Pseudo node insertion method for synchronization in drone–truck combined operations

Abstract

Drone–truck combined last-mile delivery systems present several advantages, which can be summarized in two folds: (1) enabling faster pick-up/delivery of items and (2) expanding operation areas beyond the range that could be achieved by using only one type of vehicle. Drone–truck combined operation (DTCO) solutions are based on vehicle routes and drone launch and retrieval locations, usually customer nodes. Since a perfect synchronization of both vehicles is very rare, most of the solutions obtained after designing combined delivery routes generally contain time losses, caused by the need for the first vehicle that reaches the meeting point to wait until the arrival of the other. In this paper, a pseudo node insertion method is proposed to make DTCO solutions more efficient by improving the truck–drone synchronization operations. To this end, starting from a given routing solution, pseudo nodes are created at the point where a drone and a truck can meet simultaneously. We present a detailed method to calculate the location of the pseudo nodes and provide a detailed analysis of the conditions that allow us to reduce the travel completion time for different route patterns. Furthermore, we explore a variety of scenarios to illustrate the efficiency of the pseudo node insertion method for different DTCO problem solutions. An algorithm for the pseudo node insertion method is provided, and numerical examples are presented to discuss the efficacy and efficiency of the proposed approach.