A Framework for Container Terminal Operations: Metaheuristic Optimization and Simulation Analysis

Authors

https://doi.org/10.48314/anowa.v1i3.45

Abstract

Container unloading and loading operations in ports are addressed through the Berth Allocation Problem (BAP). Developing container terminal models and methods that enhance operational efficiency is undeniably essential for supporting maritime ports in managing increasing container flows within global supply chains. Consequently, recent years have witnessed a growing body of research literature aimed at advancing quayside operations. This study first examines the theoretical framework of the Quay Crane Scheduling Problem (QCSP) and Quay Crane Assignment Problem (QCAP) as presented in existing literature. We then formally define these problems within deterministic and sequencing contexts. The research employs berth modeling alongside Genetic Algorithms (GAs) and Particle Swarm Optimization (PSO) for deterministic scenarios, while stochastic conditions are addressed through berth simulation. Given the NP-Hard nature of the problem, obtaining optimal solutions within reasonable timeframes is infeasible. Thus, we implement metaheuristic approaches—GA, PSO, and simulation of model—to allocate vessels to berths efficiently.     

Keywords:

Simulation, Mathematical modelling, Quay crane scheduling problem, Quay crane assignment problem, Genetic algorithm, Particle swarm optimization, Metaheuristic

References

  1. [1] Bierwirth, C., & Meisel, F. (2015). A follow-up survey of berth allocation and quay crane scheduling problems in container terminals. European journal of operational research, 244(3), 675–689. https://doi.org/10.1016/j.ejor.2014.12.030
  2. [2] Bierwirth, C., & Meisel, F. (2010). A survey of berth allocation and quay crane scheduling problems in container terminals. European journal of operational research, 202(3), 615–627. https://doi.org/10.1016/j.ejor.2009.05.031
  3. [3] Lee, D. H., & Qiu Wang, H. (2010). Integrated discrete berth allocation and quay crane scheduling in port container terminals. Engineering optimization, 42(8), 747–761. https://doi.org/10.1080/03052150903406571
  4. [4] Shintani, K., Imai, A., Nishimura, E., & Papadimitriou, S. (2007). The container shipping network design problem with empty container repositioning. Transportation research part e: Logistics and transportation review, 43(1), 39–59. https://doi.org/10.1016/j.tre.2005.05.003
  5. [5] Chen, X., Wang, X., & Chan, H. K. (2017). Manufacturer and retailer coordination for environmental and economic competitiveness: A power perspective. Transportation research part e: Logistics and transportation review, 97, 268–281. https://doi.org/10.1016/j.tre.2016.11.007
  6. [6] Han, X., Lu, Z., & Xi, L. (2010). A proactive approach for simultaneous berth and quay crane scheduling problem with stochastic arrival and handling time. European journal of operational research, 207(3), 1327–1340. https://doi.org/10.1016/j.ejor.2010.07.018
  7. [7] Makhado, N., Paepae, T., Sejeso, M., & Harley, C. (2025). Berth allocation and quay crane scheduling in port operations: A systematic review. Journal of marine science and engineering, 13(7), 1339. https://doi.org/10.3390/jmse13071339
  8. [8] Imai, A., Nishimura, E., & Papadimitriou, S. (2001). The dynamic berth allocation problem for a container port. Transportation research part b: methodological, 35(4), 401–417. https://doi.org/10.1016/S0191-2615(99)00057-0
  9. [9] Imai, A., Nishimura, E., & Papadimitriou, S. (2003). Berth allocation with service priority. Transportation research part b: methodological, 37(5), 437–457. https://doi.org/10.1016/S0191-2615(02)00023-1
  10. [10] Cordeau, J. F., Laporte, G., Legato, P., & Moccia, L. (2005). Models and tabu search heuristics for the berth-allocation problem. Transportation science, 39(4), 526–538. https://doi.org/10.1287/trsc.1050.0120
  11. [11] Hansen, P., Oğuz, C., & Mladenović, N. (2008). Variable neighborhood search for minimum cost berth allocation. European journal of operational research, 191(3), 636–649. https://doi.org/10.1016/j.ejor.2006.12.057
  12. [12] Moccia, L., Cordeau, J. F., Gaudioso, M., & Laporte, G. (2006). A branch-and-cut algorithm for the quay crane scheduling problem in a container terminal. Naval research logistics (nrl), 53(1), 45–59. https://doi.org/10.1002/nav.20121
