校园卡充值点最优位置的数学模型研究

选址问题目前学术界已有较多的研究成果,但大多数是将总费用作为目标函数,一般要求事先给出网络结点的位置坐标,且无需考虑结点间的最短路程,旨在确定新的地理几何中心。而对已有网络,在不改变原有路径及各结点位置的条件下,以总路程最小为目标函数,在现有网络结点中寻找其中某些结点的最优位置却是一个新的研究课题。本文以某高校校园卡充值点为例,将校园示意图转化为赋权连通图,求得该连通图的邻接矩阵,利用Floyd算法及图论软件包构造一个最短路径矩阵,得到一个赋权完全图,利用穷举法或混合整数规划法及数学软件求解,得到各学院、楼栋、学生宿舍区到三个校园卡充值点的最短总路程及三个校园卡充值点的最优位置。

Research on the Mathematical Model of Determining the Optimal Location to Fill Value for Campus Card

There are many researches on location problem in academic literature,most of which choose total cost is as objective function,generally require that the coordinate locations of network nodes are given in advance,and do not consider the shortest dis-tances between nodes,so as to determine new geographic geometric center.However,it is a new research subject to find some nodes as optimal location in the existed network,on the condition that minimizing total distance is chosen as goal,without changing the loca-tions of original paths nodes.In this paper,as a case of p-hub location problem,determining the optimal location to fill value for campus card,is solved by means of first transforming campus schema into a connected graph with weight in any edge,hence getting the adjacency matrix of the connected graph,next using Floyd algorithm and graph theory software package to construct a shortest path matrix and result in a weighted complete graph,then using enumeration method or mixed integer programming method as well as mathematical software to find three optimal locations to fill value for campus card,and the minimal total distance from the various col-leges,buildings,student dormitory areas to the three optimal campus-card-fill-value locations.