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.
Accepté le :
DOI : 10.1051/ro/2017019
Keywords: Two-dimensional bin packing, lower bounds, dual feasible functions, dominance results
Serairi, Mehdi 1 ; Haouari, Mohamed 1
@article{RO_2018__52_2_391_0,
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},
year = {2018},
publisher = {EDP Sciences},
volume = {52},
number = {2},
doi = {10.1051/ro/2017019},
zbl = {1405.90027},
mrnumber = {3880534},
language = {en},
url = {https://www.numdam.org/articles/10.1051/ro/2017019/}
}
TY - JOUR AU - Serairi, Mehdi AU - Haouari, Mohamed TI - A theoretical and experimental study of fast lower bounds for the two-dimensional bin packing problem JO - RAIRO - Operations Research - Recherche Opérationnelle PY - 2018 SP - 391 EP - 414 VL - 52 IS - 2 PB - EDP Sciences UR - https://www.numdam.org/articles/10.1051/ro/2017019/ DO - 10.1051/ro/2017019 LA - en ID - RO_2018__52_2_391_0 ER -
%0 Journal Article %A Serairi, Mehdi %A Haouari, Mohamed %T A theoretical and experimental study of fast lower bounds for the two-dimensional bin packing problem %J RAIRO - Operations Research - Recherche Opérationnelle %D 2018 %P 391-414 %V 52 %N 2 %I EDP Sciences %U https://www.numdam.org/articles/10.1051/ro/2017019/ %R 10.1051/ro/2017019 %G en %F RO_2018__52_2_391_0
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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