Abstract: The right-hand side in linear programming is changed to solve the more-for-less paradox in current researches, while this paper points out and verifies that the reason why the paradox occurs is the unreasonable collocation of the technological coefficient matrix, the objective function coefficient and the right-hand side. First, the original-dual model is constructed to judge whether there exists the paradox. Then, through transforming the paradox problem into inverse optimal value problem, we construct two models to solve the paradox by changing the objective function coefficient and the technological coefficient matrix. Finally, the inverse optimal value method is provided to judge and solve the paradox. The advantages and economic significance of the method is described next. It is found that the method exhibits excellent face validity for a numerical example.

Key words: operational research, original-dual model, inverse optimal value method, more-for-less paradox

摘要： 现有研究通过调整线性规划模型的右端项来消除“多反而少”悖论,而该文提出并验证了悖论是由技术系数矩阵、目标函数系数以及右端项三者的不合理搭配造成的。首先,通过建立原-对偶模型来判断悖论现象存在与否;然后,将悖论问题转换成逆最优值问题进行解决,构建了通过调整目标函数系数以及技术系数矩阵来消除悖论的模型;最后,提出了判断并解决悖论的逆最优值解法,阐述了其优势与经济意义,并通过数值算例验证其有效性。

关键词: 运筹学, 原-对偶模型, 逆最优值解法, “多反而少”悖论