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A Generated Cut for Primal Integer Programming

Author

Listed:
  • Larry R. Arnold

    (Tulane University, New Orleans, Louisiana)

  • Mandell Bellmore

    (Block, McGibony and Associates, Silver Spring, Maryland)

Abstract

This paper develops a new cutting plane for primal integer programming. This cut, when it exists and is vised as pivot row, has the property that the minimum of the simplex evaluators of the next tableau is strictly larger (by an integer) than the minimum for the current tableau. The paper gives a sufficient condition in the form of a linear program for the existence of such a cut, and proposes an algorithm for generating such cuts. It also presents two additional sufficient conditions. The process of cut generation is then imbedded into a convergent primal algorithm to be used in an attempt to overcome the proof-of-optimality problem experienced with the primal algorithm.

Suggested Citation

  • Larry R. Arnold & Mandell Bellmore, 1974. "A Generated Cut for Primal Integer Programming," Operations Research, INFORMS, vol. 22(1), pages 137-143, February.
    • Handle: RePEc:inm:oropre:v:22:y:1974:i:1:p:137-143
    DOI: 10.1287/opre.22.1.137
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    Cited by:

    1. Santanu S. Dey & Jean-Philippe Richard, 2009. "Linear-Programming-Based Lifting and Its Application to Primal Cutting-Plane Algorithms," INFORMS Journal on Computing, INFORMS, vol. 21(1), pages 137-150, February.

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