Abstract
The more-dimensional bin packing problem (BPP) considered here requires packing a set of rectangular-shaped items into a minimum number of identical rectangular-shaped bins. All items may be rotated and the guillotine cut constraint has to be respected. A straightforward heuristic is presented that is based on a method for the container loading problem following a wall-building approach and on a method for the one-dimensional BPP. 1,800 new benchmark instances are introduced for the two-dimensional and three-dimensional BPP. The instances include more than 1,500 items on average. Applied to these very large instances, the heuristic generates solutions of acceptable quality in short computation times. Moreover, the influence of different instance parameters on the solution quality is investigated by an extended computational study.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Bengtsson B-E (1982) Packing rectangular pieces—a heuristic approach. Comput J 25: 353–357
Berkey JO, Wang PY (1987) Two dimensional finite bin packing algorithms. J Oper Res Soc 38: 423–429
Bischoff EE, Ratcliff MSW (1995) Issues in the development of approaches to container loading. Omega 23: 377–390
Bortfeldt A (2000) Eine Heuristik für multiple containerladeprobleme. OR Spectr 22: 239–261
Bortfeldt A (2005) A hybrid procedure for the one-dimensional bin packing problem. Presentation on the 2th ESICUP-Meeting, Southampton 2005 Siehe. http://paginas.fe.up.pt/~esicup/
Bortfeldt A (2007) Verfahren für das eindimensionale Bin Packing Problem. Vortrag in der Forschungswerkstatt der Fakultät Wirtschaftswiss. der FernUniversität in Hagen, März 2007. S. http://www.fernuni-hagen.de/WINF
Coffman EG Jr, Csirik J, Johnson DS, Woeginger GJ (2004) An Introduction to Bin Packing. Bibliography. See. http://www.inf.u-szeged.hu/~csirik
Crainic TG, Perboli G, Tadei R (2008) Extreme point-based Heuristics for three-dimensional bin packing. INFORMS J Comput 20: 368–384
Davies AP, Bischoff EE (1998) Weight distribution considerations in container loading. In: European business management school. University of Wales, Swansea, Technical report
de Castro Silva JL, Soma NY, Maculan N (2003) A greedy search for the tree-dimensional bin packing problem: the packing stability case. Int Trans Oper Res 10: 141–153
Dell’Amico M, Martello S, Vigo D (2002) A lower bound for the non-oriented two-dimensional bin packing problem. Discrete Appl Math 118: 13–24
El Bouri A, Popplewell N, Balakrishnan S, Alfa A (1994) A search based heuristic for the two-dimensional bin-packing problem. INFOR 32: 265–274
Eley M (2003) A bottleneck assignment approach to the multiple container loading problem. OR Spectr 25: 45–60
Faroe O, Pisinger D, Zachariasen M (2003) Guided local search for the three-dimensional bin-packing problem. INFORMS J Comput 15: 267–283
Glover F, Kochenberger G (2003) Handbook of metaheuristics. Kluwer Academic Publishers, Dordrecht
Ivancic N, Mathur K, Mohanty BB (1989) An integer-programming based heuristic approach to the three-dimensional packing problem. J Manuf Oper Manag 2: 268–298
Lodi A, Martello S, Vigo D (1998) Neighborhood search algorithm for the guillotine non-oriented two-dimensional bin packing problem. In: Voss S, Martello S, Osman IH, Roucairol C (eds) Meta- heuristics: advances and trends in local search paradigms for optimisation. Kluwer Academic Publishers, Boston, pp 125–139
Lodi A, Martello S, Vigo D (1999a) Heuristic and metaheuristic approaches for a class of two-dimensional bin packing problems. INFORMS J Comput 11: 345–357
Lodi A, Martello S, Vigo D (1999b) Approximation algorithms for the oriented two-dimensional bin packing problem. Eur J Oper Res 112: 158–166
Lodi A, Martello S, Vigo D (2002) Heuristic algorithms for the three-dimensional bin packing problem. Eur J Oper Res 141: 410–420
Lodi A, Martello S, Vigo D (2004) TSpack: a unified tabu search code for multi-dimensional bin packing problems. Ann Oper Res 131: 203–213
Martello S, Pisinger D, Vigo D (2000) The three-dimensional bin packing problem. Oper Res 48: 256–267
Martello S, Vigo D (1998) Exact solution of the two-dimensional finite bin packing problem. Manage Sci 44: 388–399
Moura A, Oliveira JF (2005) A GRASP approach to the container-loading problem. IEEE Intell Syst 20: 50–57
Mumford-Valenzuela CL, Vick J, Wang PY (2003) Heuristics for large strip packing problems with guillotine patterns: an empirical study. In: Metaheuristics: computer-decision making. Kluwer Academic Publishers B.V., pp 510–522
Pisinger D (2002) Heuristics for the container loading problem. Eur J Oper Res 141: 143–153
Pisinger D, Sigurd M (2007) Using decomposition techniques and constraint programming for solving the two-dimensional bin-packing problem. INFORMS J Comput 19: 36–51
Terno J, Scheithauer G, Sommerweiß U, Riehme J (2000) An efficient approach for the multi-pallet loading problem. Eur J Oper Res 123: 372–381
Wäscher 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
Rights and permissions
About this article
Cite this article
Mack, D., Bortfeldt, A. A heuristic for solving large bin packing problems in two and three dimensions. Cent Eur J Oper Res 20, 337–354 (2012). https://doi.org/10.1007/s10100-010-0184-1
Published:
Issue Date:
DOI: https://doi.org/10.1007/s10100-010-0184-1