Parallel drone scheduling vehicle routing problems with collective drones

TL;DR

This paper introduces new models for last-mile delivery using trucks and collaborative drones, including a novel multi-truck variant, with extensive experiments demonstrating their effectiveness.

Contribution

It presents the first models for the multi-truck variant of the collective drone scheduling problem, expanding the scope of drone-assisted delivery optimization.

Findings

State-of-the-art results for single-truck problem

Insight into model performance for multi-truck variant

Discussion of future research directions

Abstract

We study last-mile delivery problems where trucks and drones collaborate to deliver goods to final customers. In particular, we focus on problem settings where either a single truck or a fleet with several homogeneous trucks work in parallel to drones, and drones have the capability of collaborating for delivering missions. This cooperative behaviour of the drones, which are able to connect to each other and work together for some delivery tasks, enhance their potential, since connected drone has increased lifting capabilities and can fly at higher speed, overcoming the main limitations of the setting where the drones can only work independently. In this work, we contribute a Constraint Programming model and a valid inequality for the version of the problem with one truck, namely the \emph{Parallel Drone Scheduling Traveling Salesman Problem with Collective Drones} and we introduce for the first time the variant with multiple trucks, called the \emph{Parallel Drone Scheduling Vehicle Routing Problem with Collective Drones}. For the latter variant, we propose two Constraint Programming models and a Mixed Integer Linear Programming model. An extensive experimental campaign leads to state-of-the-art results for the problem with one truck and some understanding of the presented models' behaviour on the version with multiple trucks. Some insights about future research are finally discussed.