Annals of Operations Research

, Volume 192, Issue 1, pp 123–140

Robust berth scheduling with uncertain vessel delay and handling time


DOI: 10.1007/s10479-010-0820-0

Cite this article as:
Xu, Y., Chen, Q. & Quan, X. Ann Oper Res (2012) 192: 123. doi:10.1007/s10479-010-0820-0


In container terminals, the actual arrival time and handling time of a vessel often deviate from the scheduled ones. Being the input to yard space allocation and crane planning, berth allocation is one of the most important activities in container terminals. Any change of berth plan may lead to significant changes of other operations, deteriorating the reliability and efficiency of terminal operations. In this paper, we study a robust berth allocation problem (RBAP) which explicitly considers the uncertainty of vessel arrival delay and handling time. Time buffers are inserted between the vessels occupying the same berthing location to give room for uncertain delays. Using total departure delay of vessels as the service measure and the length of buffer time as the robustness measure, we formulate RBAP to balance the service level and plan robustness. Based on the properties of the optimal solution, we develop a robust berth scheduling algorithm (RBSA) that integrates simulated annealing and branch-and-bound algorithm. To evaluate our model and algorithm design, we conduct computational study to show the effectiveness of the proposed RBSA algorithm, and use simulation to validate the robustness and service level of the RBAP formulation.


Container terminal Berth allocation problem Simulated annealing algorithm Robustness 


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Copyright information

© Springer Science+Business Media, LLC 2011

Authors and Affiliations

  1. 1.Department of Logistics Management, TEDA CollegeNankai UniversityTianjinChina
  2. 2.Center for Logistics TechnologyNankai UniversityTianjinChina

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