Implementation of a steepest-edge primal - dualsimplex method for network linear programs

Abstract

A primal - dual simplex variant is presented that incrementally builds up the optimal LPbasis matrix. For network LPs, the incremental primal - dual algorithm can adopt steepest-edgedirections of movement utilizing standard graph data structures without additionalcomputational overhead. Computational results indicate the resulting implementation isuniformly superior to other direction movement schemes, and achieves order of magnitudespeedups versus a primal network simplex code on medium size NETGEN problems. Thesespeedups carry over to the generalized network problem domain as well. Some comparisonsare also made against the relaxation method on NETGEN uncapacitated transportation andtransshipment problems.