The multi-vehicle truck-and-robot routing problem for last-mile delivery

Abstract

Last-mile delivery with autonomous robots launched from dedicated delivery trucks is a promising approach to reducing logistics costs and inner-city traffic. Current literature for this innovative concept bases upon the use of a single truck to pick up multiple robots from robot depots and release them for delivery. This limits the practical use for industry applications in bigger cities. The demand for home deliveries is steadily increasing, and with that, the requirements for potential delivery by robots. The truck-and-robot concept therefore needs to be refined to meet these requirements by a fleet of delivery trucks.We generalize the truck-and-robot delivery with robot depots for the simultaneous routing of multiple trucks. This means that a fleet of trucks is available, and customer orders and robot deliveries must be assigned to delivery tours. We formulate this problem as multi-vehicle truck-and-robot routing problem. This extension includes routing multiple trucks and the corresponding clustering decisions while choosing the optimal drop-off points for robots and their delivery. We develop a tailored heuristic solution approach based on a novel neighborhood search, the Set Improvement Neighborhood Search (SINS). We show that transportation costs can be reduced by up to 24% using our integrated multi-vehicle routing and robot scheduling approach compared to a sequential cluster-first-route-second approach. Complementary experiments show a 62% savings potential compared to conventional truck delivery. We derive structural insights into the novel delivery system by analyzing the impact of changing customer distributions, delivery time windows, and truck or robot availability.