Lifted cover facets of the 0-1 knapsack polytope with GUB constraints

Authors:
George L. Nemhauser;Pamela H. Vance
Affiliations:
School of Industrial and Systems Engineering, Georgia Institute of Technology, Atlanta, GA 30332-0205, USA;Department of Industrial Engineering, Auburn University, Auburn, AL 36849-5346, USA
Venue:
Operations Research Letters
Year:
1994

Citing 3
Cited 5

Easily computable facets of the knapsack polytope

Mathematics of Operations Research
The complexity of lifted inequalities for the knapsack problem

Discrete Applied Mathematics
Software section: MINTO, a mixed INTeger optimizer

Operations Research Letters

A polyhedral study on 0-1 knapsack problems with disjoint cardinality constraints: Strong valid inequalities by sequence-independent lifting

Discrete Optimization
A polyhedral study on 0-1 knapsack problems with disjoint cardinality constraints: Facet-defining inequalities by sequential lifting

Discrete Optimization
Higher-order cover cuts from zero-one knapsack constraints augmented by two-sided bounding inequalities

Discrete Optimization
An O(nlog n) procedure for identifying facets of the knapsack polytope

Operations Research Letters
Separation and Extension of Cover Inequalities for Conic Quadratic Knapsack Constraints with Generalized Upper Bounds

INFORMS Journal on Computing

Quantified Score

Hi-index	0.00

Visualization

Abstract

Facet-defining inequalities lifted from minimal covers are used as strong cutting planes in algorithms for solving 0-1 integer programming problems. In this paper we extend the result of Balas and Zemel by giving a set of inequalities that determines the lifting coefficients of facet-defining inequalities of the 0-1 knapsack polytope for any ordering of the variables to be lifted. We further generalize the result to obtain facet-defining inequalities for the 0-1 knapsack problem with generalized upper bound constraints.