# Drone-assisted deliveries: new formulations for the Flying Sidekick Traveling Salesman Problem

## TL;DR

This paper advances the optimization of drone-assisted delivery routes by proposing new mathematical formulations and solution methods for the Flying Sidekick Traveling Salesman Problem, considering drone waiting policies.

## Contribution

It introduces improved formulations and branch-and-cut algorithms for the problem, and compares drone waiting strategies, enhancing solution efficiency and applicability.

## Key findings

- Optimal solutions found for most benchmark instances.
- New formulations outperform previous models in solution quality.
- Waiting policies impact delivery completion times.

## Abstract

In this paper we consider a problem related to deliveries assisted by an unmanned aerial vehicle, so-called drone. In particular we consider the Flying Sidekick Traveling Salesman Problem, where a truck and a drone cooperate to delivery parcels to customers minimizing the completion time. In the following we improve the formulation found in the related literature. We propose three-indexed and two-indexed formulations and a set of inequalities that can be implemented in a branch-and-cut fashion. We could find the optimal solutions for most of the literature instances. Moreover, we consider two versions of the problem: one in which the drone is allowed to wait at the customers, as in the literature, and one where waiting is allowed only in flying mode. The solving methodologies are adapted to both versions. A comparison between the two versions is provided.