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The exact solutions of several types of container loading problems

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  • Kurpel, Deidson Vitorio
  • Scarpin, Cassius Tadeu
  • Pécora Junior, José Eduardo
  • Schenekemberg, Cleder Marcos
  • Coelho, Leandro C.

Abstract

In this paper, we address multiple container loading problems, consisting of placing rectangular boxes, orthogonally and without overlapping, inside containers in order to optimize a given objective function, generally maximizing the value of the packed boxes or minimizing the number of containers required to pack all available boxes. Four techniques to enumerate the possible locations of boxes inside a container, some of them not yet tested in the literature, are evaluated. We also propose new techniques to obtain primal and dual bounds for these problems. In addition, we study the constraints related to box orientation, load stability, and separation of boxes. Detailed analysis on well-known benchmark instances shows that our method is very competitive, generating mathematical models containing significantly fewer variables and constraints than the traditional approach existing in the literature. We test our methods on five different benchmark sets. We provide a detailed comparison with different approaches from the CLP literature, proving new optimal solutions and improving the best-known results for several instances.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:ejores:v:284:y:2020:i:1:p:87-107
    DOI: 10.1016/j.ejor.2019.12.012
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    1. Nicos Christofides & Charles Whitlock, 1977. "An Algorithm for Two-Dimensional Cutting Problems," Operations Research, INFORMS, vol. 25(1), pages 30-44, February.
    2. Allen, S.D. & Burke, E.K. & Kendall, G., 2011. "A hybrid placement strategy for the three-dimensional strip packing problem," European Journal of Operational Research, Elsevier, vol. 209(3), pages 219-227, March.
    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. Jean-François Côté & Manuel Iori, 2018. "The Meet-in-the-Middle Principle for Cutting and Packing Problems," INFORMS Journal on Computing, INFORMS, vol. 30(4), pages 646-661, November.
    5. 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.
    6. Andreas Bortfeldt & Sabine Jungmann, 2012. "A tree search algorithm for solving the multi-dimensional strip packing problem with guillotine cutting constraint," Annals of Operations Research, Springer, vol. 196(1), pages 53-71, July.
    7. 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.
    8. 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.
    9. Gonçalves, José Fernando & Resende, Mauricio G.C., 2013. "A biased random key genetic algorithm for 2D and 3D bin packing problems," International Journal of Production Economics, Elsevier, vol. 145(2), pages 500-510.
    10. Eley, Michael, 2002. "Solving container loading problems by block arrangement," European Journal of Operational Research, Elsevier, vol. 141(2), pages 393-409, September.
    11. 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.
    12. 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.
    13. Mohanty, Bidhu B. & Mathur, Kamlesh & Ivancic, Nancy J., 1994. "Value considerations in three-dimensional packing -- A heuristic procedure using the fractional knapsack problem," European Journal of Operational Research, Elsevier, vol. 74(1), pages 143-151, April.
    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.
    15. 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.
    16. 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.
    17. 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.
    18. J. E. Beasley, 1985. "An Exact Two-Dimensional Non-Guillotine Cutting Tree Search Procedure," Operations Research, INFORMS, vol. 33(1), pages 49-64, February.
    19. 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.
    20. Silvano Martello & David Pisinger & Daniele Vigo, 2000. "The Three-Dimensional Bin Packing Problem," Operations Research, INFORMS, vol. 48(2), pages 256-267, April.
    21. Alonso, M.T. & Alvarez-Valdes, R. & Iori, M. & Parreño, F. & Tamarit, J.M., 2017. "Mathematical models for multicontainer loading problems," Omega, Elsevier, vol. 66(PA), pages 106-117.
    22. Ramos, António G. & Silva, Elsa & Oliveira, José F., 2018. "A new load balance methodology for container loading problem in road transportation," European Journal of Operational Research, Elsevier, vol. 266(3), pages 1140-1152.
    23. Martin Grunewald & Thomas Volling & Christoph Müller & Thomas S. Spengler, 2018. "Multi-item single-source ordering with detailed consideration of transportation capacities," Journal of Business Economics, Springer, vol. 88(7), pages 971-1007, September.
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