Multi-station flexible scheduling for UAV emergency delivery under uncertain demand

Unmanned Aerial Vehicles (UAVs), or drones, are gaining attention in emergency logistics due to their rapid deployment, obstacle avoidance, and access to isolated areas. However, their effectiveness is limited by short endurance and small payloads, requiring reliance on ground stations for recharging and material handling. Traditional methods restrict UAVs to their original stations post-mission, causing inefficiencies in dynamic emergencies with unpredictable demand, scarce resources, and vulnerable infrastructure. To overcome this limitation, this study formulates the Multi-Station Flexible Scheduling Problem (MSFSP-D), which permits drones to be replenished and deployed across multiple stations, thereby decentralizing resource dependency and enabling dynamic route optimization. Employing graph theory, node connectivity is analyzed to establish feasibility conditions, and a two-stage optimization framework is developed: the first stage constructs a multi-drone delivery network via a branch-and-cut algorithm, and the second stage refines individual drone routes through path recombination, with both stages coordinated iteratively by cutting planes. To handle demand uncertainty, a robust optimization model with a budgeted uncertainty set is introduced, strengthened by custom valid inequalities. Tests show MSFSP-D improves scheduling efficiency by 10%–36% and cuts response times by 20% compared to conventional approaches, while reducing supply shortages and disruption risks under changing demand and limited resources.