IDEAS home Printed from https://ideas.repec.org/a/eee/ejores/v223y2012i1p27-39.html
   My bibliography  Save this article

A prototype column generation strategy for the multiple container loading problem

Author

Listed:
  • Zhu, Wenbin
  • Huang, Weili
  • Lim, Andrew

Abstract

The multiple container loading cost minimization problem (MCLCMP) is a practical and useful problem in the transportation industry, where products of various dimensions are to be loaded into containers of various sizes so as to minimize the total shipping cost. The MCLCMP can be naturally formulated as a set cover problem and solved using column generation techniques, which is a popular method for handling huge numbers of variables. However, the direct application of column generation is not effective because feasible solutions to the pricing subproblem is required, which for the MCLCMP is NP-hard. We show that efficiency can be greatly improved by generating prototypes that approximate feasible solutions to the pricing problem rather than actual columns. For many hard combinatorial problems, the subproblem in column generation based algorithms is NP-hard; if suitable prototypes can be quickly generated that approximate feasible solutions, then our strategy can also be applied to speed up these algorithms.

Suggested Citation

  • Zhu, Wenbin & Huang, Weili & Lim, Andrew, 2012. "A prototype column generation strategy for the multiple container loading problem," European Journal of Operational Research, Elsevier, vol. 223(1), pages 27-39.
  • Handle: RePEc:eee:ejores:v:223:y:2012:i:1:p:27-39
    DOI: 10.1016/j.ejor.2012.05.039
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0377221712004286
    Download Restriction: Full text for ScienceDirect subscribers only

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. Zhu, Wenbin & Lim, Andrew, 2012. "A new iterative-doubling Greedy–Lookahead algorithm for the single container loading problem," European Journal of Operational Research, Elsevier, vol. 222(3), pages 408-417.
    2. Bischoff, E. E. & Ratcliff, M. S. W., 1995. "Issues in the development of approaches to container loading," Omega, Elsevier, vol. 23(4), pages 377-390, August.
    3. Wascher, Gerhard & Hau[ss]ner, Heike & Schumann, Holger, 2007. "An improved typology of cutting and packing problems," European Journal of Operational Research, Elsevier, vol. 183(3), pages 1109-1130, December.
    4. 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.
    5. L. R. Ford, Jr. & D. R. Fulkerson, 1958. "A Suggested Computation for Maximal Multi-Commodity Network Flows," Management Science, INFORMS, vol. 5(1), pages 97-101, October.
    6. Terno, Johannes & Scheithauer, Guntram & Sommerwei[ss], Uta & Riehme, Jan, 2000. "An efficient approach for the multi-pallet loading problem," European Journal of Operational Research, Elsevier, vol. 123(2), pages 372-381, June.
    7. Crainic, Teodor Gabriel & Perboli, Guido & Tadei, Roberto, 2009. "TS2PACK: A two-level tabu search for the three-dimensional bin packing problem," European Journal of Operational Research, Elsevier, vol. 195(3), pages 744-760, June.
    8. Eley, Michael, 2002. "Solving container loading problems by block arrangement," European Journal of Operational Research, Elsevier, vol. 141(2), pages 393-409, September.
    9. Che, Chan Hou & Huang, Weili & Lim, Andrew & Zhu, Wenbin, 2011. "The multiple container loading cost minimization problem," European Journal of Operational Research, Elsevier, vol. 214(3), pages 501-511, November.
    10. Fekete, Sandor P. & van der Veen, Jan C., 2007. "PackLib2: An integrated library of multi-dimensional packing problems," European Journal of Operational Research, Elsevier, vol. 183(3), pages 1131-1135, December.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Hu, Qian & Lim, Andrew & Zhu, Wenbin, 2015. "The two-dimensional vector packing problem with piecewise linear cost function," Omega, Elsevier, vol. 50(C), pages 43-53.
    2. Wei, Lijun & Zhu, Wenbin & Lim, Andrew, 2015. "A goal-driven prototype column generation strategy for the multiple container loading cost minimization problem," European Journal of Operational Research, Elsevier, vol. 241(1), pages 39-49.
    3. Wei, Lijun & Tian, Tian & Zhu, Wenbin & Lim, Andrew, 2014. "A block-based layer building approach for the 2D guillotine strip packing problem," European Journal of Operational Research, Elsevier, vol. 239(1), pages 58-69.
    4. Wei, Lijun & Lim, Andrew, 2015. "A bidirectional building approach for the 2D constrained guillotine knapsack packing problem," European Journal of Operational Research, Elsevier, vol. 242(1), pages 63-71.
    5. Tian, Tian & Zhu, Wenbin & Lim, Andrew & Wei, Lijun, 2016. "The multiple container loading problem with preference," European Journal of Operational Research, Elsevier, vol. 248(1), pages 84-94.
    6. Sheng, Liu & Hongxia, Zhao & Xisong, Dong & Changjian, Cheng, 2016. "A heuristic algorithm for container loading of pallets with infill boxes," European Journal of Operational Research, Elsevier, vol. 252(3), pages 728-736.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:eee:ejores:v:223:y:2012:i:1:p:27-39. See general information about how to correct material in RePEc.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (Dana Niculescu). General contact details of provider: http://www.elsevier.com/locate/eor .

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service hosted by the Research Division of the Federal Reserve Bank of St. Louis . RePEc uses bibliographic data supplied by the respective publishers.