Exact algorithm for the integrated berth and quay crane allocation problem considering tidal impact

To address the operational challenges caused by tidal fluctuations and limited anchorage capacity, we study the integrated berth allocation and quay crane assignment problem under tidal impact from a tactical perspective. We propose a novel mixed-integer model that, for the first time, simultaneously incorporates both tidal fluctuations in the navigation channel and the limited accommodation capacity of the anchorage area in the port basin. A tailored branch-and-price-and-cut (B&P&C) algorithm is developed, featuring heuristics for column initialisation, subgradient-based Lagrangian relaxation, two sets of valid inequalities, and a polynomial-time pricing algorithm. Extensive computational experiments based on real-world data demonstrate the effectiveness of the proposed method and reveal the impact of tides and anchorage capacity, providing actionable insights for port operations and planning.