A continuous approximation approach to integrated truck and drone delivery systems

Abstract

Home package delivery by drones as an alternative or complement to traditional delivery by trucks is attracting considerable attention from the commercial sector as well as academia. While drone delivery may offer considerable benefits, the fundamental issues of how best to deploy drones for small package delivery are still not well understood. Unlike most studies in the literature that consider either truck-drone tandems or drone standalone delivery operations, our research provides a strategic analysis for the optimal design of an integrated drone delivery system in which customers in a service region can be served by a combination of truck-drone (TD) delivery, drone-only (DO) delivery, and truck-only (TO) delivery. We formulate and optimize continuous approximation models to identify the optimal delivery service combination that minimizes the total delivery costs including truck and drone operating and stop costs. We evaluate the impact of a wide range of operating characteristics and delivery environments on the optimal delivery system and the benefits of using drones. Our results suggest that an optimal delivery system design often uses a mix of DO and TD, but TD is the dominant delivery service in most scenarios. The magnitude of the cost savings afforded by the use of drones, relative to truck-only delivery, can be large but strongly depends on the values of key parameters.