A lock and port resource collaborative scheduling method based on mathematical programming model and heuristic

Congestions caused by insufficient ship lock capacity is a significant challenge for inland waterway transportation. This research addresses the lock and port resources collaborative scheduling problem (LPRCSP), aiming to minimize the overall stay time of ships within the lock-port system. The LPRCSP is mapped to a variant of flexible job shop scheduling problem (FJSP), considering various ship routes, lock chambers, berths, and quay crane allocation. A mixed integer linear programming (MILP) model is developed, and a solution framework based on hybrid heuristic is proposed. The LPRCSP is converted to a discrete combinatorial optimization problem for searching the optimal ship-lockage-berth allocation scheme, with ship placement and lockage-berth scheduling problems integrated. The adaptive large neighborhood search (ALNS) framework is adopted with destroy and repair operators tailored, where ship placement heuristic and Floyd-Warshall algorithm are integrated for solving the ship placement and lockage-berth scheduling problems. To evaluate the proposed model and methods, instances derived from the Albertkanaal and Yangtze River are tested. Numerical results demonstrate that the MILP-based method can efficiently solve instances with up to 60 ships considering a time horizon of one day, while the hybrid heuristic (HH) provides high-quality solutions for varying instance sizes. Sensitivity analysis on the Three Gorges lock-port system suggests the optimal ship passing ratios and quay crane numbers under different traffic conditions. The results also demonstrate that coordinated scheduling of lock and port effectively reduce ship’s waiting time, especially during heavy traffic.