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线性规划运输问题中的图上作业法是我国科技工作者独创的一种优秀方法。利用此法,可以很方便地求出支路、单圈和多圈等运输问题的最优解。那么,对于这些问题,究竟只有唯一解,还是有多解?若有多解(即多个最优解,下同),条件是什么?本文即在于解决这些重要问题:①在支路问题中,若存在两个以上的发点,对两个以上的每个收点,都可以产生重流;②在有圈的问题中,若求出任一最优解后,外(或内)圈流向长度等于全圈长之半,则①、②均产生多解。本文分支路、单圈与综合问题三种情况,进行讨论。
The map-based method in the transportation problem of linear programming is an excellent method invented by our scientists and technicians. Using this method, we can easily find the optimal solution to the transportation problems such as branch, single lap and multi lap. So, for these problems, what is the only solution or how many solutions? If there are multiple solutions (ie multiple optimal solutions, the same below), what are the conditions? This article is to solve these important problems: ① in the branch problem , If there are more than two hair points, for each of two or more points, can produce heavy flow; ② in the problem with a circle, if any of the optimal solution, the outer (or inner) ring flow Length equal to half the total length of the circle, then ①, ② have more solutions. This article branch road, single lap and three kinds of comprehensive problems, for discussion.