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Lexicographic optimization for the multi-container loading problem with open dimensions for a shoe manufacturer

Author

Listed:
  • Manuel V. C. Vieira

    (Universidade NOVA de Lisboa)

  • Margarida Carvalho

    (Université de Montréal)

Abstract

Motivated by a real-world application, we present a multi-container loading problem with 3-open dimensions. We formulate it as a biobjective mixed-integer nonlinear program with lexicographic objectives in order to reflect the decision maker’s optimization priorities. The first objective is to minimize the number of containers, while the second objective is to minimize the volume of those containers. Besides showing the NP-hardness of this sequential optimization problem, we provide bounds for it which are used in the three proposed algorithms, as well as, on their evaluation when a certificate of optimality is not available. The first is an exact parametric-based approach to tackle the lexicographic optimization through the second objective of the problem. Nevertheless, given that the parametric programs correspond to large nonlinear mixed-integer optimizations, we present a heuristic that is entirely mathematical-programming based. The third algorithm enhances the solution quality of the heuristic. These algorithms are specifically tailored for the real-world application. The effectiveness and efficiency of the devised heuristics is demonstrated with numerical experiments.

Suggested Citation

  • Manuel V. C. Vieira & Margarida Carvalho, 2023. "Lexicographic optimization for the multi-container loading problem with open dimensions for a shoe manufacturer," 4OR, Springer, vol. 21(3), pages 491-512, September.
    • Handle: RePEc:spr:aqjoor:v:21:y:2023:i:3:d:10.1007_s10288-022-00522-4
    DOI: 10.1007/s10288-022-00522-4
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    References listed on IDEAS

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    1. 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.
    2. Manuel V. C. Vieira & Flora Ferreira & José C. M. Duque & Rui M. P. Almeida, 2021. "On the packing process in a shoe manufacturer," Journal of the Operational Research Society, Taylor & Francis Journals, vol. 72(4), pages 853-864, March.
    3. Liu, D.S. & Tan, K.C. & Huang, S.Y. & Goh, C.K. & Ho, W.K., 2008. "On solving multiobjective bin packing problems using evolutionary particle swarm optimization," European Journal of Operational Research, Elsevier, vol. 190(2), pages 357-382, October.
    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. 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.
    6. 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.
    7. Delorme, Maxence & Iori, Manuel & Martello, Silvano, 2016. "Bin packing and cutting stock problems: Mathematical models and exact algorithms," European Journal of Operational Research, Elsevier, vol. 255(1), pages 1-20.
    8. 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.
    9. Matthias Ehrgott, 2005. "Multicriteria Optimization," Springer Books, Springer, edition 0, number 978-3-540-27659-3, December.
    10. Kristina Yancey Spencer & Pavel V. Tsvetkov & Joshua J. Jarrell, 2019. "A greedy memetic algorithm for a multiobjective dynamic bin packing problem for storing cooling objects," Journal of Heuristics, Springer, vol. 25(1), pages 1-45, February.
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