DVD在线租赁系统的优化设计  

Optimal Design for Online DVD Tenancy System

作　　者：李蓬蓬[1] 朱小满[1] 解炜[1] 

机构地区：[1]国防科技大学,长沙410073

出　　处：《工程数学学报》2005年第7期85-91,共7页Chinese Journal of Engineering Mathematics

摘　　要：本文在DVD在线租赁背景下,对DVD的租赁与归还,网方的购买与分配以及需求预测等相关问题进行了建模和研究。首先,对题中给出的表示会员对各DVD的偏爱程度的偏好指数进行修正,提出了绝对满意度和相对满意度的合理定义。在模型的建立和求解上,本文首先建立了基于DVD租用次数限制的通用模型和以Poission过程模拟DVD归还过程的随机服务模型解决了在预知市场需求的情况下,各DVD采购量的问题。随后,建立0-1整数线性规划模型并结合Lingo软件进行求解,很好地回答了现有碟的一次性分配问题。结合抽样统计的知识,建立0～1规划模型用以解答第三问的多目标规划问题。在双目标规划的求解处理上,采取以满意度为限制条件,以碟的总量最小为目标进行规划的方式寻优求解。针对第四问,本文引入VIP机制,分别建立并求解了VIP会员与普通会员的权重不同时的加权规划模型、VIP会员有优先权的分层规划模型。还简单讨论了会员的信用度、邮递时间、租赁规则、DVD价格因素等实际问题。We＇ve done some research about the tenancy and restitute of DVD. First, we come up with the reasonable definition about the absolute satisfaction degree index and relative satisfaction index to measure the member＇s satisfaction. During the process on solvlng the model, we use Poisson procedure to simulate DVD＇s restitute process and successfully make prediction about the market requirement on the basis of the limited tenancy times. Then we construct a binary integer programming （BIP） model to make answer about the one-off DVD distribution, and apply LINDO in our model. Next we treat the quantity of DVD as object function and satisfaction as constrains to find the optimal solution to this multiple goal programming. Finally, we introduce the VIP mechanism. We construct a weighted programming model, assuming that VIP＇s weight is higher than common members. And we also develop a hierarchical programming model, assuming that VIP has priority.

关 键 词：随机服务模型 0-1整数规划 多目标规划 抽样统计 VIP机制 

分 类 号：O221[理学—运筹学与控制论]