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Mathematical Programming

, Volume 8, Issue 1, pp 54–83 | Cite as

Analysis of mathematical programming problems prior to applying the simplex algorithm

  • A. L. Brearley
  • G. Mitra
  • H. P. Williams
Article

Abstract

Large practical linear and integer programming problems are not always presented in a form which is the most compact representation of the problem. Such problems are likely to posses generalized upper bound(GUB) and related structures which may be exploited by algorithms designed to solve them efficiently.

The steps of an algorithm which by repeated application reduces the rows, columns, and bounds in a problem matrix and leads to the freeing of some variables are first presented. The ‘unbounded solution’ and ‘no feasible solution’ conditions may also be detected by this. Computational results of applying this algorithm are presented and discussed.

An algorithm to detect structure is then described. This algorithm identifies sets of variables and the corresponding constraint relationships so that the total number of GUB-type constraints is maximized. Comparisons of computational results of applying different heuristics in this algorithm are presented and discussed.

Keywords

Feasible Solution Mathematical Method Programming Problem Computational Result Mathematical Programming 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© The Mathematical Programming Society 1975

Authors and Affiliations

  • A. L. Brearley
    • 1
  • G. Mitra
    • 2
    • 3
  • H. P. Williams
    • 4
  1. 1.School of Industrial and Business StudiesUniversity of WarwickCoventryUK
  2. 2.Dept. of Statistics & Operational ResearchBrunel UniversityMiddlesexUK
  3. 3.UNICOM ConsultantsU.K. Ltd.UK
  4. 4.Dept. of Operational ResearchUniversity of SussexFalmer, BrightonUK

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