A Parallel Implementation of the Revised Simplex Algorithm Using OpenMP: Some Preliminary Results

Linear Programming (LP) is a significant research area in the field of operations research. The simplex algorithm is the most widely used method for solving Linear Programming problems (LPs). The aim of this paper is to present a parallel implementation of the revised simplex algorithm. Our parallel implementation focuses on the reduction of the time taken to perform the basis inverse, due to the fact that the total computational effort of an iteration of simplex type algorithms is dominated by this computation. This inverse does not have to be computed from scratch at any iteration. In this paper, we compute the basis inverse with two well-known updating schemes: (1) The Product Form of the Inverse (PFI) and (2) A Modification of the Product Form of the Inverse (MPFI); and incorporate them with revised simplex algorithm. Apart from the parallel implementation, this paper presents a computational study that shows the speedup among the serial and the parallel implementations in large-scale LPs. Computational results with a set of benchmark problems from Netlib, including some infeasible ones, are also presented. The parallelism is achieved using OpenMP in a shared memory multiprocessor architecture.

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