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Scheduling vessels and container-yard operations with conflicting objectives


  • Endre Boros
  • Lei Lei
  • Yao Zhao


  • Hua Zhong


We consider the problem of coordinating the operations of two supply chain partners: a foreign shipping company and a domestic port. The two partners have conflicting business objectives, and the issue is to determine the optimal cycle time, by which the shipping company removes the empty containers from the domestic port, so that the joint profit of the two partners is maximized. The domestic port prefers a shorter cycle time to mitigate its empty container accumulation and land use problems, while the shipping company wishes a longer cycle time to save its expensive vessel capacities. We propose an iterative procedure to search for this optimal cycle time. In each iteration, a candidate cycle time is evaluated by solving a deterministic vessel scheduling problem and a stochastic container-yard capacity optimization problem. We prove the properties of the vessel scheduling problem, derive the optimality condition under which the vessel scheduling problem can be decomposed, and show that the profit function of the domestic port is convex and thus the optimal container-yard capacity can be determined efficiently. Empirical observations on the algorithm computational performance collected from over 300 randomly generated test cases under various problem settings are reported. Copyright Springer Science+Business Media, LLC 2008

Suggested Citation

  • Endre Boros & Lei Lei & Yao Zhao & Hua Zhong, 2008. "Scheduling vessels and container-yard operations with conflicting objectives," Annals of Operations Research, Springer, vol. 161(1), pages 149-170, July.
  • Handle: RePEc:spr:annopr:v:161:y:2008:i:1:p:149-170:10.1007/s10479-007-0260-7
    DOI: 10.1007/s10479-007-0260-7

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    References listed on IDEAS

    1. Sambracos, E. & Paravantis, J. A. & Tarantilis, C. D. & Kiranoudis, C. T., 2004. "Dispatching of small containers via coastal freight liners: The case of the Aegean Sea," European Journal of Operational Research, Elsevier, vol. 152(2), pages 365-381, January.
    2. Arie Harel, 1990. "Convexity Properties of the Erlang Loss Formula," Operations Research, INFORMS, vol. 38(3), pages 499-505, June.
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    4. Kjetil Fagerholt *, 2004. "Designing optimal routes in a liner shipping problem," Maritime Policy & Management, Taylor & Francis Journals, vol. 31(4), pages 259-268, October.
    5. Lode Li & Hongtao Zhang, 2000. "The Multistage Service Facility Start-Up and Capacity Model," Operations Research, INFORMS, vol. 48(3), pages 490-497, June.
    6. Marielle Christiansen & Kjetil Fagerholt & David Ronen, 2004. "Ship Routing and Scheduling: Status and Perspectives," Transportation Science, INFORMS, vol. 38(1), pages 1-18, February.
    7. H B Bendall & A F Stent, 2001. "A Scheduling Model for a High Speed Containership Service: A Hub and Spoke Short-Sea Application," Maritime Economics & Logistics, Palgrave Macmillan;International Association of Maritime Economists (IAME), vol. 3(3), pages 262-277, September.
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    Cited by:

    1. Ali Cheaitou & Pierre Cariou, 2019. "Greening of maritime transportation: a multi-objective optimization approach," Annals of Operations Research, Springer, vol. 273(1), pages 501-525, February.
    2. Kartikeya Puranam & Michael Katehakis, 2014. "On optimal bidding and inventory control in sequential procurement auctions: the multi period case," Annals of Operations Research, Springer, vol. 217(1), pages 447-462, June.
    3. Gang Chen & Liping Jiang, 2016. "Managing customer arrivals with time windows: a case of truck arrivals at a congested container terminal," Annals of Operations Research, Springer, vol. 244(2), pages 349-365, September.
    4. Pang, King-Wah & Xu, Zhou & Li, Chung-Lun, 2011. "Ship routing problem with berthing time clash avoidance constraints," International Journal of Production Economics, Elsevier, vol. 131(2), pages 752-762, June.


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