Abstract

We develop a single artificial variable technique to initialize the primal support method for solving linear programs with bounded variables. We first recall the full artificial basis technique, then we will present the proposed algorithm. In order to study the performances of the suggested algorithm, an implementation under the MATLAB programming language has been developed. Finally, we carry out an experimental study about CPU time and iterations number on a large set of the NETLIB test problems. These test problems are practical linear programs modelling various real‐life problems arising from several fields such as oil refinery, audit staff scheduling, airline scheduling, industrial production and allocation, image restoration, multisector economic planning, and data fitting. It has been shown that our approach is competitive with our implementation of the primal simplex method and the primal simplex algorithm implemented in the known open‐source LP solver LP_SOLVE.

Highlights

  • IntroductionLinear programming is a mathematical discipline which deals with solving the problem of optimizing a linear function over a domain delimited by a set of linear equations or inequations

  • We develop a single artificial variable technique to initialize the primal support method for solving linear programs with bounded variables

  • Linear programming is a mathematical discipline which deals with solving the problem of optimizing a linear function over a domain delimited by a set of linear equations or inequations

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Summary

Introduction

Linear programming is a mathematical discipline which deals with solving the problem of optimizing a linear function over a domain delimited by a set of linear equations or inequations. LP is considered as the most important technique in operations research. It is widely used in practice, and most of optimization techniques are based on LP ones. That is why many researchers have given a great interest on finding efficient methods to solve LP problems. Being inspired from the work of Fourier on linear inequalities, Dantzig 1947, 3 developed the simplex method which is Mathematical Problems in Engineering known to be very efficient for solving practical linear programs. In 1972, Klee and Minty 4 have found an example where the simplex method takes an exponential time to solve it

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