松约束运输问题模型与算法研究

运输问题存在着所谓的"多反而少"悖论现象,本文用运输问题的松约束模型,说明了运输问题产生悖论现象的原因,从而拓宽了运输问题的应用范围,增加了运输问题的适应性,本文给出的运输问题的松约束模型的表上作业算法,运算简单,能彻底解决了运输问题的"多反而少"悖论现象,用本文所介绍的算法解一些问题,得到了更省的调运方案.

A NEW MODEL AND SOLUTION FOR TRANSPORTATION PROBLEM

Transportation problem has many real-world applications, it can be solved by linear programming model, but in most time the model exists more-for-less paradox, this paper considers the reasons for the paradox and search the way to eliminate the phenomenon. First this paper formulates a loose constrained linear programming model for the transportation problem, and gives the definition of the paradox which exists in it, some preliminary notions and one example is also given. Then it gives a table-based algorithm for the loose constrained model, the steps of the algorithm and example will follow. The examples show that: (1) It is not a contradictory that transportation problem exists more-for-less paradox. (2) The loose constrained model is better used in practice for its less total cost. (3) The algorithm is easy to calculate, to study and highly speed to convergence. Finally, comparied with other ways it shows that the loose constrained model can thoroughly eliminate the paradox.