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This dissertation optimizes the problem of designing sector boundaries and assigning air traffic controllers to sectors while considering demand variation over time. For long-term planning purposes, an optimization problem of clean-sheet sectorization is defined to generate a set of sector boundaries that accommodates traffic variation across the planning horizon while minimizing staffing. The resulting boundaries should best accommodate traffic over space and time and be the most efficient in terms of controller shifts. Two integer program formulations are proposed to address the defined problem, and their equivalency is proven. The performance of both formulations is examined with randomly generated numerical examples. Then, a real-world application confirms that the proposed model can save 10%-16% controller-hours, depending on the degree of demand variation over time, in comparison with the sectorization model with a strategy that does not take demand variation into account.

Due to the size of realistic sectorization problems, a heuristic based on mathematical programming is developed for a large-scale neighborhood search and implemented in a parallel computing framework in order to obtain quality solutions within time limits. The impact of neighborhood definition and initial solution on heuristic performance has been examined. Numerical results show that the heuristic and the proposed neighborhood selection schemes can find significant improvements beyond the best solutions that are found exclusively from the Mixed Integer Program solver's global search.

For operational purposes, under given sector boundaries, an optimization model is proposed to create an operational plan for dynamically combining or splitting sectors and determining controller staffing. In particular, the relation between traffic condition and the staffing decisions is no longer treated as a deterministic, step-wise function but a probabilistic, nonlinear one. Ordinal regression analysis is applied to estimate a set of sector-specific models for predicting sector staffing decisions. The statistical results are then incorporated into the proposed sector combination model. With realistic traffic and staffing data, the proposed model demonstrates the potential saving in controller staffing achievable by optimizing the combination schemes, depending on how freely sectors can combine and split. To address concerns about workload increases resulting from frequent changes of sector combinations, the proposed model is then expanded to a time-dependent one by including a minimum duration of a sector combination scheme. Numerical examples suggest there is a strong tradeoff between combination stability and controller staffing.