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Relaxation Methods for Pure and Mixed Integer Programming Problems

Author

Listed:
  • G. Anthony Gorry

    (Massachusetts Institute of Technology)

  • Jeremy F. Shapiro

    (Massachusetts Institute of Technology)

  • Laurence A. Wolsey

    (Manchester Business School, Manchester, England)

Abstract

The usefulness of group theoretic methods in solving integer programming (IP) problems is extended by procedures for controlling the size of the groups. The main procedure given shows how an optimal linear programming basis can be altered to reduce the magnitude of its determinant thereby reducing the size of the group induced by the basis. An adaption of Benders' mixed IP algorithm is given which uses these methods. Some limited computational experience is given.

Suggested Citation

  • G. Anthony Gorry & Jeremy F. Shapiro & Laurence A. Wolsey, 1972. "Relaxation Methods for Pure and Mixed Integer Programming Problems," Management Science, INFORMS, vol. 18(5-Part-1), pages 229-239, January.
    • Handle: RePEc:inm:ormnsc:v:18:y:1972:i:5-part-1:p:229-239
    DOI: 10.1287/mnsc.18.5.229
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    Cited by:

    1. Gérard Cornuéjols & Milind Dawande, 1999. "A Class of Hard Small 0-1 Programs," INFORMS Journal on Computing, INFORMS, vol. 11(2), pages 205-210, May.

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