线性规划模型无穷多最优解的一种检验方法

A Method to Test the Multiple Alternative Optimal Solutions for Linear Programming Model

针对线性规划模型有解时的两种情形(唯一最优解和无穷多最优解),提出了一种判别最优解是否唯一的方法.该方法通过一系列线性规划模型,可计算出所有决策变量的取值范围.根据这些取值范围,判断最优解是否唯一.进一步给出了一种策略,可确定原问题的一个唯一最优解.最后,数值实验验证了该方法的可行性和有效性.

If there exists at least a solution for the linear programming model,the solutions can usually be divided into the unique optimal solution and multiple alternative optimal solutions.In this paper,a method is presented to justify whether the solution for linear programming is unique or not.The ranges of all decision variables can be calculated to test the uniqueness of optimal solution using a series of linear programming models.A strategy is provided to determine the final solution,which can be proved to be unique and optimal solution for the original linear programming model.Finally,a numerical example is given to illustrate the feasibility and effectiveness of the proposed method.