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The efficient solution of large-scale linear programming problems—some algorithmic techniques and computational results

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Abstract

First, this paper presents the results of experiments with algorithmic techniques for efficiently solving medium and large scale linear and mixed integer programming problems. The techniques presented here are either original or recent.

The solution of a great number of problems has shown that efficient problem solving requires automatic adaptation of algorithmic techniques upon problem characteristics. We show when a given technique should be used for a particular problem.

The last part of this paper describes an attempt to provide a powerful mathematical programming language, allowing an easy programming of specific studies on medium-size models such as the recursive use of LP or the build-up of algorithms based on the simplex method.

All these features have been implemented in the IBM Mathematical Programming System, MPSX/370, and its feature MIP/370. Extensive numerical results and comparisons on real-life problems are provided and commented upon.

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Authors and Affiliations

  1. IBM France, Paris, France

    M. Benichou, J. M. Gauthier, G. Hentges & G. Ribiere

Authors
  1. M. Benichou
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  2. J. M. Gauthier
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  3. G. Hentges
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  4. G. Ribiere
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Benichou, M., Gauthier, J.M., Hentges, G. et al. The efficient solution of large-scale linear programming problems—some algorithmic techniques and computational results. Mathematical Programming 13, 280–322 (1977). https://doi.org/10.1007/BF01584344

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  • DOI: https://doi.org/10.1007/BF01584344

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