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In 2019, China's air traffic control service handled approximately 10.766 million flight movements, with an increase of 7.60% compared to 2018. However, this rapid growth has resulted in flight delays due to airspace capacity limitations, and air traffic control complications. Faced with the realities of airspace capacity limitations, Air Traffic Flow Management (ATFM) plays a central role in alleviating demand-capacity imbalances and subsequently reducing airspace congestion and flight delays. Yet, in the existence of airspace capacity uncertainty, the ATFM operations may be non-practical or ineffective when the deterministic models are adopted since the latter presumes that airspace capacity is known. In this paper, the Air Traffic Sector Network Flow Optimization (ATSNFO) problem is formulated into a Chance-Constrained Optimization Program (C-COP), and a scenario approach optimization method for airspace sector capacity in the presence of uncertainties is proposed to approximately solve the C-COP with a predetermined probabilistic confidence. Then, a mixed-integer programming model is developed based on the obtained deterministic sector capacity. Computation experiment results showed that our model is more efficient and reliable in dealing with uncertainty in ATFM problems. Our findings also highlight the capability of the scenario approach method for solving these problems.

The Air Traffic Flow Management (ATFM) is considered as an effective method for air safety and efficiency guarantee. However, as one of the vital part of flight efficiency, fuel consumption is easily affected by external factors induced by various uncertainties such as severe weather conditions, which impact decision making process. Therefore, a distributionally robust mixed integer programming model for ATFM problem (DR-ATFM) is introduced in this paper to handle the uncertainty of fuel consumption while minimizing the total cost of fuel consumption, flight cancellation and flight delays. By exploiting the moment information of the fuel consumption data, a moment ambiguity set is constructed which characterizes the actual distribution of fuel consumption influctation. Based on this, an equivalent reformulation of DR-ATFM is derived to transform the problem into a mathematically solvable one, which is further solved through a cutting plane-based decomposition algorithm proposed in this paper. Finally, the effectiveness and robustness of the method are verified based on computational results of small-sized instances.