Linear Programming and Resource Allocation Modeling

10Parametric Programming

10.1 Introduction

In Chapter 8 we considered an assortment of post‐optimality problems involving discrete changes in only selected components of the matrices Therein emphasis was placed on the extent to which a given problem may be modified without breaching its feasibility or optimality. We now wish to extend this sensitivity analysis a bit further to what is called parametric analysis. That is, instead of just determining the amount by which a few individual components of the aforementioned matrices may be altered in some particular way before the feasibility or optimality of the current solution is violated, let us generate a sequence of basic solutions that, in turn, become optimal, one after the other, as all of the components of b, or a column of vary continuously in some prescribed direction. In this regard, the following parametric analysis will involve a marriage between sensitivity analysis and simplex pivoting.

10.2 Parametric Analysis

If we seek to

then an optimal basic feasible solution emerges if X_B = B⁻¹b ≥ O and (or, in terms of the ...