单纯形法求解目标规划问题教学中的一个注记

A note on the teaching of the simplex algorithm for the goal programming

建立目标规划的数学模型时,对于偏差变量dk-,dk+,总是要求dk-×dk+=0.这个约束条件是非线性的,但是并没有对单纯形法的求解造成影响.在课程教学中,学生很容易对此产生疑惑,而大部分教材中并没有对这个问题进行阐述.从单纯形法的基本求解过程出发,对此进行了分析,得出在单纯形法迭代时dk-*dk+=0总是成立的结论.

There always bed^-k×d^＋k = 0 for the deviation variable d^-k,d^＋kwhen the goal programming model is built. The condition is nonlinear, but it do not affect the solution of the goal programming by the simplex algorithm. The students may be confused about this, but most books do not explain this clearly. Based on the process of the simplex algorithm, obtained a conclusion that d^-k×d^＋k = 0 is always satisfied during the process of the simplex algorithm.