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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:
12 Feb 2024 00:40
URI:
https://eprints.lancs.ac.uk/id/eprint/155341