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AuthorCôté, Jean-François
AuthorHaouari, Mohamed
AuthorIori, Manuel
Available date2023-01-23T08:18:13Z
Publication Date2021
Publication NameINFORMS Journal on Computing
ResourceScopus
URIhttp://dx.doi.org/10.1287/ijoc.2020.1014
URIhttp://hdl.handle.net/10576/38706
AbstractThe two-dimensional bin packing problem calls for packing a set of rectangular items into a minimal set of larger rectangular bins. Items must be packed with their edges parallel to the borders of the bins, cannot be rotated, and cannot overlap among them. The problem is of interest because it models many real-world applications, including production, warehouse management, and transportation. It is, unfortunately, very difficult, and instances with just 40 items are unsolved to proven optimality, despite many attempts, since the 1990s. In this paper, we solve the problem with a combinatorial Benders decomposition that is based on a simple model in which the two-dimensional items and bins are just represented by their areas, and infeasible packings are imposed by means of exponentially many no-good cuts. The basic decomposition scheme is quite naive, but we enrich it with a number of preprocessing techniques, valid inequalities, lower bounding methods, and enhanced algorithms to produce the strongest possible cuts. The resulting algorithm behaved very well on the benchmark sets of instances, improving on average on previous algorithms from the literature and solving for the first time a number of open instances. Summary of Contribution: We address the two-dimensional bin packing problem (2D-BPP), which calls for packing a set of rectangular items into a minimal set of larger rectangular bins. The 2D-BPP is a very difficult generalization of the standard one-dimensional bin packing problem, and it has been widely studied in the past because it models many real-world applications, including production, warehouse management, and transportation. We solve the 2D-BPP with a combinatorial Benders decomposition that is based on a model in which the two-dimensional items and bins are represented by their areas, and infeasible packings are imposed by means of exponentially many no-good cuts. The basic decomposition scheme is quite naive, but it is enriched with a number of preprocessing techniques, valid inequalities, lower bounding methods, and enhanced algorithms to produce the strongest possible cuts. The algorithm we developed has been extensively tested on the most well-known benchmark set from the literature, which contains 500 instances. It behaved very well, improving on average upon previous algorithms, and solving for the first time a number of open instances. We analyzed in detail several configurations before obtaining the best one and discussed several insights from this analysis in the manuscript. Copyright: 2021 INFORMS
SponsorFunding: J.-F. Côté acknowledges financial support from the Canadian Natural Sciences and Engi-neering Research Council [Grant 2015-04893]. M. Iori acknowledges financial support from the University of Modena and Reggio Emilia [Grants FAR 2017 Multiscale modeling in science, industry and society and FAR 2018 Analysis and optimization of healthcare and pharmaceutical logistic processes].
Languageen
PublisherINFORMS Inst.for Operations Res.and the Management Sciences
SubjectBenders decomposition
Combinatorial Benders cut
Exact algorithm
Two-dimensional bin packing problem
TitleCombinatorial benders decomposition for the two-dimensional bin packing problem
TypeArticle
Pagination963-978
Issue Number3
Volume Number33


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