Minimizing Energy and Cost in Range-Limited Drone Deliveries with Speed Optimization

Abstract

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.

Keywords: drone delivery, energy consumption, freight transportation, second order cone programming, perspective cuts