运输问题理论体系的改进

On the Improvement of the Theoretical System for the Transportation Problem

本文根据运输问题的特殊性,直接利用运输表给出了它的三个基本概念和两个基本定理,并以此为基础导出了其理论与算法上的一系列重要结论,从而改进和完善了运输问题的理论体系。

From the theoretical point of view, three basic concepts, that is, the loop, process of deleting points and solving process on the tableau, are defined by means of the transportation tableau. Two basic theorems are proved by the simple properties of the concepts. It is shown that, with the three concepts and two theorems as the direct theoretical basis for the transportation problem(TP),a series of necessary theorems and conclusions concerning TP and its special algorithm can be easily obtained, and many lemmas in the conventional theoretical system of TP are found unnecessary. The principle of the tableau algorithm is made perceivable. In particular, the basic feasibility of all initially feasible solution algorithms, which is difficult to prove in the conventional system, is easily deduced from the basic theorem 1.As a result, a new theoretical system for TP is proposed, which is relatively independent of the general linear programming in theory, and is simpler than the conventional one.