Stochastic programming approaches to air traffic flow management under the uncertainty of weather
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As air traffic congestion grows, air traffic flow management (ATFM) is becoming a great concern. ATFM deals with air traffic and the efficient utilization of the airport and airspace. Air traffic efficiency is heavily influenced by unanticipated factors, or uncertainties, which can come from several sources such as mechanical breakdown; however, weather is the main unavoidable cause of uncertainty. Because weather is unpredictable, it poses a critical challenge for ATFM in current airport and airspace operations. Convective weather results in congestion at airports as well as in airspace sectors. During times of congestion, the decision as how and when to send aircraft toward an airspace sector in the presence of weather is difficult. To approach this problem, we first propose a two-stage stochastic integer program by emphasizing a given single sector. By considering ground delay, cancellation, and cruise speed for each flight on the ground in the first stage, as well as air holding and diversion recourse actions for each flight in the air in the second stage, our model determines how aircraft are sent toward a sector under the uncertainty of weather. However, due to the large number of weather scenarios, the model is intractable in practice. To overcome the intractability, we suggest a rolling horizon method to solve the problem to near optimal. Lagrangian relaxation and subgradient method are used to justify the rolling horizon method. Since the rolling horizon method can be solved in real time, we can apply it to actual aircraft schedules to reduce the costs incurred on the ground as well as in airspace. We then extend our two-stage model to a multistage stochastic program, which increases the number of possible weather realizations and results a more efficient schedule in terms of costs. The rolling horizon method as well as Lagrangian relaxation and subgradient method are applied to this multistage model. An overall comparison among the previously described methodologies are presented.