Berth allocation in dry bulk export terminals with channel restrictions

Abstract

Efficient berth allocation (BA) is critical to port management, as berthing time and location directly impact operational efficiency. In dry bulk export terminals, the BA problem becomes more complex due to deballasting delays and pre-deballasting procedures, particularly under restrictive channel conditions. Terminal operators must balance pre-deballasting requirements with timely berthing to minimize delays. To address these challenges, we formulate the BA problem as a dynamic program, enabling sequential decision-making for each ship at every stage. To address the extensive state-action space, we propose a hierarchical decision framework that divides each stage into four planning-level substages and one scheduling-level substage, each handled by a dedicated agent. The planning level determines berthing positions and ship sequence, while the scheduling level coordinates berthing, channel access, and deballasting timelines based on planning outcomes. We propose a Planning by Reinforcement Learning and Scheduling by Optimization (PRLSO) approach, where agents employ either reinforcement learning (RL) or optimization, depending on substage characteristics. By confining RL-based agents to a reduced decision space, we significantly reduce training complexity. Following this, the remaining scheduling problem is solved on a reduced scale free from computational challenge. Experimental results show that the proposed method generates high-quality solutions in near real-time, even for large-scale instances. The framework also improves training efficiency and supports industrial-scale implementation.