Implementing the simplex method for the Optimization Subroutine Library

In this paper we describe the simplex algorithm and briefly discuss the interaction of the detailed implementation of the algorithm with the changes in computer hardware over the last 30 years. Then we give one example of the design changes needed to implement the method efficiently for the IBM 3090™ vector architecture. For the later RISC System/6000™ implementation, it was necessary to rethink this yet again. Finally we discuss the issue of robustness and the steps that were taken to give maximum reliability in the simplex algorithm in the IBM Optimization Subroutine Library.