敏感性分析中退化情况与多重最优解的判别

The Discrimination of Degradation and Multiple Optimal Solutions in Sensitivity Analysis

摘要: 计算机工具求解线性规划模型的结果对应实际问题中多种解决方案，其中退化解和多重最优解对决策者进行合理决策是至关重要的。但在计算机工具所得敏感性报告中，无法直观判断线性规划模型是否存在退化解和多重最优解的情况。针对该问题，以Excel敏感性报告为例，结合单纯形法定理和对偶理论，能够得出判别敏感性分析中线性规划问题退化情况与多重最优解的一般方法，即定义法、个数相等法判定所得解是否存在退化情况，能够解决多重最优解判别的对偶关系法和递减成本法，以及判别退化解与多重最优解均适用的方法：综合法–退化解与多重解的关系法。

Abstract: The results of solving the linear programming model by computer tools correspond to many solutions in practical problems. Among them, the solution and multiple optimal solutions are crucial for decision makers to make reasonable decisions. However, in the sensitivity report obtained by computer tools, it is impossible to directly judge whether the linear programming model has degeneracy and multiple optimal solutions. Aiming at this problem, taking Excel sensitivity report as an example, combined with the simple method theorem and duality theory, a general method for judging the degradation of linear programming problems and multiple optimal solutions in sensitivity analysis can be obtained, that is, the definition method and the equal number method are used to determine whether the obtained solution has degradation. The dual relationship method and the decreasing cost method that can solve the discrimination of multiple optimal solutions, as well as the method that discriminates the regression solution and the multiple optimal solutions are applicable: The comprehensive method-the relationship method of regression solution and multiple solutions.