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Three-dimensional bin packing problem with variable bin height

Author

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  • Wu, Yong
  • Li, Wenkai
  • Goh, Mark
  • de Souza, Robert

Abstract

This paper studies a variant of the three-dimensional bin packing problem (3D-BPP), where the bin height can be adjusted to the cartons it packs. The bins and cartons to be packed are assumed rectangular in shape. The cartons are allowed to be rotated into any one of the six positions that keep the carton edges parallel to the bin edges. This greatly increases the difficulty of finding a good solution since the search space expands significantly comparing to the 3D-BPP where the cartons have fixed orientations. A mathematical (mixed integer programming) approach is modified based on [Chen, C. S., Lee, S. M., Shen, Q. S., 1995. An analytical model for the container loading problem. European Journal of Operational Research 80 (1), 68-76] and numerical experiments indicate that the mathematical approach is not suitable for the variable bin height 3D-BPP. A special bin packing algorithm based on packing index is designed to utilize the special problem feature and is used as a building block for a genetic algorithm designed for the 3D-BPP. The paper also investigates the situation where more than one type of bin are used and provides a heuristic for packing a batch of cartons using the genetic algorithm. Numerical experiments show that our proposed method yields quick and satisfactory results when benchmarked against the actual packing practice and the MIP model with the latest version of CPLEX.

Suggested Citation

  • Wu, Yong & Li, Wenkai & Goh, Mark & de Souza, Robert, 2010. "Three-dimensional bin packing problem with variable bin height," European Journal of Operational Research, Elsevier, vol. 202(2), pages 347-355, April.
  • Handle: RePEc:eee:ejores:v:202:y:2010:i:2:p:347-355
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    References listed on IDEAS

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    1. Lodi, Andrea & Martello, Silvano & Vigo, Daniele, 2002. "Heuristic algorithms for the three-dimensional bin packing problem," European Journal of Operational Research, Elsevier, vol. 141(2), pages 410-420, September.
    2. Bischoff, E. E. & Janetz, F. & Ratcliff, M. S. W., 1995. "Loading pallets with non-identical items," European Journal of Operational Research, Elsevier, vol. 84(3), pages 681-692, August.
    3. Chen, C. S. & Lee, S. M. & Shen, Q. S., 1995. "An analytical model for the container loading problem," European Journal of Operational Research, Elsevier, vol. 80(1), pages 68-76, January.
    4. Hopper, E. & Turton, B. C. H., 2001. "An empirical investigation of meta-heuristic and heuristic algorithms for a 2D packing problem," European Journal of Operational Research, Elsevier, vol. 128(1), pages 34-57, January.
    5. Pisinger, David, 2002. "Heuristics for the container loading problem," European Journal of Operational Research, Elsevier, vol. 141(2), pages 382-392, September.
    6. Bischoff, Eberhard E. & Marriott, Michael D., 1990. "A comparative evaluation of heuristics for container loading," European Journal of Operational Research, Elsevier, vol. 44(2), pages 267-276, January.
    7. Puchinger, Jakob & Raidl, Gunther R., 2007. "Models and algorithms for three-stage two-dimensional bin packing," European Journal of Operational Research, Elsevier, vol. 183(3), pages 1304-1327, December.
    8. Alves, Claudio & Valerio de Carvalho, J.M., 2007. "Accelerating column generation for variable sized bin-packing problems," European Journal of Operational Research, Elsevier, vol. 183(3), pages 1333-1352, December.
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    Citations

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    Cited by:

    1. Xianbo Xiang & Caoyang Yu & He Xu & Stuart X. Zhu, 2018. "Optimization of Heterogeneous Container Loading Problem with Adaptive Genetic Algorithm," Complexity, Hindawi, vol. 2018, pages 1-12, November.
    2. Gašper Žerovnik & Janez Žerovnik, 2011. "Constructive heuristics for the canister filling problem," Central European Journal of Operations Research, Springer;Slovak Society for Operations Research;Hungarian Operational Research Society;Czech Society for Operations Research;Österr. Gesellschaft für Operations Research (ÖGOR);Slovenian Society Informatika - Section for Operational Research;Croatian Operational Research Society, vol. 19(3), pages 371-389, September.
    3. Ardjmand, Ehsan & Sanei Bajgiran, Omid & Rahman, Shakil & Weckman, Gary R. & Young, William A., 2018. "A multi-objective model for order cartonization and fulfillment center assignment in the e-tail/retail industry," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 115(C), pages 16-34.
    4. Yaohua He & Yong Wu, 2013. "Packing non-identical circles within a rectangle with open length," Journal of Global Optimization, Springer, vol. 56(3), pages 1187-1215, July.
    5. Castro, Pedro M. & Oliveira, José F., 2011. "Scheduling inspired models for two-dimensional packing problems," European Journal of Operational Research, Elsevier, vol. 215(1), pages 45-56, November.
    6. Carlos A. Vega-Mejía & Jairo R. Montoya-Torres & Sardar M. N. Islam, 2019. "Consideration of triple bottom line objectives for sustainability in the optimization of vehicle routing and loading operations: a systematic literature review," Annals of Operations Research, Springer, vol. 273(1), pages 311-375, February.

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