【摘要】 管理部门通常要选择适当的地方建造粮库 ,所需服务范围已知 ,各部门运输量给定 .需为他们选择合适的地方 ,使总运费最少 .某乡的九个村 (A,B,C,… ,H,I)如图 1 ,各村距离给出 ,并标明它们各自上缴公粮数 .管理部门希望在村内或道路上建立一个粮库 ,最大限度地减少运输费用 .问题的解法有几种方案 ,对于本题来说 ,穷举搜索法是可行的 .另外 ,我们提出一种分析求解法 ,可找到优化解 .它利用图论的基础知识先求出图 1的各顶点间的最小路径 ,再进一步求出图的绝对中心 (即粮库的地址 ) ,其中的有关计算利用了 C++语言程序 .在此基础上 ,还可对问题的参数作更精细的分析 .概括地说 ,穷举搜索法对于简单的区域是行之有效的 .但对于更加一般化的问题 ,利用计算机可快捷准确地得到答案 .通过建立模型 ,我们得到下面两个结论 :(1 )我们找到最优解是 E点 ,其总运费为 1 2 775元 .(2 )模型具有广泛性 ,对于更一般的区域 ,可利用计算机总可以求出最优解 .更多还原

【Abstract】 This article aims to help the administration to select the optimum position to construct the grain depot with the requirement of the minimum total transportation expenses. There are nine villages, and the position, distance and the amount of grain they need to turn in are shown in Fig 1. The administration needs to set a grain depot in the village or on the road. In order to reduce the freight, we can use both the Exhaustive Search and the Absolute Center Search (i.e., to find out the Shortest Paths of Fig 1 first and then work out its Absolute Center which is the answer). The latter one uses a C++ Program to do the computation. Although the Exhaustive Search is effective for simple areas, the Absolute Center Search is faster and more accurate when more general and complicated problems are concerned. AFter constructing the model, we have drawn to two conclusions:\;(1) The Optimum position of the grain depot is point E , the total transportation expenses is 12775 yuan.\;(2) This model is a general one, we can always find out the optimum solution with the aid of computer.更多还原