Container Slot Allocation with Empty Container Repositioning: A Multi-Objective Optimization Approach

Trade imbalances and equipment shortages are making it increasingly important to coordinate container slot allocation with empty container repositioning on liner services. This paper develops an integrated bi-objective mixed-integer model for voyage-level slot planning on a fixed cyclic route. The model jointly decides booking acceptance, inter-voyage shipment, and empty repositioning with port-level empty-inventory dynamics and leg-based vessel capacity constraints. We optimize two conflicting objectives: maximizing operational profit and minimizing empty container TEU-miles. To solve the model at practical scales, we propose a hybrid evolutionary framework, NSGA-II-RL, which uses a lightweight Q-learning controller to adapt operator and repair choices during NSGA-II evolution. Computational experiments on representative service route instances show that NSGA-II-RL produces diverse Pareto-efficient solutions and improves hypervolume relative to fixed-operator and random-control variants, revealing clear trade-offs between profitability and repositioning intensity.