A multi-visit flexible-docking vehicle routing problem with drones for simultaneous pickup and delivery services.

• We study a multi-visit flexible-docking VRPD with simultaneous pickup and delivery. • A mixed-integer linear programming model for the proposed MFS-VRPD is formulated. • A tailored adaptive large neighborhood search metaheuristic is proposed. • Numerical experiments show the proposed method achieves a significant cost saving. • The performance of incorporating the three rich features into VRPD is discussed. This study investigates a multi-visit flexible-docking vehicle routing problem that uses a truck and drone fleet to fulfill pickup and delivery requests in rural areas. In this collaborative truck–drone system, each drone may serve multiple customers per trip (multi-visit services), dock to the same or different truck from where it launched (flexible docking), and perform simultaneous pickup and delivery. These characteristics complicate the temporal, spatial, and loading synchronization for trucks and drones, making the decisions of order allocation and vehicle routing highly interdependent and intractable. This problem is formulated as a mixed-integer linear programming model and solved by a tailored adaptive large neighborhood search metaheuristic. Numerical experiments are conducted on sparse rural networks to demonstrate the efficiency of the proposed method. We observe that the proposed truck–drone system shows an average cost saving of 34% compared to the truck-only case. Moreover, deep insights into the impacts of multi-visit services, flexible docking, and simultaneous pickup and delivery on the performance of the truck–drone system are discussed. [ABSTRACT FROM AUTHOR]