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 XB = B−1b ≥ O and (or, in terms of the ...