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A Constraint Programming model for fast optimal stowage of container vessel bays

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  • Delgado, Alberto
  • Jensen, Rune Møller
  • Janstrup, Kira
  • Rose, Trine Høyer
  • Andersen, Kent Høj

Abstract

Container vessel stowage planning is a hard combinatorial optimization problem with both high economic and environmental impact. We have developed an approach that often is able to generate near-optimal plans for large container vessels within a few minutes. It decomposes the problem into a master planning phase that distributes the containers to bay sections and a slot planning phase that assigns containers of each bay section to slots. In this paper, we focus on the slot planning phase of this approach and present a Constraint Programming and Integer Programming model for stowing a set of containers in a single bay section. This so-called slot planning problem is NP-hard and often involves stowing several hundred containers. Using state-of-the-art constraint solvers and modeling techniques, however, we were able to solve 90% of 236 real instances from our industrial collaborator to optimality within 1second. Thus, somewhat to our surprise, it is possible to solve most of these problems optimally within the time required for practical application.

Suggested Citation

  • Delgado, Alberto & Jensen, Rune Møller & Janstrup, Kira & Rose, Trine Høyer & Andersen, Kent Høj, 2012. "A Constraint Programming model for fast optimal stowage of container vessel bays," European Journal of Operational Research, Elsevier, vol. 220(1), pages 251-261.
    • Handle: RePEc:eee:ejores:v:220:y:2012:i:1:p:251-261
    DOI: 10.1016/j.ejor.2012.01.028
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    1. Daniela Ambrosino & Davide Anghinolfi & Massimo Paolucci & Anna Sciomachen, 2009. "A new three-step heuristic for the Master Bay Plan Problem," Maritime Economics & Logistics, Palgrave Macmillan;International Association of Maritime Economists (IAME), vol. 11(1), pages 98-120, March.
    2. Mordecai Avriel & Michal Penn & Naomi Shpirer & Smadar Witteboon, 1998. "Stowage planning for container ships to reduce the number of shifts," Annals of Operations Research, Springer, vol. 76(0), pages 55-71, January.
    3. J-G Kang & Y-D Kim, 2002. "Stowage planning in maritime container transportation," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 53(4), pages 415-426, April.
    4. I D Wilson & P A Roach, 2000. "Container stowage planning: a methodology for generating computerised solutions," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 51(11), pages 1248-1255, November.
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    Cited by:

