Abstract

This paper presents a study of the polytope defined by the minimizing form of the binary knapsack inequality, which is a greater-than-or-equal-to constraint, augmented by disjoint generalized upper bound constraints. A set of valid inequalities, called α-cover inequalities, is characterized and dominance relationships among them are established. Both sequential and sequence-independent lifting procedures are presented to tighten an α-cover inequality that is not facet defining. Computational results aimed at evaluating the strength of the non-dominated, sequentially, and sequence-independent lifted α-cover inequalities are provided.

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