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MIP-based constructive heuristics for the three-dimensional Bin Packing Problem with transportation constraints

Author

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  • Célia Paquay
  • Sabine Limbourg
  • Michaël Schyns
  • José Fernando Oliveira

Abstract

This article is about seeking a good feasible solution in a reasonable amount of computation time to the three-dimensional Multiple Bin Size Bin Packing Problem (MBSBPP). The MBSBPP studied considers additional constraints encountered in real world air transportation situations, such as cargo stability and the particular shape of containers. This MBSBPP has already been formulated as a Mixed Integer linear Programming problem, but as yet only poor results have been achieved for even fairly small problem sizes. The goal of the work this paper describes is to develop heuristics that are able to quickly provide good initial feasible solutions for the MBSBPP. Three methodologies are considered, which are based on the decomposition of the original problem into easier subproblems: the matheuristics Relax-and-Fix, Insert-and-Fix and Fractional Relax-and-Fix. They have been parametrised on real data sets and then compared to each other. In particular, two of these techniques show promising results in reasonable computational times.

Suggested Citation

  • Célia Paquay & Sabine Limbourg & Michaël Schyns & José Fernando Oliveira, 2018. "MIP-based constructive heuristics for the three-dimensional Bin Packing Problem with transportation constraints," International Journal of Production Research, Taylor & Francis Journals, vol. 56(4), pages 1581-1592, February.
    • Handle: RePEc:taf:tprsxx:v:56:y:2018:i:4:p:1581-1592
    DOI: 10.1080/00207543.2017.1355577
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    Cited by:

    1. Jianyu Long & Zhong Zheng & Xiaoqiang Gao & Panos M. Pardalos & Wanzhe Hu, 2020. "An effective heuristic based on column generation for the two-dimensional three-stage steel plate cutting problem," Annals of Operations Research, Springer, vol. 289(2), pages 291-311, June.
    2. Li, Yantong & Chu, Feng & Côté, Jean-François & Coelho, Leandro C. & Chu, Chengbin, 2020. "The multi-plant perishable food production routing with packaging consideration," International Journal of Production Economics, Elsevier, vol. 221(C).
    3. Tseremoglou, Iordanis & Bombelli, Alessandro & Santos, Bruno F., 2022. "A combined forecasting and packing model for air cargo loading: A risk-averse framework," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 158(C).
    4. Brandt, Felix & Nickel, Stefan, 2019. "The air cargo load planning problem - a consolidated problem definition and literature review on related problems," European Journal of Operational Research, Elsevier, vol. 275(2), pages 399-410.
    5. Silva, Elsa & Ramos, António G. & Oliveira, José F., 2018. "Load balance recovery for multi-drop distribution problems: A mixed integer linear programming approach," Transportation Research Part B: Methodological, Elsevier, vol. 116(C), pages 62-75.
    6. Xiangling Zhao & Yun Dong & Lei Zuo, 2023. "A Combinatorial Optimization Approach for Air Cargo Palletization and Aircraft Loading," Mathematics, MDPI, vol. 11(13), pages 1-16, June.

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