    1. Petri Helo & Henri Paukku & Tero Sairanen, 2021. "Containership cargo profiles, cargo systems, and stowage capacity: key performance indicators," Maritime Economics & Logistics, Palgrave Macmillan;International Association of Maritime Economists (IAME), vol. 23(1), pages 28-48, March.
    2. Lehnfeld, Jana & Knust, Sigrid, 2014. "Loading, unloading and premarshalling of stacks in storage areas: Survey and classification," European Journal of Operational Research, Elsevier, vol. 239(2), pages 297-312.
    3. Fazi, Stefano, 2019. "A decision-support framework for the stowage of maritime containers in inland shipping," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 131(C), pages 1-23.
    4. Buddhi A. Weerasinghe & H. Niles Perera & Xiwen Bai, 2024. "Optimizing container terminal operations: a systematic review of operations research applications," Maritime Economics & Logistics, Palgrave Macmillan;International Association of Maritime Economists (IAME), vol. 26(2), pages 307-341, June.
    5. Franzkeit, Janna & Schwientek, Anne Kathrina & Jahn, Carlos, 2020. "Stowage planning for inland container vessels: A literature review," Chapters from the Proceedings of the Hamburg International Conference of Logistics (HICL), in: Jahn, Carlos & Kersten, Wolfgang & Ringle, Christian M. (ed.), Data Science in Maritime and City Logistics: Data-driven Solutions for Logistics and Sustainability. Proceedings of the Hamburg International Conferen, volume 30, pages 247-280, Hamburg University of Technology (TUHH), Institute of Business Logistics and General Management.
    6. R. Roberti & D. Pacino, 2018. "A Decomposition Method for Finding Optimal Container Stowage Plans," Service Science, INFORMS, vol. 52(6), pages 1444-1462, December.
    7. Gao, Yinping & Zhen, Lu, 2024. "A decision framework for decomposed stowage planning for containers," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 183(C).
    8. Christensen, Jonas & Erera, Alan & Pacino, Dario, 2019. "A rolling horizon heuristic for the stochastic cargo mix problem," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 123(C), pages 200-220.
    9. Goerigk, Marc & Knust, Sigrid & Le, Xuan Thanh, 2016. "Robust storage loading problems with stacking and payload constraints," European Journal of Operational Research, Elsevier, vol. 253(1), pages 51-67.
    10. Dalia Rashed & Amr Eltawil & Mohamed Gheith, 2021. "A Fuzzy Logic-Based Algorithm to Solve the Slot Planning Problem in Container Vessels," Logistics, MDPI, vol. 5(4), pages 1-24, September.
    11. Byung Kwon Lee & Joyce M. W. Low, 2022. "A constraint programming approach to capacity planning in container vessels," Maritime Economics & Logistics, Palgrave Macmillan;International Association of Maritime Economists (IAME), vol. 24(2), pages 415-438, June.
    12. Monaco, Maria Flavia & Sammarra, Marcello & Sorrentino, Gregorio, 2014. "The Terminal-Oriented Ship Stowage Planning Problem," European Journal of Operational Research, Elsevier, vol. 239(1), pages 256-265.
    13. Christensen, Jonas & Pacino, Dario, 2017. "A matheuristic for the Cargo Mix Problem with Block Stowage," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 97(C), pages 151-171.
    14. Parreño, Francisco & Pacino, Dario & Alvarez-Valdes, Ramon, 2016. "A GRASP algorithm for the container stowage slot planning problem," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 94(C), pages 141-157.
    15. Bruns, Florian & Knust, Sigrid & Shakhlevich, Natalia V., 2016. "Complexity results for storage loading problems with stacking constraints," European Journal of Operational Research, Elsevier, vol. 249(3), pages 1074-1081.
    16. Maroua Nouiri & Damien Trentesaux & Abdelghani Bekrar, 2019. "Towards Energy Efficient Scheduling of Manufacturing Systems through Collaboration between Cyber Physical Production and Energy Systems," Energies, MDPI, vol. 12(23), pages 1-30, November.
    17. Jonas Ahmt & Jonas Skott Sigtenbjerggaard & Richard Martin Lusby & Jesper Larsen & David Ryan, 2016. "A new approach to the Container Positioning Problem," Flexible Services and Manufacturing Journal, Springer, vol. 28(4), pages 617-643, December.
    18. Kong, Lingrui & Ji, Mingjun & Gao, Zhendi, 2021. "Joint optimization of container slot planning and truck scheduling for tandem quay cranes," European Journal of Operational Research, Elsevier, vol. 293(1), pages 149-166.
    19. Chien-Chang Chou & Pao-Yi Fang, 2021. "Applying expert knowledge to containership stowage planning: an empirical study," Maritime Economics & Logistics, Palgrave Macmillan;International Association of Maritime Economists (IAME), vol. 23(1), pages 4-27, March.
    20. Ding, Ding & Chou, Mabel C., 2015. "Stowage planning for container ships: A heuristic algorithm to reduce the number of shifts," European Journal of Operational Research, Elsevier, vol. 246(1), pages 242-249.
    21. Rune Larsen & Dario Pacino, 2021. "A heuristic and a benchmark for the stowage planning problem," Maritime Economics & Logistics, Palgrave Macmillan;International Association of Maritime Economists (IAME), vol. 23(1), pages 94-122, March.
    22. Berit Dangaard Brouer & Christian Vad Karsten & David Pisinger, 2017. "Optimization in liner shipping," 4OR, Springer, vol. 15(1), pages 1-35, March.
    23. Korach, Aleksandra & Brouer, Berit Dangaard & Jensen, Rune Møller, 2020. "Matheuristics for slot planning of container vessel bays," European Journal of Operational Research, Elsevier, vol. 282(3), pages 873-885.
    24. Gharehgozli, A.H. & Roy, D. & de Koster, M.B.M., 2014. "Sea Container Terminals," ERIM Report Series Research in Management ERS-2014-009-LIS, Erasmus Research Institute of Management (ERIM), ERIM is the joint research institute of the Rotterdam School of Management, Erasmus University and the Erasmus School of Economics (ESE) at Erasmus University Rotterdam.
    25. Berit Dangaard Brouer & Christian Vad Karsten & David Pisinger, 2018. "Optimization in liner shipping," Annals of Operations Research, Springer, vol. 271(1), pages 205-236, December.

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