Integrated Two-Stage Optimization of Strategic Unmanned Aerial Vehicle Allocation and Operational Scheduling Under Demand Uncertainty

The rapid growth of e-commerce has intensified the need for efficient last-mile delivery, making unmanned aerial vehicles (UAVs) a promising solution. However, despite their potential, practical deployment remains limited by how to effectively plan depot locations and UAV fleet sizes under stochastic customer demands with probabilistic same-day modifications. Existing approaches often address the strategic and operational decisions separately, leading to inefficiencies and infeasible solutions in practice. This study develops a unified two-stage decision framework integrating strategic depot location and UAV fleet allocation with operational assignment and scheduling. Three strategic models are considered: a deterministic model, a stochastic model solved via Sample Average Approximation (SAA), and a robust optimization model. Operational decisions assign UAV trips to realized requests while respecting time-slot and UAV availability constraints. Deterministic and SAA models are solved directly as integer programs, whereas the robust model is tackled via a logic-based Benders decomposition framework, with all approaches evaluated through simulation. The results show that the robust model provides overly conservative solutions, resulting in higher costs; the deterministic model minimizes cost but risks service failures; and the SAA approach balances cost and service across demand scenarios. The findings demonstrate the value of jointly considering strategic and operational decisions in UAV delivery design and provide practical guidance for UAV logistics operators. The proposed framework helps firms select appropriate planning models that align with their risk tolerance and service reliability goals, thereby improving the feasibility and competitiveness of UAV-based delivery systems.