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A Variable Neighborhood Search Algorithm for the Integrated Berth Allocation and Quay Crane Assignment Problem

Author

Listed:
  • Xiafei Xie

    (School of Traffic & Transportation Engineering, Central South University, Changsha 410075, China)

  • Bin Ji

    (School of Traffic & Transportation Engineering, Central South University, Changsha 410075, China)

  • Samson S. Yu

    (School of Engineering, Deakin University, Melbourne, VIC 31125, Australia)

Abstract

To improve the utilization of port resources and reduce the consumption of resources due to vessel waiting and delays, this paper investigates the Berth Allocation and Quay Crane Assignment Problem (BACAP) in container ports, focusing on the Quay Crane (QC) profile. The objective is to assign berths, berthing times, and QC profiles to vessels arriving at the port within a given planning horizon, thereby extending the traditional BACAP framework. To minimize the sum of idle time costs caused by vessel waiting and delay time costs due to late vessel departures, a mixed-integer linear programming (MILP) model is proposed. Additionally, a variable neighborhood search (VNS) algorithm is designed to solve the model, tailored to the specific characteristics of the problem. The proposed MILP model and VNS algorithm are evaluated using two sets of BACAP instances. The numerical results demonstrate the effectiveness of both the model and the algorithm, showing that VNS efficiently and reliably solves instances of various sizes. Furthermore, each neighborhood structure contributes uniquely to the iterative process. This study also analyzes the impact of different idle and delay costs on BACAP, providing valuable managerial insights. The proposed framework contributes to enhancing operational efficiency and supports sustainable port management.

Suggested Citation

  • Xiafei Xie & Bin Ji & Samson S. Yu, 2025. "A Variable Neighborhood Search Algorithm for the Integrated Berth Allocation and Quay Crane Assignment Problem," Sustainability, MDPI, vol. 17(9), pages 1-29, April.
    • Handle: RePEc:gam:jsusta:v:17:y:2025:i:9:p:4022-:d:1645955
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    References listed on IDEAS

    as
    1. Fanrui Xie & Tao Wu & Canrong Zhang, 2019. "A Branch-and-Price Algorithm for the Integrated Berth Allocation and Quay Crane Assignment Problem," Transportation Science, INFORMS, vol. 53(5), pages 1427-1454, September.
    2. Türkoğulları, Yavuz B. & Taşkın, Z. Caner & Aras, Necati & Altınel, İ. Kuban, 2016. "Optimal berth allocation, time-variant quay crane assignment and scheduling with crane setups in container terminals," European Journal of Operational Research, Elsevier, vol. 254(3), pages 985-1001.
    3. Türkoğulları, Yavuz B. & Taşkın, Z. Caner & Aras, Necati & Altınel, İ. Kuban, 2014. "Optimal berth allocation and time-invariant quay crane assignment in container terminals," European Journal of Operational Research, Elsevier, vol. 235(1), pages 88-101.
    4. Feng Li & Jiuh-Biing Sheu & Zi-You Gao, 2015. "Solving the Continuous Berth Allocation and Specific Quay Crane Assignment Problems with Quay Crane Coverage Range," Transportation Science, INFORMS, vol. 49(4), pages 968-989, November.
    5. Wagner, Stefan & Mönch, Lars, 2023. "A variable neighborhood search approach to solve the order batching problem with heterogeneous pick devices," European Journal of Operational Research, Elsevier, vol. 304(2), pages 461-475.
    6. Meisel, Frank & Bierwirth, Christian, 2009. "Heuristics for the integration of crane productivity in the berth allocation problem," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 45(1), pages 196-209, January.
    7. Hansen, Pierre & Mladenovic, Nenad, 2001. "Variable neighborhood search: Principles and applications," European Journal of Operational Research, Elsevier, vol. 130(3), pages 449-467, May.
    8. Xiang, Xi & Liu, Changchun, 2021. "An almost robust optimization model for integrated berth allocation and quay crane assignment problem," Omega, Elsevier, vol. 104(C).
    9. Wang, Tingsong & Wang, Xinchang & Meng, Qiang, 2018. "Joint berth allocation and quay crane assignment under different carbon taxation policies," Transportation Research Part B: Methodological, Elsevier, vol. 117(PA), pages 18-36.
    10. Correcher, Juan F. & Alvarez-Valdes, Ramon & Tamarit, Jose M., 2019. "New exact methods for the time-invariant berth allocation and quay crane assignment problem," European Journal of Operational Research, Elsevier, vol. 275(1), pages 80-92.
    11. Imai, Akio & Chen, Hsieh Chia & Nishimura, Etsuko & Papadimitriou, Stratos, 2008. "The simultaneous berth and quay crane allocation problem," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 44(5), pages 900-920, September.
    12. Giallombardo, Giovanni & Moccia, Luigi & Salani, Matteo & Vacca, Ilaria, 2010. "Modeling and solving the Tactical Berth Allocation Problem," Transportation Research Part B: Methodological, Elsevier, vol. 44(2), pages 232-245, February.
    13. Li, Bokang & Afkhami, Payam & Khayamim, Razieh & Borowska-Stefańska, Marta & Wiśniewski, Szymon & Fathollahi-Fard, Amir M. & Ozkul, Seckin & Dulebenets, Maxim A., 2025. "An intelligent hyperheuristic algorithm for the berth allocation and scheduling problem at marine container terminals," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 198(C).
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