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1、DVD在线租赁的数学模型 摘 要 在科学技术高速发展的今天，特别是因特网建立后,网络更是成为我们传播信息的主渠道以及1种莫大的经济资源。许多网站利用其强大的资源和知名度，面向其会员群提供日益专业化和便捷化的服务，如：DVD在线租赁。 本文解决的是1个DVD在线租赁问题，模型主要涉及到DVD的数量，1个月中租用的次数以及会员对各DVD的满意度。模型中运用了0-1型整数规划，并采用LINGO数学软件来求解模型。在处理第1问时，对于1个月满足50%的情况，分析完后用了1个简易包络图来描述。并依照分析建立了1个以调查表
2、中各DVD愿意观看的人数为参数的数学模型。在第2问的模型建立的时候，本文是用会员们的在线定单上所显示出来的意愿顺序数的倒数，来表示会员对该DVD的满意度。以满意度最大为目标函数。同时根据题目列出其约束条件，运用LINGO 8.0编程、并计算得出了所有DVD的分配情况（附录1）。在解决问题3的时候，也以满意度最大为目标函数。改变3个约束条件，也同样运用LINGO 8.0编程、并计算得出分配情况（附录2），在本文中运用了表格的形式表述出了各种DVD的购买量。关键字： DVD在线租赁；0-1型整数规划；LINGO数学软件；满意度Abstract Today science and tech
3、nology have been developing in high speed. The network is becomes us to disseminate the information main channel as well as one kind of greatest economical resources. Many websites use its formidable resources and well-knownness, provides the daily specialization and the convenient service face its
4、member group, for example: DVD on-line rents. This article solves is DVD on-line rents the question, the model mainly involves to the DVD quantity, in a month rents number of times as well as member to each DVD degree of satisfaction. In the model has utilized 0-1 integer plan, and uses LINGO mathem
5、atics software to solve the model. In processes when asks, satisfies 50% situation regarding a month, after analyzed uses a simple enveloping chart to describe. And deferred to the analysis to establish the population which each DVD was willing to watch by the examination table in for the parameter
6、mathematical model. In second asked the model establishes, this article is demonstrated with the members on-line order form in the wish order figure reciprocal, expresses the member to this DVD degree of satisfaction. Take the degree of satisfaction most greatly as the objective function. Meanwhile
7、lists its restraint condition according to the topic, using the LINGO 8.0 programming, and the computation has obtained all DVD assignment situation (appendix one). Is solving question three times, also take degree of satisfaction most greatly as objective function. Changes three restraints conditio
8、ns, also similarly using the LINGO 8.0 programming, and the computation obtains the assignment situation (appendix two), utilized the form form in this article to indicate each kind of DVD purchase quantity. Keywords：DVD on-line rents；0-1 integer plan；LINGO mathematics software；Degree of satisfaction
