J.A.J. Hall and K.I.M. McKinnon
This paper describes a asynchronous variant of the revised simplex method which is suitable for parallel implementation on MIMD computers with fast inter-processor communication. The method overlaps simplex iterations on different processors. Candidates to enter the basis are tentatively selected using reduced costs which may be out of date. Later the up-to-date reduced costs of the tentative candidates are calculated and candidates are either discarded or accepted to enter the basis. The implementation of this algorithm on a Cray T3D is described and results demonstrating significant speed-up are presented.
Key words: Linear programming, revised simplex method, parallelism, Cray T3D.