Abstract
In our research, we are interested in a practical problem closely related to the three-dimensional multiple-bin-size bin packing problem. We deal with the real word application of cutting mousse blocks proposed by a Tunisian industrial company. First, we present the general context related to this optimization problem. Second, for solving this practical problem, we propose an upper bound based on a MILP formulation (mixed integer linear programming). Finally, computational and comparative results are presented to evaluate the performance of the proposed bound by testing a large instance from the same industrial company.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
References
Baazaoui M, Hanafi S, Kamoun H (2014) A mathematical formulation and a lower bound for the three-dimensional multiple-bin-size bin packing problem (MBSBPP): a Tunisian industrial case. In: International conference on control, decision and information technologies (CoDIT), janvier. IEEE, Metz, pp 219–224
Bortfeldt A, Wascher G (2012) Container loading problems—a state- of-the- art-review. Working Paper 7
Chen CS, Lee SM, Shen QS (1995) An analytical model for the container loading problem”. Eur J Oper Res 80(1):68–76
Correia I, Gouveia L, Saldanha-da-Gama F (2008) Solving the variable size bin packing problem with discretized formulations”. Comput Oper Res 35:03–13
Crainic TG, Perboli G, Tadei R (2008) Extreme point-based heuristics for three dimensional bin packing. INFORMS J Comput 20:368–384
Crainic TG, Perboli G, Tadei R (2009) TS2 PACK: a two-level Tabu search for the three-dimensional bin packing problem”. Eur J Oper Res 195:744–760
deQueiroz TA, Miyazawa FK, Wakabayashi Y, Xavier EC (2012) Algorithms for 3D guillotine cutting problems: unbounded knapsack, cutting stock and strip packing. Comput Oper Res 39:200–212
Ertek G, Kilic K (2006) Decision support for packing in warehouses”. Lect Notes Comput Sci 4263:115–124
Faroe O, Pisinger D, Zachariasen M (2003) Guided local search for the three dimensional bin-packing problem”. INFORMS J Comput 15:267–283
Fekete SP, van der Veen JC (2007) PackLib2: an integrated library of multidimensional packing problems. Eur J Oper Res 183:1131–1135
Furini F, Malaguti E (2013) Models for the two-dimensional two-stage cutting stock problem with multiple stock size. Comput Oper Res 40:1953–1962
Hifi M, Negre S, Wu L (2014) Hybrid greedy heuristics based on linear programming for the three-dimensional single bin-size bin packing problem. Int Trans Oper Res 21:59–79
Hopper E (2000) Two-dimensional packing utilising evolutionary algorithms and other meta-heuristic methods, PhD dissertation. University of Wales, Cardiff
Joaquim V, Susana V, Elsa H, João S (2014) A Tabu search algorithm for the 3D bin packing problem in the steel industry. In: CONTROLO’2014—Proceedings of the 11th Portuguese conference on automatic control, Volume 321 of the series Lecture Notes in Electrical Engineering, pp 355–364
Lodi A, Martello S, Vigo D (2002) Heuristic algorithms for the three-dimensional bin packing problem. Eur J Oper Res 141:410–420
Lu H, Huang Y, Tseng K (2013) An integrated algorithm for cutting stock problems in the thin-film transistor liquid crystal display industry”. Comput Ind Eng 64:1084–1092
Martello S, Pisinger D, Vigo D (2000) The three-dimensional bin packing problem. Oper Res 48:256–267
Ortmann FG, Ntene N, Van Vuuren JH (2010) New and improved level heuristics for the rectangular strip packing and variable-sized bin packing problems. Eur J Oper Res 203(2):306–315
Parreño F, Alvarez-Valdes R, Oliveira JF, Tamarit JM (2008) A hybrid GRASP/VND algorithm for two- and three-dimensional bin packing. Ann Oper Res 179:203–220
Pisinger P, Sigurd M (2005) The two-dimensional bin packing problem with variable bin sizes and costs”. Discret Optim 2:154–167
Tae Park K, Ryu J, Lee H, Lee I (2013) Developing a heuristics for glass cutting process optimization: a case of two-dimensional two-stage guillotine cutting with multiple stock sizes. Korean J Chem Eng 30(2):278–285
Verweij B (1996) Multiple destination bin packing. Technical report CS-1996-39. Department of Information and Computing Sciences, Faculty of Science, Utrecht University 3508 TC Utrecht, Netherlands
Wascher G, Haussner H, Schumann H (2007) An improved typology of cutting and packing problems. Eur J Oper Res 183:1109–1130
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2017 Springer International Publishing Switzerland
About this paper
Cite this paper
Baazaoui, M., Hanafi, S., Kamoun, H. (2017). Three-Dimensional Multiple-Bin-Size Bin Packing: A Case Study with a New MILP-Based Upper Bound. In: Grigoroudis, E., Doumpos, M. (eds) Operational Research in Business and Economics. Springer Proceedings in Business and Economics. Springer, Cham. https://doi.org/10.1007/978-3-319-33003-7_11
Download citation
DOI: https://doi.org/10.1007/978-3-319-33003-7_11
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-319-33001-3
Online ISBN: 978-3-319-33003-7
eBook Packages: Business and ManagementBusiness and Management (R0)