Computational Aspects of the Simplex Method: Revised Simplex Algorithm; Bounded Variables

Abstract

Up to this point, we have introduced linear programming and its method of solution, the simplex algorithm, in a purely theoretical fashion. We paid no attention to the effectiveness of the algorithm nor to the fact that one has to face special problems (and in particular, numerical ones) when the algorithm is implemented on a computer. In this chapter, we give a brief account of the efficiency of the simplex algorithm (both from a theoretical and a practical standpoint). Then we show how harmful rounding errors may be for a practical applicatione In the third section, we describe the “revised simplex algorithm,” which has essentially been designed for computer implementation, Finally, we describe how bounded variables can be taken care of in a way that reduces computation as much as possible.