Multi-terminal continuous and dynamic berth allocation problem considering tidal time windows and channel constraints

Berth allocation is a crucial scheduling task for port operations, as it influences all subsequent arrangements. Inefficient berth allocation often results in port congestion, which is a major challenge for many ports nowadays. To alleviate container port congestion and enhance operational efficiency, this study proposes a novel multi-terminal dynamic berth allocation problem considering tidal time windows and channel constraints (MDBAP_TC). An integer programming model is developed to minimize total costs. To solve the MDBAP_TC, a cluster-enhanced hybrid particle swarm optimization (HCPSO) algorithm with an embedded solver is developed. This algorithm incorporates a linearly decreasing inertia weight strategy (to update its inertia weight), and introduces an adaptive adjustment mechanism that guides the population toward improved solutions with a specified probability. For comparative analysis, three additional algorithms are also developed: a hybrid particle swarm optimization algorithm with solver (HPSO), a hybrid genetic algorithm (HGA) with solver, and a Lagrange relaxation with sub-gradient (LS) optimization. Numerical experiments, conducted on 100 small- and 30 medium-scale instances, validate the effectiveness of the proposed model. The results show that HCPSO achieves solution quality comparable to that of the Gurobi solver in 93 instances and outperforms HGA, HPSO, and LS. Furthermore, the robustness of the model is demonstrated through tests on 20 sets of instances, highlighting its ability to handle variations in the number of vessels. A simulation study with 100 vessels validates that more effective berth allocation can be obtained by taking into account tidal time windows. Sensitivity analysis results indicate that key parameters of the proposed model should be adjusted by potential users based on specific real-world scenarios. Overall, this study offers a valuable decision-making tool for port schedulers seeking to optimize berth resource allocation, alleviate port congestion, and improve terminal operational efficiency.