Construction of the largest sensitivity region for general linear programs

摘要

This paper develops an alternative approach to post optimality analysis for general linear program models which provides the largest sensitivity region of any single or simultaneous change of right hand side of constraints and the coefficients of decision variables in the objective function. The goal is a theoretical unification of various types of sensitivity analyses, as well as advancement in the practical implementation of post optimality analysis. We extend our proposed approach in the construction of sensitivity region to maintain the degenerate vertex for models with degenerate optimal solution as well as maintaining the multiple solutions for the models with non-unique optimal solutions. As a by product, the paper resolves the paradoxical situation known as the more-for-less/less-for-more situations. The proposed method is based on the given optimal solution(s), therefore it is easy to understand, easy to implement, and provides useful information to the decision makers. The methodology and their computational algorithms are presented and discussed in the context of some illustrative numerical examples.