Traveling salesman problem with time windows and a drone-utilizing intermediate points (TSPTWD-IP)

The fast growing of e-commerce has raised challenges to the last-mile logistics. Our study focuses on an emerging mode of transportation, i.e., a collaboration of a truck and an autonomous drone to deliver parcels. We develop a novel model of traveling salesman problem with time windows that jointly utilizes a truck and a drone in a coordinated manner. This model allows operating a drone not only on customers’ sites but also on other discrete intermediate points on arcs, and incorporates characteristics not considered previously, such as drone inoperable areas. We formulate this problem as a mixed integer linear program. We also develop a metaheuristic method that can solve the problems with up to 100 customers. Numerical experiments showed that our metaheuristic can find good solutions for many instances. Our model can cut the total delivery time by as much as 26% when compared to the traditional delivery model with only a single truck, and by 4% when compared to the existing model of a truck-and-drone operations that allows a drone to be launched or received at customers’ sites only.