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A Modified Benders' Partitioning Algorithm for Mixed Integer Programming

Author

Listed:
  • Dale McDaniel

    (California State University at Northridge)

  • Mike Devine

    (University of Oklahoma)

Abstract

As applied to mixed-integer programming, Benders' original work made two primary contributions: (1) development of a "pure integer" problem (Problem P) that is equivalent to the original mixed-integer problem, and (2) a relaxation algorithm for solving Problem P that works iteratively on an LP problem and a "pure integer" problem. In this paper a modified algorithm for solving Problem P is proposed, in which the solution of a sequence of integer programs is replaced by the solution of a sequence of linear programs plus some (hopefully few) integer programs. The modified algorithm will still allow for taking advantage of any special structures (e.g., an LP subproblem that is a "network problem") just as in Benders' original algorithm. The modified Benders' algorithm is explained and limited computational results are given.

Suggested Citation

  • Dale McDaniel & Mike Devine, 1977. "A Modified Benders' Partitioning Algorithm for Mixed Integer Programming," Management Science, INFORMS, vol. 24(3), pages 312-319, November.
    • Handle: RePEc:inm:ormnsc:v:24:y:1977:i:3:p:312-319
    DOI: 10.1287/mnsc.24.3.312
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