Geodesic
A theoretical and experimental study of fast lower bounds for the two-dimensional bin packing problem
RAIRO - Operations Research - Recherche Opérationnelle, Tome 52 (2018) no. 2, pp. 391-414

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We address the two-dimensional bin packing problem with fixed orientation. This problem requires packing a set of small rectangular items into a minimum number of standard two-dimensional bins. It is a notoriously intractable combinatorial optimization problem and has numerous applications in packing and cutting. The contribution of this paper is twofold. First, we propose a comprehensive theoretical analysis of lower bounds and we elucidate dominance relationships. We show that a previously presented dominance result is incorrect. Second, we present the results of an extensive computational study that was carried out, on a large set of 500 benchmark instances, to assess the empirical performance of the lower bounds. We found that the so-called Carlier-Clautiaux-Moukrim lower bounds exhibits an excellent relative performance and yields the tightest value for all of the benchmark instances.

Reçu le :
Accepté le :
DOI : 10.1051/ro/2017019
Classification : 90-08
Keywords: Two-dimensional bin packing, lower bounds, dual feasible functions, dominance results

Serairi, Mehdi 1 ; Haouari, Mohamed 1

1 
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     author = {Serairi, Mehdi and Haouari, Mohamed},
     title = {A theoretical and experimental study of fast lower bounds for the two-dimensional bin packing problem},
     journal = {RAIRO - Operations Research - Recherche Op\'erationnelle},
     pages = {391--414},
     publisher = {EDP-Sciences},
     volume = {52},
     number = {2},
     year = {2018},
     doi = {10.1051/ro/2017019},
     zbl = {1405.90027},
     mrnumber = {3880534},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.1051/ro/2017019/}
}
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Serairi, Mehdi; Haouari, Mohamed. A theoretical and experimental study of fast lower bounds for the two-dimensional bin packing problem. RAIRO - Operations Research - Recherche Opérationnelle, Tome 52 (2018) no. 2, pp. 391-414. doi: 10.1051/ro/2017019

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