Collaborative Scheduling of Yard Cranes, External Trucks, and Rail-Mounted Gantry Cranes for Sea–Rail Intermodal Containers Under Port–Railway Separation Mode

The spatial separation of port yards and railway hubs, which relies on external truck drayage as a necessary link, hampers the seamless transshipment of sea–rail intermodal containers between ports and railway hubs. This creates challenges in synchronizing yard cranes (YCs) at the port terminal, external trucks (ETs) on the road, and rail-mounted gantry cranes (RMGs) at the railway hub. However, most existing studies focus on equipment scheduling or container transshipment organization under the port–railway integration mode, often overlooking critical time window constraints, such as train schedules and export container delivery deadlines. Therefore, this study investigates the collaborative scheduling of YCs, ETs, and RMGs for synchronized loading and unloading under the port–railway separation mode. A mixed-integer programming (MIP) model is developed to minimize the maximum makespan of all tasks and the empty-load time of ETs, considering practical time window constraints. Given the NP-hard complexity of this problem, an improved genetic algorithm (GA) integrated with a “First Accessible Machinery” rule is designed. Extensive numerical experiments are conducted to validate the correctness of the proposed model and the performance of the solution algorithm. The improved GA demonstrates a 6.08% better solution quality and a 97.94% reduction in computation time compared to Gurobi for small-scale instances. For medium to large-scale instances, it outperforms the adaptive large neighborhood search (ALNS) algorithm by 1.51% in solution quality and reduces computation time by 45.71%. Furthermore, the impacts of objective weights, equipment configuration schemes, port–railway distance, and time window width are analyzed to provide valuable managerial insights for decision-making to improve the overall efficiency of sea–rail intermodal systems.