A Discrete Particle Swarm Optimization for Same-Day Delivery with Vehicles and Drones

Same-day delivery (SDD) has experienced rapid growth due to customers’ increasing demand for faster and more reliable delivery solutions. To address these demands, integrating drones and vehicles has emerged as an effective solution, exploiting the strengths of both fleets. This paper explores the same-day delivery with heterogeneous fleets (SDDPHF) problem, where stochastic customer requests arise over the course of the day with deadline constraints, requiring dynamic real-time assignment of drones and vehicles while optimizing delivery routes for each fleet. While prior works primarily focus on maximizing served requests, this study proposes a metaheuristic approach based on Discrete Particle Swarm Optimization (DPSO) that explicitly integrates total travel time as a critical decision variable in the assignment process. Computational experiments demonstrate the superiority of the proposed approach over benchmark methods, achieving up to 17.0% more served requests while reducing total travel time by up to 3.7%. Furthermore, we conduct sensitivity analyses on key system parameters, including fitness weights, delivery deadlines, and fleet composition, to better understand their influence on performance. These findings highlight the potential of metaheuristic techniques in enhancing the efficiency of same-day delivery services.