Positive Sensitivity Analysis In Linear Programming With Bounded Variables

The present paper discusses positive sensitivity analysis (PSA) in linear programming with bounded variables. Positive sensitivity analysis is a sensitivity analysis method for linear programming that finds the range of perturbations within which the components of a given optimal solution which are strictly between their bounds remain strictly between bounds and which are at their lower and upper bounds remain at lower and upper bounds respectively. Its main advantage is that it is applicable to both an optimal basic and non-basic optimal solution. In this paper, 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. We also discuss the relationship between PSA and sensitivity analysis using optimal basis and the relationship between PSA and sensitivity analysis using the optimal partition. We show that the sensitivity analysis using optimal partition is a special case of PSA. In order to study these relationships and the properties, some results on duality have been discussed and existence of strictly complementary solution has been established for linear programming with bounded variables.