  13. [13] Sammarra, M., Cordeau, J. F., Laporte, G., & Monaco, M. F. (2007). A tabu search heuristic for the quay crane scheduling problem. Journal of scheduling, 10(4), 327–336. https://doi.org/10.1007/s10951-007-0029-5
  14. [14] Lu, Z., Han, X., Xi, L., & Erera, A. L. (2012). A heuristic for the quay crane scheduling problem based on contiguous bay crane operations. Computers & operations research, 39(12), 2915–2928. https://doi.org/10.1016/j.cor.2012.02.013
  15. [15] Li, H., & Li, X. (2022). A branch-and-bound algorithm for the bi-objective quay crane scheduling problem based on efficiency and energy. Mathematics, 10(24), 4705. https://doi.org/10.3390/math10244705
  16. [16] Park, K., & Bae, H. (2024). A surrogate model for quay crane scheduling problem. https://arxiv.org/abs/2411.03324
  17. [17] Liu, C. I., Jula, H., & Ioannou, P. A. (2002). Design, simulation, and evaluation of automated container terminals. IEEE transactions on intelligent transportation systems, 3(1), 12–26. https://doi.org/10.1109/6979.994792
  18. [18] Meisel, F., & Bierwirth, C. (2009). Heuristics for the integration of crane productivity in the berth allocation problem. Transportation research part e: Logistics and transportation review, 45(1), 196–209. https://doi.org/10.1016/j.tre.2008.03.001
  19. [19] Giallombardo, G., Moccia, L., Salani, M., & Vacca, I. (2010). Modeling and solving the tactical berth allocation problem. Transportation research part b: methodological, 44(2), 232–245. https://doi.org/10.1016/j.trb.2009.07.003
  20. [20] Duan, Y., Ren, H., Xu, F., Yang, X., & Meng, Y. (2023). Bi-objective integrated scheduling of quay cranes and automated guided vehicles. Journal of marine science and engineering, 11(8), 1492. https://doi.org/10.3390/jmse11081492
  21. [21] Nishimura, E., Imai, A., & Papadimitriou, S. (2001). Berth allocation planning in the public berth system by genetic algorithms. European journal of operational research, 131(2), 282–292. https://doi.org/10.1016/S0377-2217(00)00128-4
  22. [22] Borumand, A., & Beheshtinia, M. A. (2018). A developed genetic algorithm for solving the multi-objective supply chain scheduling problem. Kybernetes, 47(7), 1401–1419. https://doi.org/10.1108/K-07-2017-0275
  23. [23] Xu, D., Li, C. L., & Leung, J. Y. T. (2012). Berth allocation with time-dependent physical limitations on vessels. European journal of operational research, 216(1), 47–56. https://doi.org/10.1016/j.ejor.2011.07.012
  24. [24] P Pérez-Rodríguez, R. (2021). A hybrid estimation of distribution algorithm for the quay crane scheduling problem. Mathematical and computational applications, 26(3), 64. https://doi.org/10.3390/mca26030064
  25. [25] Dehghani, M., Trojovská, E., & Trojovský, P. (2022). A new human-based metaheuristic algorithm for solving optimization problems on the base of simulation of driving training process. Scientific reports, 12(1), 9924. https://www.nature.com/articles/s41598-022-14225-7
  26. [26] Almufti, S. M. (2025). Metaheuristics algorithms: Overview, applications, and modifications. Publisher: Deep Science Publishing. https://doi.org/10.70593/978-93-7185-454-2
  27. [27] Tomar, V., Bansal, M., & Singh, P. (2024). Metaheuristic algorithms for optimization: A brief review. Engineering proceedings, 59(1), 238. https://doi.org/10.3390/engproc2023059238
  28. [28] Dragović, B., Park, N. K., Radmilović, Z., & Maraš, V. (2005). Simulation modelling of ship-berth link with priority service. Maritime economics & logistics, 7(4), 316–335. https://doi.org/10.1057/palgrave.mel.9100141
  29. [29] Thengvall, B. G., Hall, S. N., & Deskevich, M. P. (2025). Measuring the effectiveness and efficiency of simulation optimization metaheuristic algorithms. Journal of heuristics, 31(1), 12. https://doi.org/10.1007/s10732-025-09549-2
  30. [30] Gambardella, L. M., Rizzoli, A. E., & Zaffalon, M. (1998). Simulation and planning of an intermodal container terminal. Simulation, 71(2), 107–116. https://doi.org/10.1177/003754979807100205

Downloads

Published

2025-09-27

Issue

Vol. 1 No. 3 (2025): Annals of Optimization With Applications (ANOWA)

Section

Articles

How to Cite

Haddad, R. ., Hamisheh Bahar, M. ., & Varmazyar, M. . (2025). A Framework for Container Terminal Operations: Metaheuristic Optimization and Simulation Analysis. Annals of Optimization With Applications, 1(3), 141-152. https://doi.org/10.48314/anowa.v1i3.45