Global Pricing and Feasible Directions in Linear Programming

Abstract

We present a linear programming approach based on a global pricing function and feasible directions. It is embedded in the framework of the simplex method through the use of external columns, which are combinations of original columns. The global pricing function is composed by the pricing function of the simplex method, which captures the objective’s behaviour over the cone of feasible directions, and an exterior penalty function that captures information about the topology of the entire feasible set. Given a non-degenerate basic feasible solution, a global pricing problem yields a non-edge improving feasible direction, which is translated into an external column that enters the basis.

Preliminary computational results indicate that the global pricing principle may have a significant advantage over the ordinary pricing of the simplex method. Further, our new approach allows for several computational strategies, which need to be investigated in future research in order to explore its full potential.