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

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.