Positive sensitivity analysis in linear programming

Positive sensitivity analysis (PSA) is a sensitivity analysis method for linear programming that finds the range of perturbations within which positive value components of a given optimal solution remain positive. Its main advantage is that it is applicable to both an optimal basic and nonbasic optimal solution. The first purpose of this paper is to present some properties of PSA that are useful for establishing the relationship between PSA and sensitivity analysis using optimal bases, and between PSA and sensitivity analysis using the optimal partition. We examine how the range of PSA varies according to the optimal solution used for PSA, and discuss the relationship between the ranges of PSA using different optimal solutions. The second purpose is to clarify the relationship between PSA and sensitivity analysis using an optimal basis, and the relationship between PSA and sensitivity analysis using the optimal partition. We show that sensitivity analysis using the optimal partition is a special case of PSA, and its properties can be derived from the properties of PSA. The comparison among the three sensitivity analysis methods will lead to a better understanding of the difference among sensitivity analysis methods.