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A branch‐and‐cut algorithm for the quay crane scheduling problem in a container terminal

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  • Luigi Moccia
  • Jean‐François Cordeau
  • Manlio Gaudioso
  • Gilbert Laporte

Abstract

The quay crane scheduling problem consists of determining a sequence of unloading and loading movements for cranes assigned to a vessel in order to minimize the vessel completion time as well as the crane idle times. Idle times originate from interferences between cranes since these roll on the same rails and a minimum safety distance must be maintained between them. The productivity of container terminals is often measured in terms of the time necessary to load and unload vessels by quay cranes, which are the most important and expensive equipment used in ports. We formulate the quay crane scheduling problem as a vehicle routing problem with side constraints, including precedence relationships between vertices. For small size instances our formulation can be solved by CPLEX. For larger ones we have developed a branch‐and‐cut algorithm incorporating several families of valid inequalities, which exploit the precedence constraints between vertices. © 2005 Wiley Periodicals, Inc. Naval Research Logistics, 2006

Suggested Citation

  • Luigi Moccia & Jean‐François Cordeau & Manlio Gaudioso & Gilbert Laporte, 2006. "A branch‐and‐cut algorithm for the quay crane scheduling problem in a container terminal," Naval Research Logistics (NRL), John Wiley & Sons, vol. 53(1), pages 45-59, February.
    • Handle: RePEc:wly:navres:v:53:y:2006:i:1:p:45-59
    DOI: 10.1002/nav.20121
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    1. Defeng Sun & Lixin Tang & Roberto Baldacci & Zihan Chen, 2024. "A Decomposition Method for the Group-Based Quay Crane Scheduling Problem," INFORMS Journal on Computing, INFORMS, vol. 36(2), pages 543-570, March.
    2. Nils Boysen & Florian Jaehn & Erwin Pesch, 2011. "Scheduling Freight Trains in Rail-Rail Transshipment Yards," Transportation Science, INFORMS, vol. 45(2), pages 199-211, May.
    3. Yongpei Guan & Kang-Hung Yang & Zhili Zhou, 2013. "The crane scheduling problem: models and solution approaches," Annals of Operations Research, Springer, vol. 203(1), pages 119-139, March.
    4. Frank Meisel, 2011. "The quay crane scheduling problem with time windows," Naval Research Logistics (NRL), John Wiley & Sons, vol. 58(7), pages 619-636, October.
    5. Wang, Chong & Liu, Kaiyuan & Zhang, Canrong & Miao, Lixin, 2024. "Distributionally robust chance-constrained optimization for the integrated berth allocation and quay crane assignment problem," Transportation Research Part B: Methodological, Elsevier, vol. 182(C).
    6. Kizilay, Damla & Hentenryck, Pascal Van & Eliiyi, Deniz T., 2020. "Constraint programming models for integrated container terminal operations," European Journal of Operational Research, Elsevier, vol. 286(3), pages 945-962.
    7. Qin, Tianbao & Du, Yuquan & Chen, Jiang Hang & Sha, Mei, 2020. "Combining mixed integer programming and constraint programming to solve the integrated scheduling problem of container handling operations of a single vessel," European Journal of Operational Research, Elsevier, vol. 285(3), pages 884-901.
    8. Abdellah Salhi & Ghazwan Alsoufi & Xinan Yang, 2019. "An evolutionary approach to a combined mixed integer programming model of seaside operations as arise in container ports," Annals of Operations Research, Springer, vol. 272(1), pages 69-98, January.
    9. Sun, Defeng & Tang, Lixin & Baldacci, Roberto, 2019. "A Benders decomposition-based framework for solving quay crane scheduling problems," European Journal of Operational Research, Elsevier, vol. 273(2), pages 504-515.
    10. Shoufeng Ma & Hongming Li & Ning Zhu & Chenyi Fu, 2021. "Stochastic programming approach for unidirectional quay crane scheduling problem with uncertainty," Journal of Scheduling, Springer, vol. 24(2), pages 137-174, April.
    11. J Blazewicz & T C E Cheng & M Machowiak & C Oguz, 2011. "Berth and quay crane allocation: a moldable task scheduling model," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 62(7), pages 1189-1197, July.
    12. Zhixing Luo & Hu Qin & Wenbin Zhu & Andrew Lim, 2016. "Branch‐and‐price‐and‐cut for the manpower routing problem with synchronization constraints," Naval Research Logistics (NRL), John Wiley & Sons, vol. 63(2), pages 138-171, March.
    13. Shucheng Yu & Shuaian Wang & Lu Zhen, 2017. "Quay crane scheduling problem with considering tidal impact and fuel consumption," Flexible Services and Manufacturing Journal, Springer, vol. 29(3), pages 345-368, December.
    14. Frank Meisel & Christian Bierwirth, 2013. "A Framework for Integrated Berth Allocation and Crane Operations Planning in Seaport Container Terminals," Transportation Science, INFORMS, vol. 47(2), pages 131-147, May.
    15. Jayanth Krishna Mogali & Joris Kinable & Stephen F. Smith & Zachary B. Rubinstein, 2021. "Scheduling for multi-robot routing with blocking and enabling constraints," Journal of Scheduling, Springer, vol. 24(3), pages 291-318, June.
    16. Bektaş, Tolga & Ehmke, Jan Fabian & Psaraftis, Harilaos N. & Puchinger, Jakob, 2019. "The role of operational research in green freight transportation," European Journal of Operational Research, Elsevier, vol. 274(3), pages 807-823.
    17. Guvenc Dik & Erhan Kozan, 2017. "A flexible crane scheduling methodology for container terminals," Flexible Services and Manufacturing Journal, Springer, vol. 29(1), pages 64-96, March.
    18. T. R. Lalita & G. S. R. Murthy, 2022. "Compact ILP formulations for a class of solutions to berth allocation and quay crane scheduling problems," OPSEARCH, Springer;Operational Research Society of India, vol. 59(1), pages 413-439, March.
    19. Lu Zhen & Shuaian Wang & Kai Wang, 2016. "Terminal allocation problem in a transshipment hub considering bunker consumption," Naval Research Logistics (NRL), John Wiley & Sons, vol. 63(7), pages 529-548, October.

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