The flying sidekick traveling salesman problem with multiple drops: A simple and effective heuristic approach

TL;DR

This paper introduces a simple heuristic for the Flying Sidekick Traveling Salesman Problem with Multiple Drops, optimizing drone and truck routes for last-mile delivery to significantly reduce completion times.

Contribution

It presents a novel polynomial-time split algorithm and a heuristic approach that outperform existing methods for FSTSP-MD and FSTSP problems.

Findings

Heuristic consistently outperforms state-of-the-art solutions.

FSTSP-MD reduces delivery completion times compared to truck-only systems.

Drone capabilities and customer distribution significantly impact delivery efficiency.

Abstract

We study the Flying Sidekick Traveling Salesman Problem with Multiple Drops (FSTSP-MD), a multi-modal last-mile delivery model where a single truck and a single drone cooperatively deliver customer packages. In the FSTSP-MD, the drone can be launched from the truck to deliver multiple packages before it returns to the truck for a new delivery operation. The objective is to find the synchronized truck and drone delivery routes that minimize the completion time of the delivery process. We develop a simple and effective heuristic to solve the FSTSP-MD based on an order-first, split-second scheme. The core component of our heuristic is a novel split algorithm that finds FSTSP-MD solutions in polynomial time for a given sequence of customers. We embed this split algorithm into a simple heuristic approach that combines standard local search and diversification techniques. The simplicity of our heuristic does not sacrifice performance: we show that it consistently outperforms state-of-the-art solution approaches developed for both the FSTSP-MD and the FSTSP (i.e., the single-drop case) through extensive numerical experiments. Based on both stylized and real-world instances, we also show that the FSTSP-MD substantially reduces completion times compared to traditional truck-only delivery systems. We provide extensive managerial insights into the impacts of drone capabilities and customer distribution on delivery efficiency. Our discussion compares the benefits of drones with greater payload capacity and those with greater speed. We highlight which service area characteristics increase savings but also require enhanced drone capabilities.