The drone latency location routing problem under uncertainty

This paper addresses a location routing problem arising in the last-mile drone delivery context, where drones are used to deliver small packages to a set of customers. Each drone is launched from a fulfillment center to serve multiple customers on a single trip. The goal is to find the optimal subset of fulfillment centers to use as drone launching and landing platforms and the optimal drone routes with the aim of minimizing the sum of customers’ waiting times. We study the problem under two realistic assumptions. First, the drone energy consumption is a nonlinear function of the drone load that varies along the route, as parcels are delivered. Second, the drone flight time is not deterministically known. To hedge against drone flight time uncertainty, we adopt a robust optimization approach. Due to the complex nature of the problem, which turns out to be a nonlinear mixed-integer problem, we design an exact method based on a tailored efficient Branch & Check algorithm that uses customized no-good cuts. The computational experiments show the validity of the proposed model and the promising performance of the exact method. Moreover, we present a case study on last-mile parcel delivery in Turin, Italy, providing insights into the advantages of a drone-based delivery system.