERISTICS OF DYNAMIC PROGRAMMING PROBLEMS The stagecoach problem is a literal prototype of dynamic programming problems。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 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 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 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 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。s decision as to his next destination led him from his current state to the next state on his journey. 重慶大學(xué)制造工程研究所副所長 鄢萍 教授 博士 ?2022SYSTEMS ENGINEERING ?The work would consist of columns of nodes, with each column corresponding to a stage, so that the flow from a node can go only to a node in the next column to the right. ?The links from a node to nodes in the next column correspond to the possible policy decisions on which state to go to next. ?The value assigned to each link usually can be interpreted as the immediate contribution to the objective function from making that policy decision. In most cases, the objective corresponds to finding either
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