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The multiple container loading cost minimization problem

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  • Che, Chan Hou
  • Huang, Weili
  • Lim, Andrew
  • Zhu, Wenbin

Abstract

In the shipping and transportation industry, there are several types of standard containers with different dimensions and different associated costs. In this paper, we examine the multiple container loading cost minimization problem (MCLCMP), where the objective is to load products of various types into containers of various sizes so as to minimize the total cost. We transform the MCLCMP into an extended set cover problem that is formulated using linear integer programming and solve it with a heuristic to generate columns. Experiments on standard bin-packing instances show our approach is superior to prior approaches. Additionally, since the optimal solutions for existing test data is unknown, we propose a technique to generate test data with known optimal solutions for MCLCMP.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:ejores:v:214:y:2011:i:3:p:501-511
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    References listed on IDEAS

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    1. Lins, Lauro & Lins, Sostenes & Morabito, Reinaldo, 2002. "An n-tet graph approach for non-guillotine packings of n-dimensional boxes into an n-container," European Journal of Operational Research, Elsevier, vol. 141(2), pages 421-439, September.
    2. 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.
    3. 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.
    4. Michele Monaci & Paolo Toth, 2006. "A Set-Covering-Based Heuristic Approach for Bin-Packing Problems," INFORMS Journal on Computing, INFORMS, vol. 18(1), pages 71-85, February.
    5. Eley, Michael, 2002. "Solving container loading problems by block arrangement," European Journal of Operational Research, Elsevier, vol. 141(2), pages 393-409, September.
    6. 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.
    7. 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.
    8. 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.
    9. 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.
    10. Silvano Martello & David Pisinger & Daniele Vigo, 2000. "The Three-Dimensional Bin Packing Problem," Operations Research, INFORMS, vol. 48(2), pages 256-267, April.
    11. 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.
    12. 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.
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    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. 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.
    3. 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.
    4. 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.
    5. 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.
    6. 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.
    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. Christoph Martius & Lutz Kretschmann & Miriam Zacharias & Carlos Jahn & Ole John, 2022. "Forecasting worldwide empty container availability with machine learning techniques," Journal of Shipping and Trade, Springer, vol. 7(1), pages 1-24, December.
    9. Hu, Qian & Wei, Lijun & Lim, Andrew, 2018. "The two-dimensional vector packing problem with general costs," Omega, Elsevier, vol. 74(C), pages 59-69.
    10. 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.
    11. Vélez-Gallego, Mario C. & Teran-Somohano, Alejandro & Smith, Alice E., 2020. "Minimizing late deliveries in a truck loading problem," European Journal of Operational Research, Elsevier, vol. 286(3), pages 919-928.
    12. 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.
    13. 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.
    14. 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.

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