Two-Stage Robust Optimization for Collaborative Flight Slot in Airport Group Under Capacity Uncertainty

Airport congestion in metropolitan clusters (Metroplex systems) poses significant challenges, particularly when capacity reductions occur due to adverse weather conditions. This study introduces a two-stage robust optimization model aimed at improving the robustness of flight slot allocation in multi-airport systems under such uncertainties. In the first stage, the model minimizes deviations from requested slots while respecting airport and waypoint capacities, turnaround times, and adjustment limits. The second stage dynamically adjusts slot allocations to minimize worst-case displacement costs under potential capacity constraints, ensuring robustness against disruptions. The model is validated using real data from the Beijing–Tianjin–Hebei Metroplex, which includes 468 peak-hour flights. The results demonstrate the model’s effectiveness in eliminating demand–capacity violations, particularly at critical airports such as Beijing Daxing, where initial peak demand exceeded capacity by 36.2%. Post-optimization, the model ensures dynamic capacity adherence and adaptive resource allocation, with varying adjustment intensities across airports (12.7% at Beijing Capital, 28.4% at Daxing, and 39.0% at Tianjin Binhai). Compared to a single-stage robust optimization approach, the two-stage model reduces worst-case displacement by 28.2%, highlighting its superior adaptability. This computationally efficient framework, solved via Gurobi 12.0.2/Python 3.11.9, enhances operational robustness through integrated waypoint modeling and a two-stage decision architecture.