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A new binary formulation of the restricted Container Relocation Problem based on a binary encoding of configurations

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  • Galle, Virgile
  • Barnhart, Cynthia
  • Jaillet, Patrick

Abstract

The Container Relocation Problem (CRP), also called Block Relocation Problem (BRP), is concerned with finding a sequence of moves of containers that minimizes the number of relocations needed to retrieve all containers, while respecting a given order of retrieval. The restricted CRP enforces that only containers blocking the target container can be relocated. We improve upon and enhance an existing binary encoding and using it, formulate the restricted CRP as a binary integer programming problem in which we exploit structural properties of the optimal solution. This integer programming formulation reduces significantly the number of variables and constraints compared to existing formulations. Its efficiency is shown through computational results on small and medium sized instances taken from the literature.

Suggested Citation

  • Galle, Virgile & Barnhart, Cynthia & Jaillet, Patrick, 2018. "A new binary formulation of the restricted Container Relocation Problem based on a binary encoding of configurations," European Journal of Operational Research, Elsevier, vol. 267(2), pages 467-477.
    • Handle: RePEc:eee:ejores:v:267:y:2018:i:2:p:467-477
    DOI: 10.1016/j.ejor.2017.11.053
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    References listed on IDEAS

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    1. Ku, Dusan & Arthanari, Tiru S., 2016. "Container relocation problem with time windows for container departure," European Journal of Operational Research, Elsevier, vol. 252(3), pages 1031-1039.
    2. Jin, Bo & Zhu, Wenbin & Lim, Andrew, 2015. "Solving the container relocation problem by an improved greedy look-ahead heuristic," European Journal of Operational Research, Elsevier, vol. 240(3), pages 837-847.
    3. Petering, Matthew E.H. & Hussein, Mazen I., 2013. "A new mixed integer program and extended look-ahead heuristic algorithm for the block relocation problem," European Journal of Operational Research, Elsevier, vol. 231(1), pages 120-130.
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    6. Caserta, Marco & Schwarze, Silvia & Voß, Stefan, 2012. "A mathematical formulation and complexity considerations for the blocks relocation problem," European Journal of Operational Research, Elsevier, vol. 219(1), pages 96-104.
    7. Zehendner, Elisabeth & Caserta, Marco & Feillet, Dominique & Schwarze, Silvia & Voß, Stefan, 2015. "An improved mathematical formulation for the blocks relocation problem," European Journal of Operational Research, Elsevier, vol. 245(2), pages 415-422.
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    Cited by:

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    2. Feng, Yuanjun & Song, Dong-Ping & Li, Dong & Zeng, Qingcheng, 2020. "The stochastic container relocation problem with flexible service policies," Transportation Research Part B: Methodological, Elsevier, vol. 141(C), pages 116-163.
    3. Azab, Ahmed & Morita, Hiroshi, 2022. "Coordinating truck appointments with container relocations and retrievals in container terminals under partial appointments information," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 160(C).
    4. de Melo da Silva, Marcos & Toulouse, Sophie & Wolfler Calvo, Roberto, 2018. "A new effective unified model for solving the Pre-marshalling and Block Relocation Problems," European Journal of Operational Research, Elsevier, vol. 271(1), pages 40-56.
    5. Azab, Ahmed & Morita, Hiroshi, 2022. "The block relocation problem with appointment scheduling," European Journal of Operational Research, Elsevier, vol. 297(2), pages 680-694.
    6. Jin, Bo, 2020. "On the integer programming formulation for the relaxed restricted container relocation problem," European Journal of Operational Research, Elsevier, vol. 281(2), pages 475-482.
    7. Bacci, Tiziano & Mattia, Sara & Ventura, Paolo, 2020. "A branch-and-cut algorithm for the restricted Block Relocation Problem," European Journal of Operational Research, Elsevier, vol. 287(2), pages 452-459.
    8. Boschma, René & Mes, Martijn R.K. & de Vries, Leon R., 2023. "Approximate dynamic programming for container stacking," European Journal of Operational Research, Elsevier, vol. 310(1), pages 328-342.
    9. Tanaka, Shunji & Voß, Stefan, 2019. "An exact algorithm for the block relocation problem with a stowage plan," European Journal of Operational Research, Elsevier, vol. 279(3), pages 767-781.
    10. Tanaka, Shunji & Voß, Stefan, 2022. "An exact approach to the restricted block relocation problem based on a new integer programming formulation," European Journal of Operational Research, Elsevier, vol. 296(2), pages 485-503.
    11. Galle, Virgile & Barnhart, Cynthia & Jaillet, Patrick, 2018. "Yard Crane Scheduling for container storage, retrieval, and relocation," European Journal of Operational Research, Elsevier, vol. 271(1), pages 288-316.
    12. Huiling Zhu & Mingjun Ji & Wenwen Guo & Qingbin Wang & Yongzhi Yang, 2019. "Mathematical formulation and heuristic algorithm for the block relocation and loading problem," Naval Research Logistics (NRL), John Wiley & Sons, vol. 66(4), pages 333-351, June.
    13. Zhang, Canrong & Guan, Hao & Yuan, Yifei & Chen, Weiwei & Wu, Tao, 2020. "Machine learning-driven algorithms for the container relocation problem," Transportation Research Part B: Methodological, Elsevier, vol. 139(C), pages 102-131.
    14. Andresson Silva Firmino & Ricardo Martins Abreu Silva & Valéria Cesário Times, 2019. "A reactive GRASP metaheuristic for the container retrieval problem to reduce crane’s working time," Journal of Heuristics, Springer, vol. 25(2), pages 141-173, April.
    15. Fan, Tijun & Pan, Qianlan & Pan, Fei & Zhou, Wei & Chen, Jingyi, 2020. "Intelligent logistics integration of internal and external transportation with separation mode," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 133(C).

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