The Flying Sidekick Traveling Salesman Problem with Multiple Drops: A Simple and Effective Heuristic Approach

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 FSTSP-MD aims 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 approach based on an order-first, split-second scheme. This heuristic combines standard local search and diversification techniques with a novel shortest-path problem that finds FSTSP-MD solutions in polynomial time. We show that our heuristic consistently outperforms state-of-the-art heuristics developed for the FSTSP-MD and the FSTSP (i.e., the single-drop case) through extensive numerical experiments. We also show that the FSTSP-MD substantially reduces completion times compared to a traditional truck-only delivery system. Several managerial insights are described regarding the effects of drone capacity, drone speed, drone flight endurance, and customer distribution.