PARALLEL-VECTOR PROCESSING FOR LINEAR-PROGRAMMING

The basic Simplex algorithm for solving linear programming problems is re-examined. Computational steps which can be done in parallel are identified. Both parallel and vector speed are incorporated in the Simplex procedure. Special solution strategies are used to take further advantage of the cases where artificial and unrestricted (in sign) variables need to be introduced. Using FORCE (FORtran with Concurrent Extension) language, the developed parallel Simplex subroutine can be ported to seven different parallel and high performance computers. Small, medium and large scale numerical examples are used to demonstrate the effectiveness of the proposed Simplex method. Speed-up factors of up to 3.6 (using four Cray-2 processors) and 14.5 (using 15 Sequent processors) were obtained in this study.