BAP and Time-variant QCSP Modeling and Optimization

Abstract

Enhanced data sharing between shipping companies and ports fosters seamless cooperation and more efficient use of terminal resources. This study addresses the integrated Berth Allocation Problem (BAP) and Time-variant Quay Crane Scheduling Problem (QCSP) in container terminals, aiming to optimize vessel berthing order, timing, and dynamic quay crane assignments. A Mixed Integer Linear Programming (MILP) model is introduced alongside a novel solution framework that combines Adaptive Large Neighborhood Search (ALNS) with Reinforcement Learning (RL). The integrated ALNS-RL framework sequentially updates ship sequences and quay crane schedules, enabling efficient convergence to high-quality solutions within limited iterations. Numerical experiments demonstrate that: 1) The proposed method yields superior solutions, reducing port stay time by 7.61% and quay crane idle rate by 13.48%; 2) The ratio of terminal berths to quay cranes significantly impacts operational efficiency, with an optimal allocation ratio identified; 3) The approach effectively handles instances from small to large scale, including problems with 30 berths and 90 vessels. Furthermore, the ALNS-RL framework outperforms both standard ALNS and a Hybrid Genetic Algorithm (HGA), achieving a minimal average deviation of 0.5% from the best solution—significantly better than ALNS (2.64%) and HGA (4.07%). While computationally efficient for small problems, the method demonstrates particular strength in large-scale instances, establishing its robustness for complex, real-world terminal scheduling applications.