摘要
本文讨论了DVD在线租赁的服务供应商可能遇到的问题与其解决方案。模型Ⅱ解决了在已知订单与各种DVD数量的情况下,如何分配DVD使得满意的人数最多,且总的满意度最大。模型Ⅲ解决了在已知订单的情况下,在一定的满意率与总满意度最大的约束下,如何以最小的成本购买各种DVD,并确定分配方案。模型V对原问题作了更深入的推广,解决了在DVD数量有限且租赁费用与租赁时间成正比的条件下如何选择性地出租DVD以获得最大收入的问题。本文所讨论的问题均为最优化问题,但是各题的约束条件均不相同。本文对各个问题建立不同的网络模型,经过严密的理论论证,并用统一的费用流算法在微机上实现,充分利用了网络流模型适用面广,结果精确,计算简单的优点,对DVD租赁的现实问题提供了高效的解决方案。
In this paper, we discuss the problems and their solutions of the online service of DVD disk hire. Using model 2, we find out the optimal distribution program of DVD disk to maximize the satisfaction level of customers, and using model 3, we also fine out the optimal distribution program of DVD disk to minimize the cost under the constraint conditions that a certain satisfaction rate must be reached. We use model 5 to extend the results to much more general cases. We design different network flow models for above problems, which are problems of optimization with different constraint conditions, and use minimum cost maximum flow method to solve them by computer.
出处
《工程数学学报》
CSCD
北大核心
2005年第7期92-100,共9页
Chinese Journal of Engineering Mathematics
关键词
数学模型
网络流
最小费用最大流
mathematical model
network
minimum cost maximum flow
