A hybrid clustering–optimization framework for continuous hub location in drone delivery networks

This study aims to develop a scalable methodology for identifying optimal locations of micro-hubs and intermediate hubs within an intermodal drone delivery network. It addresses the need for novel facility location models tailored to the unique constraints of drone logistics, especially in continuous geographic spaces without predefined candidate sites. The research adopts a hybrid approach combining density-based clustering (DBSCAN) with an uncapacitated facility location model. DBSCAN is employed as a preprocessing tool to identify initial micro-hub candidate locations based on customer distribution. These are refined by a mathematical optimization model that assigns customers to the nearest feasible facility within drone range while penalizing unassigned customers. To quantify the impact of spatial discretization, a discretization loss analysis is conducted, assessing the deviation between continuous customer locations and centroid-based candidate hubs. For customers beyond drone range, intermediate hubs are introduced heuristically at fixed intervals, while a GIS-based relocation step ensures all facilities are placed in viable land areas, avoiding restricted or unusable zones, with displacement statistics reported to quantify real-world feasibility impacts. The methodology is applied in a case study involving two logistics companies in Germany. Results show that the proposed approach ensures complete customer coverage via drones, both with and without intermediate hubs, while maintaining operational feasibility and reducing complexity. Benchmark comparisons against optimal formulations, range sensitivity analysis, and scalability experiments demonstrate that the framework achieves near-optimal performance while scaling efficiently to larger urban instances. A final simulation confirms the efficiency and practicality of the designed delivery network. This work contributes a scalable decision-support tool for drone logistics planning, bridging clustering heuristics, mathematical optimization, and feasibility validation, and providing a foundation for future extensions incorporating capacity, routing, and sustainability considerations.