Minimizing energy and cost in range-limited drone deliveries with speed optimization

This paper introduces the Energy Minimizing and Range Constrained Drone Delivery Problem (ERDDP) in which drones are used to make deliveries to a number of customers and the drones themselves are transported by traditional vehicles that act as launch points. The ERDDP consists of (i) selecting the launch points from a potential set of sites from where drones will take off to serve a number of customers, (ii) assignments of customers to the launch points, and (iii) the speed at which drones are to travel between the customers and the launch points. The paper presents a nonlinear model for the ERDDP, which minimizes the total operational cost including an explicit calculation of the energy consumption of the drone as a function of the drone speed. The deliveries are limited by both a service time bound and the range of the drone. The model is reformulated using second order cone programming, and subsequently strengthened by the use of perspective cuts, that allows the use of off-the-shelf optimization software to solve the problem. Computational results are presented on a realistic data set that quantifies the effect of various parameters on location, assignment and speed decisions.