Networks and Spatial Economics

, Volume 19, Issue 3, pp 903–927 | Cite as

A Dynamic and Flexible Berth Allocation Model with Stochastic Vessel Arrival Times

  • Shangyao Yan
  • Chung-Cheng LuEmail author
  • Jun-Hsiao Hsieh
  • Han-Chun Lin


This study proposes a berth-flow network modeling approach to deal with the dynamic berth allocation problem (DBAP) with stochastic vessel arrival times. In this approach, uncertain vessel arrival times are represented using discrete probability distributions and a flexible berth allocation scheme based on the blocking plan concept is incorporated into the model to effectively utilize wharf space. This new model is referred to as the stochastic dynamic (vessel arrival) and flexible (berth space) berth allocation problem (SDFBAP) model. The aim is to minimize the sum of the expected values of unanticipated schedule delay costs and the penalties for being unable to service all vessels within the planning horizon. The proposed model is formulated as an integer multi-commodity network flow problem which can be solved with off-the-shelf solvers. Computational experiments are conducted using a real example to demonstrate the effectiveness and efficiency of the SDFBAP model. A simulation-based approach is adopted to evaluate the SDFBAP model. A number of scenario analyses are also conducted to gain insight into important model parameters.


Maritime transport Berth allocation Network flow Stochastic vessel arrival times Multi-commodity network flow problem 



This research was supported by the grants (MOST-107-2221-E-008-019 and MOST 105-2410-H-009-062-MY3) from the Ministry of Science and Technology, Taiwan. The authors would also like to thank the anonymous referees for their helpful comments and suggestions on the paper. The work presented in this paper remains the sole responsibility of the authors.


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© Springer Science+Business Media, LLC, part of Springer Nature 2019

Authors and Affiliations

  1. 1.Department of Civil EngineeringNational Central UniversityTaoyuanTaiwan
  2. 2.Department of Transportation and Logistics ManagementNational Chiao Tung UniversityHsinchuTaiwan

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