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Technical Note—Surrogate Constraints and the Strength of Bounds Derived from 0-1 Benders' Partitioning Procedures

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  • Ronald L. Rardin

    (Georgia Institute of Technology, Atlanta, Georgia)

  • V. E. Unger

    (Georgia Institute of Technology, Atlanta, Georgia)

Abstract

One commonly employed branch-and-bound approach to 0-1 mixed-integer programming problems is to use bounds obtained from the Benders' partitioning of the problem as a device to restrict the enumeration. We investigate the strength of such bounds through the development of a Geoffrion-type strongest surrogate constraint for the Benders' problems. We show that such a surrogate constraint can be developed for the complete Benders' integer problem without explicit enumeration of any of the extreme-point constraints. The bound obtained from this surrogate constraint is then shown to be as strong as that obtained from any of the more common Benders-based approaches, but yet exactly equal to the bound obtained from the linear relaxation of the original mixed-integer program.

Suggested Citation

  • Ronald L. Rardin & V. E. Unger, 1976. "Technical Note—Surrogate Constraints and the Strength of Bounds Derived from 0-1 Benders' Partitioning Procedures," Operations Research, INFORMS, vol. 24(6), pages 1169-1175, December.
    • Handle: RePEc:inm:oropre:v:24:y:1976:i:6:p:1169-1175
    DOI: 10.1287/opre.24.6.1169
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    Cited by:

    1. H. D. Sherali & R. S. Krishnamurthy & F. A. Al-Khayyal, 1998. "Enumeration Approach for Linear Complementarity Problems Based on a Reformulation-Linearization Technique," Journal of Optimization Theory and Applications, Springer, vol. 99(2), pages 481-507, November.

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