关于运输问题的几个注记

Some Notes on Transportation Problem

摘要: 产销平衡的运输问题是《运筹学》课程的重要内容，可采用表上作业法进行求解。在课堂讲解完基本方法后，提出三个问题供学生思考与讨论：1) 利用位势法求解非基变量的检验数时，位势不唯一，为何检验数是唯一的？2) 如果目标函数是一个极大化问题，相应的表上作业法该如何修改？3) 如果用Lagrange乘子法对产销平衡的运输问题进行求解，则Lagrange乘子与位势之间的关系如何？这些问题的讨论，使学生学会思考，融会贯通。

Abstract: Transportation problem with balanced production and marketing is an important part of opera-tions research course. This kind of problem can be solved by table dispatching method on a transportation simplex tableau. After explaining the basic methods in class, three questions are put forward for students to think and discuss. 1) When using the potential method to solve the test number of nonbasic variables, the potentials are not unique. Why is the test number unique? 2) How to modify the table dispatching method on the transportation simplex tableau when we want to maximize the objective function of transportation problem? 3) If we use the Lagrange multiplier method to solve this problem, what is the relationship between Lagrange multiplier and potentials? Through the discussion of these problems, students can learn to think and understand.