A tractable optimization framework for Air Traffic Flow Management addressing fairness, collaboration and stochasticity

Abstract

We propose a tractable optimization framework for network Air Traffic Flow Management (ATFM) with an eye towards the future. The thesis addresses two issues in ATFM research: a) fairness and collaboration amongst airlines; and b) uncertainty inherent in capacity forecasts. A unifying attraction of the overall dissertation is that the Collaborative Decision-Making (CDM) paradigm, which is the current philosophy governing the design of new ATFM initiatives, is treated as the starting point in the research agenda. In the first part of the thesis, we develop an optimization framework to extend the CDM paradigm from a single-airport to a network setting by incorporating both fairness and airline collaboration. We introduce different notions of fairness emanating from a) First-Scheduled First-Served (FSFS) fairness; and b) Proportional fairness. We propose exact discrete optimization models to incorporate them. The first fairness paradigm which entails controlling number of reversals and total amount of overtaking is especially appealing in the ATFM context as it is a natural extension of Ration-By-Schedule (RBS). We allow for further airline collaboration by proposing discrete optimization models for slot reallocation. We provide empirical results of the proposed optimization models on national-scale, real world datasets that show interesting tradeoffs between fairness and efficiency. In particular, schedules close to the RBS policy (with single digit reversals) are possible for a less than 10% increase in delay costs. We utilize case studies to highlight the considerable improvements in the internal objective functions of the airlines as a result of slot exchanges. Finally, the proposed models are computationally tractable (running times of less than 30 minutes). In the second part, we address the important issue of capacity uncertainty by presenting the first application of robust and adaptive optimization in the ATFM problem. We introduce a weather-front based approach to model the uncertainty inherent in airspace capacity estimates resulting from the impact of a small number of weather fronts. We prove the equivalence of the robust problem to a modified instance of the deterministic problem; solve the LP relaxation of the adaptive problem using affine policies; and report extensive empirical results to study the inherent tradeoffs.