Analysing conflicts in large optimization problems is an intricate and difficult task. In this paper we present a tool for infeasible LP, to guide the decision maker towards an adequate strategy for dealing with the infeasibility. We propose a mathematical formulation for the ranking of the optimal values and solutions among all feasible subsets of constraints, that is, to find (feasible) clusters of constraints that yield the K-best optimal values (K-Best Feasible Clusters). This, practical and easily interpretable information can be crucial for deciding which constraints to drop from the original infeasible model. Even for small problems this analysis cannot be conducted manually as a simple two-dimensional problem shows. Exploiting the structure of the formulation, an iterative procedure is proposed to solve the problem.

分析大型优化问题中的冲突是一项复杂而艰巨的任务。在本文中，我们介绍了不可行LP的工具，以指导决策者制定适当的策略来应对不可行。我们提出了一种数学公式，用于对所有可行约束子集之间的最优值和解决方案进行排名，也就是说，找到产生K个最佳最优值的约束（可行）簇（K个最佳可行簇）。对于决定从原始的不可行模型中删除哪些约束，这种实用且易于解释的信息至关重要。即使是小问题，也无法像一个简单的二维问题所示手动进行分析。利用配方的结构，提出了一种迭代程序来解决该问题。