Abstract
In this paper, we study the 3-D container packing problem. The problem is divided into box selection, space selection, box orientation and new space generation sub-problems. As a first step, a basic heuristic is devised. From results using this heuristic, problems are categorized as homogeneous and heterogeneous. Two augmenting heuristics are then formulated to deal with these categories. They are complementary in their capabilities in dealing with a range of practical problems, and in terms of their computational consumption. Results using our algorithmsexceed the benchmark by 4.5% on average.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
Explore related subjects
Discover the latest articles, news and stories from top researchers in related subjects.References
S. Martello, D. Pisinger, and D.Vigo, “The three dimensional bin packing problem,” Operations Research, vol. 48, pp. 256–267,2000.
H. Gehring, K. Menschner, and M. Meyer, “A computer-based heuristic for packing pooled shipment containers,” European Journal of Operational Research, 1990
D. Pisinger “The container loading problem,” in Proceedings NOAS’97, 1997.
Y. Wakabayashi and F.K. Miyazawa, “An algorithm for the three dimensional packing problem with asymptotic performance analysis,” Algorithmica, vol. 18, pp. 122–144, 1997.
,L. Faina, “A global optimization algorithm for the three dimensional packing problem,” European Journal of Operational Research, vol. 126, pp. 340–354, 2000.
J.A. George and B.F. Robinson, “A heuristic for packing boxes into a container,” Computer and Operational Research, vol. 7, pp. 147–156, 1980
H. Dyckhoff, “A typology of cutting and packing problems,” European Journal of Operational Research, vol. 44, pp. 145–159, 1990.
Cutting and Packing in Production and Distribution, Physica Verlag, Heidelberg: Germany, 1992. H. Dyckhoff and U. Finke,
W.B. Dowsland, “Three dimensional packing-solution approaches and heuristic development,” International Journal of Operational Research, vol. 29, pp. 1637–1685, 1991
K.A. Dowsland andW.B. Dowsland, “Packing problems,” European Journal of Operational Research, vol. 56, pp. 2–14, 1992.
K.A. Dowsland andW.B. Dowsland,“A comparative analysis of heuristics for the two dimensional packing problem,” in EURO 6 Conference Paper, 1983.
H. Dyckhoff, G. Scheithauer, and J. Terno, “In Annotated Bibliographies in Combinatorial Optimization,” edited by M. Dell’Amico, F. Maffioli and S. Martello, John Wiley and Sons, 1997.
E.E. Bischoff and M.S.W. Ratcliff, “Issues in the development of approaches to container loading,” OMEGA, 1995.
E.E. Bischoff, F. Janetz, and M.S.W. Ratcliff, “Loading pallets with non-identical items,” European Journal of Operational Research, 1995.
A. Bortfeldt, “A genetic algorithm for the container loading problem,” in Proceedings of the Conference on Adaptive Computing and Information Processing, London, 1994.
J.A. George, “A method for solving container packing for a single size of box,” J. Opl Res., 1992.
E. Bischoff and W.B. Dowsland, “An application of the microcomputer to product design and distribution,” Operational Research Society Journal, 1982.
C.P. Han, K. Knott, and J.P. Egbelu, “A heuristic approach to the three-dimensional cargo-loading problem,” Int. J. Prod. Res., vol. 27, no. 5, pp. 757–774, 1989.
J. Xue and K.K. Lai, “ Effective methods for a container packing operation,” Mathl. Comput. Modelling, 1997.
M.A. Nadim, “A computer-aided box stacking model for truck transport and pallets,” Computers in Industry, 1991.
B.K.A. Ngoi, M.L. Tay, and E.S. Chua, “Applying spatial representation techniques to the container packing problem,” Int. J. Prod. Res., 1994.
C.K. Chua, V. Narayanan, and J. Loh, “Constraint-based spatial representation technique for the container packing problem,” Integrated Manufacturing Systems, 1998.
K.K. Lai, J. Xue, and B. Xu, “Container packing in a multi-customer delivering operation,” Computers ind. Eng., 1998.
N. Christofides and C. Whitlock, “An algorithm for two-dimensional cutting problems,” Operations Research, 1977.
N. Ivancic, K. Mathur, and B.B. Mohanty, “An integer programming based heuristic approach to the three dimensional packing problem,” Journal of Manufacturing and Operations Management, 1989.
B.D. William, “Three-dimensional packing-solutions approaches and heuristic development,” Int. J. Prod. Res., 1991.
E.E. Bischoff and M.S.W. Ratcliff, “Issues in the development of approaches to container loading,” Omega. Int. J. Mgmt Sci., vol. 23, no. 4, pp. 337–390, 1995.
E.E. Bischoff and M.D. Marriott, “A comparative evaluation of heuristics for container loading,” European Journal of Operational Research, 1990.
OR-Library, http://mscmga.ms.ic.ac.uk/info.html.
T.H. Loh and A.Y.C. Nee, “A packing algorithm for hexahedral boxes,” in Proceedings of the Conference of Industrial Automation, Singapore, 1992, pp. 115–126.
B.K.A. Ngoi and K. Whybrew, “A fast spatial representation method,” Journal of International Advance Manufacturing Technology, 1993.
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Lim, A., Rodrigues, B. & Yang, Y. 3-D Container Packing Heuristics. Appl Intell 22, 125–134 (2005). https://doi.org/10.1007/s10489-005-5601-0
Issue Date:
DOI: https://doi.org/10.1007/s10489-005-5601-0