DVD在线租赁

摘要：问题是1个DVD在线租赁中，网站方如何对于市场进行需求预测，如何对DVD进行分配才能同时最好的实现其经济效益和社会效益。
  第1问中，基于需求预测基础上的DVD购买方案设计中，我们分别考虑了悲观情况和均值情况。为了保证希望看到某种DVD的会员中，有50%以上在1个月内能看到该DVD，在悲观情况下，各种DVD的购买量分别为：9000，4500，2250，1125，450。在均值情况下，各种DVD的购买量分别为：6250，3125，1563，720，313。为了保证在3个月内95%以上的会员能够看到，在悲观情况下，各种DVD的购买量分别为：3959，1980，990，495，198。最后，在不考虑具体的会员的借还DVD时间，我们使用概率的方法解决了该问题。结果与均值情况相近。
 对于第2问，对于当前问题的分配方案确定。我们建立了0-1规划模型，求得此时的最大满意度为24746，我们给了此时的最优分配方案。
 第3问，是1个多目标规划问题，既要考虑使得会员的满意度尽量大，还要使得网站购买的中的DVD数目最少，在具体处理时，我们让会员满意度在1定的范围内变动，给出各种情况下使得总DVD数最少的方案。其中当会员相对满意度为0.8时的最少DVD总数为2059张。
 分析第3问的结果，我们发现了有趣的双峰现象，并对其合理性进行了阐述。同时，我们还可以发现，会员相对满意度与最少DVD之间呈现总数近似线性的关系。如下表所示：
相对满意度 0.5 0.6 0.7 0.8 0.8 1.0
所需DVD数 1202 1486 1760 2059 2567 3098
对于网站而言，其经营的目的是获得最大的经济效益，不同的租赁模式设置下网站会得到不同的经济效益，第4问中我们讨论网站经营管理的最优模式。求得了在1种情况下，限定每月最多租赁两次的情况下，得到使得网站的效益达到最大时，应该限定每个会员每次租赁最多2张DVD。同时讨论了对于限定每次最多租赁3张DVD的情况下，最佳的租赁次数限制。 本文来自中国科教评价网
 本文论证严密，所给出的结果具有启发性和借鉴意义。
关键字 ： 正态分布；悲观情况；均值分布；

DVD on-line rents
Information and computation science：zhanghaitao  Instructs teacher：tanmin
Abstract：The issue is a DVD rental online, the Web site for how the market demand forecast How to distribute the DVD can also best achieve its economic and social benefits. I asked, based on demand forecasts based on the DVD-buying program design, We consider separately the mean pessimistic and the situation. To ensure that the DVD would like to see some of the members, more than 50% within one month will see the DVD, In a pessimistic case, the various DVD purchases were : 9000,4500,2250,1125,450. In the mean circumstances, the various DVD purchases were : 6250,3125,1563,720,313. To ensure that within three months 95% of the members will be able to see the gloomy situation, all DVD purchases were : 3959,1980,990,495,198. Finally, in consideration of specific members of the DVD also take time, we used probabilistic methods to solve the problem. With the results of similar means. Regarding the second question, the current allocation formulas. We established a 0-1 programming model, then seek the greatest satisfaction to 24,746, At this time we gave the optimal distribution program. Question 3 is a multi-objective planning issue, we should consider making membership of the largest possible degree of satisfaction, Terms of the purchase also makes a number of DVD at least, in terms of handling, We let the membership in a certain satisfaction within the scope of changes in the given circumstances under total DVD makes the least number of programs. When the members of which relative to the satisfaction of at least 0.8 DVD total of 2,059. Analysis third question the results, we found an interesting phenomenon bimodal, and the reasonableness of the paper. Meanwhile, we also can be found, Member relative satisfaction with at least between the DVD has a total approximate linear relationship. As shown in the table below :

For the site, the purpose of the operation is to maximize the economic benefits, different mode of leasing site will be under different economic benefits, Fourth, we asked for management to discuss the optimal model. Obtained by the case, the maximum monthly leasing limit twice circumstances, be made for maximum efficiency, Each Member should be limited to a maximum of each lease two DVD. Discussed the limit for the maximum number of leasing three DVD cases, the number of the best leasing restrictions. This paper demonstrated tight, given the results enlightening and learn.
Keywords：Normal; Pessimistic; Mean distribution;