Linear Programming and Resource Allocation Modeling

8Sensitivity Analysis

8.1 Introduction

Throughout this chapter we shall invoke the assumption that we have already obtained an optimal basic feasible solution to a linear programming problem in standard form, i.e. to a problem of the form

We then seek to employ the information contained within the optimal simplex matrix to gain some insight into the solution of a variety of linear programming problems that are essentially slight modifications of the original one. Specifically, we shall undertake a sensitivity analysis of the initial linear programming problem, i.e. this sort of post‐optimality analysis involves the introduction of discrete changes in any of the components of the matrices , in which case the values of c_j, b_i, or a_ij, i = 1, …, m; j = 1, …, n − m, respectively, are altered (increased or decreased) in order to determine the extent to which the original problem may be modified without violating the feasibility or optimality of the original solution. (It must be remembered, however, that any change in, say, the objective function coefficient c_k is a ceteris paribus change, e.g. all other c_j’s are held constant. This type of change also holds for the components of )

8.2 Sensitivity Analysis

Turning again to our linear programming problem in standard form, let ...