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
    File URL: https://libkey.io/10.1016/j.ejor.2012.05.039?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    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. Tobias Fanslau & Andreas Bortfeldt, 2010. "A Tree Search Algorithm for Solving the Container Loading Problem," INFORMS Journal on Computing, INFORMS, vol. 22(2), pages 222-235, May.
    4. 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.
    5. 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.
    6. Martin Desrochers & François Soumis, 1989. "A Column Generation Approach to the Urban Transit Crew Scheduling Problem," Transportation Science, INFORMS, vol. 23(1), pages 1-13, February.
    7. George B. Dantzig & Philip Wolfe, 1960. "Decomposition Principle for Linear Programs," Operations Research, INFORMS, vol. 8(1), pages 101-111, February.
    8. F. Parreño & R. Alvarez-Valdes & J. M. Tamarit & J. F. Oliveira, 2008. "A Maximal-Space Algorithm for the Container Loading Problem," INFORMS Journal on Computing, INFORMS, vol. 20(3), pages 412-422, August.
    9. 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.
    10. 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.
    11. P. C. Gilmore & R. E. Gomory, 1961. "A Linear Programming Approach to the Cutting-Stock Problem," Operations Research, INFORMS, vol. 9(6), pages 849-859, December.
    12. 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.
    13. Marco E. Lübbecke & Jacques Desrosiers, 2005. "Selected Topics in Column Generation," Operations Research, INFORMS, vol. 53(6), pages 1007-1023, December.
    14. Teodor Gabriel Crainic & Guido Perboli & Roberto Tadei, 2008. "Extreme Point-Based Heuristics for Three-Dimensional Bin Packing," INFORMS Journal on Computing, INFORMS, vol. 20(3), pages 368-384, August.
    15. Silvano Martello & David Pisinger & Daniele Vigo, 2000. "The Three-Dimensional Bin Packing Problem," Operations Research, INFORMS, vol. 48(2), pages 256-267, April.
    16. Alberto Ceselli & Giovanni Righini & Matteo Salani, 2009. "A Column Generation Algorithm for a Rich Vehicle-Routing Problem," Transportation Science, INFORMS, vol. 43(1), pages 56-69, February.
    17. Oluf Faroe & David Pisinger & Martin Zachariasen, 2003. "Guided Local Search for the Three-Dimensional Bin-Packing Problem," INFORMS Journal on Computing, INFORMS, vol. 15(3), pages 267-283, August.
    18. P. C. Gilmore & R. E. Gomory, 1963. "A Linear Programming Approach to the Cutting Stock Problem---Part II," Operations Research, INFORMS, vol. 11(6), pages 863-888, December.
    19. Eley, Michael, 2002. "Solving container loading problems by block arrangement," European Journal of Operational Research, Elsevier, vol. 141(2), pages 393-409, September.
    20. 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.
    21. Cynthia Barnhart & Ellis L. Johnson & George L. Nemhauser & Martin W. P. Savelsbergh & Pamela H. Vance, 1998. "Branch-and-Price: Column Generation for Solving Huge Integer Programs," Operations Research, INFORMS, vol. 46(3), pages 316-329, June.
    22. 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. Kurpel, Deidson Vitorio & Scarpin, Cassius Tadeu & Pécora Junior, José Eduardo & Schenekemberg, Cleder Marcos & Coelho, Leandro C., 2020. "The exact solutions of several types of container loading problems," European Journal of Operational Research, Elsevier, vol. 284(1), pages 87-107.
    2. 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.
    3. 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.
    4. 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.
    5. 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.
    6. 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.
    7. 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.
    8. 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.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. 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.
    2. 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.
    3. Bortfeldt, Andreas & Wäscher, Gerhard, 2013. "Constraints in container loading – A state-of-the-art review," European Journal of Operational Research, Elsevier, vol. 229(1), pages 1-20.
    4. Toffolo, Túlio A.M. & Esprit, Eline & Wauters, Tony & Vanden Berghe, Greet, 2017. "A two-dimensional heuristic decomposition approach to a three-dimensional multiple container loading problem," European Journal of Operational Research, Elsevier, vol. 257(2), pages 526-538.
    5. 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.
    6. Zhu, Wenbin & Zhang, Zhaoyi & Oon, Wee-Chong & Lim, Andrew, 2012. "Space defragmentation for packing problems," European Journal of Operational Research, Elsevier, vol. 222(3), pages 452-463.
    7. 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.
    8. 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.
    9. Araya, Ignacio & Moyano, Mauricio & Sanchez, Cristobal, 2020. "A beam search algorithm for the biobjective container loading problem," European Journal of Operational Research, Elsevier, vol. 286(2), pages 417-431.
    10. Daniel Mack & Andreas Bortfeldt, 2012. "A heuristic for solving large bin packing problems in two and three dimensions," 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. 20(2), pages 337-354, June.
    11. 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.
    12. Andreas Bortfeldt & Gerhard Wäscher, 2012. "Container Loading Problems - A State-of-the-Art Review," FEMM Working Papers 120007, Otto-von-Guericke University Magdeburg, Faculty of Economics and Management.
    13. Hu, Qian & Zhu, Wenbin & Qin, Hu & Lim, Andrew, 2017. "A branch-and-price algorithm for the two-dimensional vector packing problem with piecewise linear cost function," European Journal of Operational Research, Elsevier, vol. 260(1), pages 70-80.
    14. Bonet Filella, Guillem & Trivella, Alessio & Corman, Francesco, 2023. "Modeling soft unloading constraints in the multi-drop container loading problem," European Journal of Operational Research, Elsevier, vol. 308(1), pages 336-352.
    15. Gajda, Mikele & Trivella, Alessio & Mansini, Renata & Pisinger, David, 2022. "An optimization approach for a complex real-life container loading problem," Omega, Elsevier, vol. 107(C).
    16. Wei, Lijun & Oon, Wee-Chong & Zhu, Wenbin & Lim, Andrew, 2012. "A reference length approach for the 3D strip packing problem," European Journal of Operational Research, Elsevier, vol. 220(1), pages 37-47.
    17. Wang, Ning & Lim, Andrew & Zhu, Wenbin, 2013. "A multi-round partial beam search approach for the single container loading problem with shipment priority," International Journal of Production Economics, Elsevier, vol. 145(2), pages 531-540.
    18. F. Parreño & R. Alvarez-Valdes & J. Oliveira & J. Tamarit, 2010. "A hybrid GRASP/VND algorithm for two- and three-dimensional bin packing," Annals of Operations Research, Springer, vol. 179(1), pages 203-220, September.
    19. François Clautiaux & Cláudio Alves & José Valério de Carvalho & Jürgen Rietz, 2011. "New Stabilization Procedures for the Cutting Stock Problem," INFORMS Journal on Computing, INFORMS, vol. 23(4), pages 530-545, November.
    20. Schmid, Verena & Doerner, Karl F. & Laporte, Gilbert, 2013. "Rich routing problems arising in supply chain management," European Journal of Operational Research, Elsevier, vol. 224(3), pages 435-448.

    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.

    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 bibliographic 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.

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

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

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.