Population growth and economic development lead to increasing demand for travel and pose mobility challenges on capacity-limited air traffic networks. The U.S. National Airspace System (NAS) has been operated near the capacity, and air traffic congestion is expected to remain as a top concern for the related system operators, passengers and airlines. This dissertation develops a number of model reformulations and efficient solution algorithms to address resource allocation problems in air traffic flow management, while explicitly accounting for equitable objectives in order to encourage further collaborations by different stakeholders.

This dissertation first develops a bi-criteria optimization model to offload excess demand from different competing airlines in the congested airspace when the predicted traffic demand is higher than available capacity. Computationally efficient network flow models with side constraints are developed and extensively tested using datasets obtained from the Enhanced Traffic Management System (ETMS) database (now known as the Traffic Flow Management System). Representative Pareto-optimal tradeoff frontiers are consequently generated to allow decision-makers to identify best-compromising solutions based on relative weights and systematical considerations of both efficiency and equity.

This dissertation further models and solves an integrated flight re-routing problem on an airspace network. Given a network of airspace sectors with a set of waypoint entries and a set of flights belonging to different air carriers, the optimization model aims to minimize the total flight travel time subject to a set of flight routing equity, operational and safety requirements. A time-dependent network flow programming formulation is proposed with stochastic sector capacities and rerouting equity for each air carrier as side constraints. A Lagrangian relaxation based method is used to dualize these constraints and decompose the original complex problem into a sequence of single flight rerouting/scheduling problems.

Finally, within a multi-objective utility maximization framework, the dissertation proposes several practically useful heuristic algorithms for the long-term airport slot assignment problem. Alternative models are constructed to decompose the complex model into a series of hourly assignment sub-problems. A new paired assignment heuristic algorithm is developed to adapt the round robin scheduling principle for improving fairness measures across different airlines. Computational results are presented to show the strength of each proposed modeling approach.