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Analysis of mathematical programming problems prior to applying the simplex algorithm

Brearley, A. L., Mitra, G. and Williams, H. Paul (1975) Analysis of mathematical programming problems prior to applying the simplex algorithm. Mathematical Programming, 8 (1). pp. 54-83. ISSN 0025-5610

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Identification Number: 10.1007/BF01580428


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 lsquounbounded solutionrsquo and lsquono feasible solutionrsquo 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.

Item Type: Article
Official URL:
Additional Information: © 1975 North-Holland Publishing Company
Divisions: Management
Subjects: Q Science > QA Mathematics
Sets: Research centres and groups > Management Science Group
Departments > Management
Date Deposited: 24 Jan 2011 09:53
Last Modified: 17 Feb 2021 10:52

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