Routing and scheduling problem for mothership and drones in shore-to-ship delivery

As vessel delays and port congestion intensify, shore-to-ship deliveries face increasing challenges. While drones provide fast and flexible delivery, their limited payload and battery endurance restrict independent operations in maritime environments. Existing studies largely overlook the coordination of a mothership and drones under dynamic constraints in shore-to-ship delivery. To address these gaps, this study explores a mothership-drone system, where the mothership supports drone takeoff and landing, provides battery resupply, and delivers supplies to customer vessels, thereby extending drone range and improving delivery efficiency. An integer linear programming (ILP) model based on a time-expanded network is developed to optimize routing and scheduling, minimizing total delivery costs, including mothership sailing time, drone flight time, and fixed deployment costs. The model accounts for critical operational constraints, such as drone payload capacity, maximum flight duration, takeoff and landing nodes selection, and mothership-drone synchronization. To solve large-scale instances efficiently, an adaptive large neighborhood search (ALNS) algorithm with a tailored adjustment strategy is proposed. Experimental results show that the algorithm outperforms commercial solvers and benchmark heuristics in solution quality and computational efficiency, significantly improving the efficiency of generating feasible solutions. In addition, compared with the mothership-drone mode and the drone-only mode, the proposed mothership-drone coordination mode substantially reduces operating cost and improves service coverage.