DVD在线租赁的数学模型

The Mathematical Model of On-line DVD Leasing

为解决问题(1),使得所需购买的DVD数量达到最小,从DVD本身入手,分析其不同的利用率,满足一定的约束条件,然后用目标规划建立数学模型,利用相关的数学软件(lingo)求出最优解;为解决问题(2),本文从客户入手,通过客户的偏爱程度得到他们对不同DVD的满意程度,并进而得到一个总体的满意矩阵,利用0—1规划建立相应的数学模型,代入matlab的linprog函数可求解;问题(3)的目标函数有两个,DVD数量最小和客户满意度最大.正因为如此,本文建立了一个双目标规划的模型,给出问题(3)的解法.

On-line DVD leasing is profitable for both company and users. As to the company, emphasis is laid on the optimal quantity of DVD and the balance between users＇ satisfaction and the company＇ s profit. For problem one, we analyze the different utility ratio of DVDs, then set up the model using the method of objective programming. The software Lingo is used to get the results. For problem two, we obtain a wholly satisfactory matrix from the users＇ preference on various DVD, establish our model with 0 -1 programming, and get our results by Matlab. Problem three concerns two objective functions, the minimum of DVD＇s quantity and the maximum of users＇ satisfaction, which is an extension of problem one and two, by using bi-objective programming. The model is built and all the solutions have been out.