OR Spectrum

, Volume 32, Issue 3, pp 501–517 | Cite as

Robust cyclic berth planning of container vessels

  • Maarten Hendriks
  • Marco Laumanns
  • Erjen Lefeber
  • Jan Tijmen Udding
Open Access
Regular Article


We consider a container terminal operator who faces the problem of constructing a cyclic berth plan. Such a plan defines the arrival and departure times of each cyclically calling vessel on a terminal, taking into account the expected number of containers to be handled and the necessary quay and crane capacity to do so. Conventional berth planning methods ignore the fact that, in practice, container terminal operator and shipping line agree upon an arrival window rather than an arrival time: if a vessel arrives within that window then a certain vessel productivity and hence departure time is guaranteed. The contributions of this paper are twofold. We not only minimize the peak loading of quay cranes in a port, but also explicitly take into account the arrival window agreements between the terminal operator and shipping lines. We present a robust optimization model for cyclic berth planning. Computational results on a real-world scenario for a container terminal in Antwerp show that the robust planning model can reach a substantial reduction in the crane capacity that is necessary to meet the window arrival agreements, as compared to a deterministic planning approach.


Container operations Berth planning Robustness Linear programming 


Open Access

This article is distributed under the terms of the Creative Commons Attribution Noncommercial License which permits any noncommercial use, distribution, and reproduction in any medium, provided the original author(s) and source are credited.


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Copyright information

© The Author(s) 2010

Authors and Affiliations

  • Maarten Hendriks
    • 1
  • Marco Laumanns
    • 2
  • Erjen Lefeber
    • 1
  • Jan Tijmen Udding
    • 1
    • 3
  1. 1.Systems Engineering Group, Department of Mechanical EngineeringEindhoven University of TechnologyEindhovenThe Netherlands
  2. 2.Institute for Operations ResearchETH ZurichZurichSwitzerland
  3. 3.PSA HNNAntwerpBelgium

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