Collaborative delivery problem of trucks and multiple drones: an en-route operation with flexible launch positions

Abstract

Drones are gradually being used in logistics, and collaborative systems combining trucks and drones are proposed for last-mile delivery. Therefore, it is a meaningful study to improve the efficiency of collaborative delivery of truck–drone system. Based on the truck–drone collaborative delivery problem with en-route operations, this paper introduces a new concept of flexible launch point, which is to set up multiple non-customer stops in the truck's route for launching drones. In light of this concept, an en-route operation with flexible positions in the truck–drone collaborative delivery problem is proposed. The problem is formulated as a mixed integer linear program that aims to minimize customer waiting times, determine the optimal route for the truck with multi-drones, and establish the optimal flexible launch positions for the drones. We developed a variable neighborhood search algorithm and conducted large-scale experiments. The experiments have demonstrated that the new collaborative approach maximizes drone utilization, expands the range of drone services, and ensures flexible launch. The en-route operation with flexible launch positions presented in this paper provides innovative ideas for further application of trucks with multi-drones in last-mile delivery. This is also relevant for other scenarios, such as emergency management and routine inspections, which involve collaboration between trucks and drones.