Runway systems at airports have been identified as a major source of delay in the aviation system and efficient runway operations are, therefore, important to maintain and/or increase the capacity of the entire aviation system. The goal of the airport runway scheduling problem is to schedule a set of aircraft and minimize a given objective while maintaining separation requirements and enforcing other operational constraints. Uncertain factors such as weather, surrounding traffic and pilot behavior affect when aircraft can be scheduled, and these factors need to be considered in planning models. In this thesis we propose two stochastic programs to address the stochastic airport runway scheduling problem and similarly structured machine scheduling problems. In the first part, we develop a two-stage stochastic integer programming model and analyze it by developing alternative formulations and solution methods. As part of our analysis, we first show that a restricted version of the stochastic runway scheduling problem is equivalent to a machine scheduling problem on a single machine with sequence dependent setup times and stochastic due dates. We then extend this restricted model by considering characteristics specific to the runway scheduling problem and present two different stochastic integer programming models. We derive some tight valid inequalities for these formulations, and we propose a solution methodology based on sample average approximation and Lagrangian based scenario decomposition. Realistic data sets are then used to perform a detailed computational study involving implementations and analyses of several different configurations of the models. The results from the computational tests indicate that practically implementable truncated versions of the proposed solution algorithm almost always produce very high quality solutions. In the second part, we propose a sampling based stochastic program for a general machine scheduling problem with similar characteristics as the airport runway scheduling problem. The sampling based approach allows us to capture more detailed aspects of the problem, such as taxiway operations crossing active runways. The model is based on the stochastic branch and bound algorithm with several enhancements to improve the computational performance. More specifically, we incorporate a method to dynamically update the sample sizes in various parts of the branching tree, effectively decreasing the runtime without worsening the solution quality. When applied to runway scheduling, the algorithm is able to produce schedules with makespans that are 5% to 7% shorter than those obtained by optimal deterministic methods. Additional contributions in this thesis include the development of a global cost function, capturing all relevant costs in airport runway scheduling and trading off different, sometimes conflicting, objectives. We also analyze the impact of including environmental factors in the scheduling process.

Air traffic flow management is a critical component of air transport operations because at some point in time, often very frequently, one of more of the critical resources in the air transportation network has significantly reduced capacity, resulting in congestion and delay for airlines and other entities and individuals who use the network. Typically, these “bottlenecks” are noticed at a given airport or terminal area, but they also occur in en route airspace. The two-stage combinatorial optimization framework for air traffic flow management under constrained capacity that is presented in this thesis, represents a important step towards the full consideration of the combinatorial nature of air traffic flow management decision that is often ignored or dealt with via priority-based schemes. It also illustrates the similarities between two traffic flow management problems that heretofore were considered to be quite distinct. The runway systems at major airports are highly constrained resources. From the perspective of arrivals, unnecessary delays and emissions may occur during peak periods when one or more runways at an airport are in great demand while other runways at the same airport are operating under their capacity. The primary cause of this imbalance in runway utilization is that the traffic flow into and out of the terminal areas is asymmetric (as a result of airline scheduling practices), and arrivals are typically assigned to the runway nearest the fix through which they enter the terminal areas. From the perspective of departures, delays and emissions occur because arrivals take precedence over departures with regard to the utilization of runways (despite the absence of binding safety constraints), and because arrival trajectories often include level segments that ensure “procedural separation” from arriving traffic while planes are not allowed to climb unrestricted along the most direct path to their destination. Similar to the runway systems, the terminal radar approach control facilities (TRACON) boundary fixes are also constrained resources of the terminal airspace. Because some arrival traffic from different airports merges at an arrival fix, a queue for the terminal areas generally starts to form at the arrival fix, which are caused by delays due to heavy arriving traffic streams. The arrivals must then absorb these delays by path stretching and adjusting their speed, resulting in unplanned fuel consumption. However, these delays are often not distributed evenly. As a result, some arrival fixes experience severe delays while, similar to the runway systems, the other arrival fixes might experience no delays at all. The goal of this thesis is to develop a combined optimization approach for terminal airspace flow management that assigns a TRACON boundary fix and a runway to each flight while minimizing the required fuel burn and emissions. The approach lessens the severity of terminal capacity shortage caused by and imbalance of traffic demand by shunting flights from current positions to alternate runways. This is done by considering every possible path combination. To attempt to solve the congestion of the terminal airspace at both runways and arrival fixes, this research focuses on two sequential optimizations. The fix assignments are dealt with by considering, simultaneously, the capacity constraints of fixes and runways as well as the fuel consumption and emissions of each flight. The research also develops runway assignments with runway scheduling such that the total emissions produced in the terminal area and on the airport surface are minimized. The two-stage sequential framework is also extended to en route airspace. When en route airspace loses its capacity for any reason, e.g. severe weather condition, air traffic controllers and flight operators plan flight schedules together based on the given capacity limit, thereby maximizing en route throughput and minimizing flight operators' costs. However, the current methods have limitations due to the lacks of consideration of the combinatorial nature of air traffic flow management decision. One of the initial attempts to overcome these limitations is the Collaborative Trajectory Options Program (CTOP), which will be initiated soon by the Federal Aviation Administration (FAA). The developed two-stage combinatorial optimization framework fits this CTOP perfectly from the flight operator's perspective. The first stage is used to find an optimal slot allocation for flights under satisfying the ration by schedule (RBS) algorithm of the FAA. To solve the formulated first stage problem efficiently, two different solution methodologies, a heuristic algorithm and a modified branch and bound algorithm, are presented. Then, flights are assigned to the resulting optimized slots in the second stage so as to minimize the flight operator's costs.