An optimisation model of hierarchical facility location problem for urban last-mile delivery with drones

Drones have, in recent years, been considered as a promising way for the last-mile delivery of urban logistics. In view of limited or short battery life of drones in every operation, the drone recharging stations and their locations are crucial to ensure delivery accessibility and to accomplish the required mission. Therefore, in addition to considering the selection of service centres and demand nodes, the location of recharging stations should also be incorporated into the proposed model of hierarchical facility location problem (HFLP). Many existing researches on drone recharging station locations assume that the delivery demand is known and only a single path is designed to meet the demand by using queuing theory models to describe node-based service waiting time. However, the reality is that we are still in the infrastructure planning stage for drone delivery, in which the demand is unknown in most cases. Our research proposes a novel mix-integer programming model to solve the HFLP for the last-mile drone delivery in urban areas, aiming to minimise the deployment, operation, and maintenance (DOM) costs of recharging stations, service centres, and paths. We have also incorporated a demand satisfaction constraint into the selection of effective alternative paths that meet the delivery accessibility. On the other hand, a sensitivity analysis in our study reveals varying degrees of impact on DOM costs and effective alternative path quantities, whose results would be useful to practical drone logistics delivery in urban areas.