On the complexity of surrogate and group relaxation for integer linear programs

Dokka, Trivikram and Letchford, Adam and Mansoor, Hasan (2021) On the complexity of surrogate and group relaxation for integer linear programs. Operations Research Letters, 49 (4). pp. 530-534. ISSN 0167-6377

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Abstract

Surrogate and group relaxation have been used to compute bounds for various integer linear programming problems. We prove that (a) when only inequalities are surrogated, the surrogate dual is NP-hard, but solvable in pseudo-polynomial time under certain conditions; (b) when equations are surrogated, the surrogate dual exhibits unusual complexity behaviour; (c) the group relaxation is NP-hard for the integer and 0-1 knapsack problems, and strongly NP-hard for the set packing problem.

Item Type:

Journal Article

Journal or Publication Title:

Operations Research Letters

Additional Information:

This is the author’s version of a work that was accepted for publication in Operations Research Letters. Changes resulting from the publishing process, such as peer review, editing, corrections, structural formatting, and other quality control mechanisms may not be reflected in this document. Changes may have been made to this work since it was submitted for publication. A definitive version was subsequently published in Operations Research Letters, vol. 49, issue 4, 2021 DOI:10.1016/j.orl.2021.05.011

Uncontrolled Keywords:

/dk/atira/pure/subjectarea/asjc/1800/1803

Subjects:

?? integer programmingsurrogate relaxationgroup relaxationmanagement science and operations researchsoftwareapplied mathematicsindustrial and manufacturing engineering ??

Departments:

Lancaster University Management School > Management Science

ID Code:

155341

Deposited By:

ep_importer_pure

Deposited On:

26 May 2021 09:40

Refereed?:

Yes

Published?:

Published

Last Modified:

17 Sep 2024 10:41

URI:

https://eprints.lancs.ac.uk/id/eprint/155341