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Generalized Cuts in Diophantine Programming

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  • Fred Glover

    (University of California, Berkeley)

Abstract

In the generation of an additional constraint or cut for integer programming introduced by Ralph Gomory, there is a certain parameter whose value is customarily chosen so that one of the original variables has a zero coefficient in the cut-equation. In this paper we consider alternative values of the parameter and refer to any linear combination of the original source equation and this cut as a "generalised cut". Attention is then focused, as customary, on those cuts of this type for which the original variable has a zero coefficient. In particular, we show how to determine values for Gomory's parameter so that only a subset of the feasible solutions to the cuts used by Gomory's method of integer forms are feasible for the generalised cuts.

Suggested Citation

  • Fred Glover, 1966. "Generalized Cuts in Diophantine Programming," Management Science, INFORMS, vol. 13(3), pages 254-268, November.
  • Handle: RePEc:inm:ormnsc:v:13:y:1966:i:3:p:254-268
    DOI: 10.1287/mnsc.13.3.254
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    Cited by:

    1. Gérard Cornuéjols & Yanjun Li & Dieter Vandenbussche, 2003. "K-Cuts: A Variation of Gomory Mixed Integer Cuts from the LP Tableau," INFORMS Journal on Computing, INFORMS, vol. 15(4), pages 385-396, November.

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