MODELS AND SOLUTION ALGORITHMS FOR EQUITABLE RESOURCE ALLOCATION IN AIR TRAFFIC FLOW MANAGEMENT

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

Stochastic programming approaches to air traffic flow management under the uncertainty of weather

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.Ph.D.Committee Chair: Johnson, Ellis; Committee Co-Chair: Clarke, John-Paul; Committee Member: Ahmed, Shabbir; Committee Member: Sokol, Joel; Committee Member: Solak, Sena

COMPUTATIONALLY TRACTABLE STOCHASTIC INTEGER PROGRAMMING MODELS FOR AIR TRAFFIC FLOW MANAGEMENT

A primary objective of Air Traffic Flow Management (ATFM) is to ensure the orderly flow of aircraft through airspace, while minimizing the impact of delays and congestion on airspace users. A fundamental challenge of ATFM is the vulnerability of the airspace to changes in weather, which can lower the capacities of different regions of airspace. Considering this uncertainty along with the size of the airspace system, we arrive at a very complex problem. The development of efficient algorithms to solve ATFM problems is an important and active area of research. Responding to predictions of bad weather requires the solution of resource allocation problems that assign a combination of ground delay and route adjustments to many flights. Since there is much uncertainty associated with weather predictions, stochastic models are necessary. We address some of these problems using integer programming (IP). In general, IP models can be difficult to solve. However, if "strong" IP formulations can be found, then problems can be solved quickly by state of the art IP solvers. We start by describing a multi-period stochastic integer program for the single airport stochastic dynamic ground holding problem. We then show that the linear programming relaxation yields integer optimal solutions. This is a fairly unusual property for IP formulations that can significantly reduce the complexity of the corresponding problems. The proof is achieved by defining a new class of matrices with the Monge property and showing that the formulation presented belongs to this class. To further improve computation times, we develop alternative compact formulations. These formulations are extended to show that they can also be used to model different concepts of equity and fairness as well as efficiency. We explore simple rationing methods and other heuristics for these problems both to provide fast solution times, but also because these methods can embody inherent notions of fairness. The initial models address problems that seek to restrict flow into a single airport. These are extended to problems where stochastic weather affects en route traffic. Strong formulations and efficient solutions are obtained for these problems as well

Computational optimization of networks of dynamical systems under uncertainties: application to the air transportation system

To efficiently balance traffic demand and capacity, optimization of air traffic management relies on accurate predictions of future capacities, which are inherently uncertain due to weather forecast. This dissertation presents a novel computational efficient approach to address the uncertainties in air traffic system by using chance constrained optimization model. First, a chance constrained model for a single airport ground holding problem is proposed with the concept of service level, which provides a event-oriented performance criterion for uncertainty. With the validated advantage on robust optimal planning under uncertainty, the chance constrained model is developed for joint planning for multiple related airports. The probabilistic capacity constraints of airspace resources provide a quantized way to balance the solution’s robustness and potential cost, which is well validated against the classic stochastic scenario tree-based method. Following the similar idea, the chance constrained model is extended to formulate a traffic flow management problem under probabilistic sector capacities, which is derived from a previous deterministic linear model. The nonlinearity from the chance constraint makes this problem difficult to solve, especially for a large scale case. To address the computational efficiency problem, a novel convex approximation based approach is proposed based on the numerical properties of the Bernstein polynomial. By effectively controlling the approximation error for both the function value and gradient, a first-order algorithm can be adopted to obtain a satisfactory solution which is expected to be optimal. The convex approximation approach is evaluated to be reliable by comparing with a brute-force method.Finally, the specially designed architecture of the convex approximation provides massive independent internal approximation processes, which makes parallel computing to be suitable. A distributed computing framework is designed based on Spark, a big data cluster computing system, to further improve the computational efficiency. By taking the advantage of Spark, the distributed framework enables concurrent executions for the convex approximation processes. Evolved from a basic cloud computing package, Hadoop MapReduce, Spark provides advanced features on in-memory computing and dynamical task allocation. Performed on a small cluster of six workstations, these features are well demonstrated by comparing with MapReduce in solving the chance constrained model

Restless bandit marginal productivity indices I: singleproject case and optimal control of a make-to-stock M/G/1 queue

This paper develops a framework based on convex optimization and economic ideas to formulate and solve by an index policy the problem of optimal dynamic effort allocation to a generic discrete-state restless bandit (i.e. binary-action: work/rest) project, elucidating a host of issues raised by Whittle (1988)Žs seminal work on the topic. Our contributions include: (i) a unifying definition of a projectŽs marginal productivity index (MPI), characterizing optimal policies; (ii) a complete characterization of indexability (existence of the MPI) as satisfaction by the project of the law of diminishing returns (to effort); (iii) sufficient indexability conditions based on partial conservation laws (PCLs), extending previous results of the author from the finite to the countable state case; (iv) application to a semi-Markov project, including a new MPI for a mixed longrun-average (LRA)/ bias criterion, which exists in relevant queueing control models where the index proposed by Whittle (1988) does not; and (v) optimal MPI policies for service-controlled make-to-order (MTO) and make-to-stock (MTS) M/G/1 queues with convex back order and stock holding cost rates, under discounted and LRA criteria

Applications of stochastic modeling in air traffic management:Methods, challenges and opportunities for solving air traffic problems under uncertainty

In this paper we provide a wide-ranging review of the literature on stochastic modeling applications within aviation, with a particular focus on problems involving demand and capacity management and the mitigation of air traffic congestion. From an operations research perspective, the main techniques of interest include analytical queueing theory, stochastic optimal control, robust optimization and stochastic integer programming. Applications of these techniques include the prediction of operational delays at airports, pre-tactical control of aircraft departure times, dynamic control and allocation of scarce airport resources and various others. We provide a critical review of recent developments in the literature and identify promising research opportunities for stochastic modelers within air traffic management

Combinatorial Optimization

This report summarizes the meeting on Combinatorial Optimization where new and promising developments in the field were discussed. Th

The achievable region method in the optimal control of queueing systems : formulations, bounds and policies

Cover title.Includes bibliographical references (p. 44-48).Supported in part by a Presidential Young Investigator Award, with matching funds from Draper Laboratory. DDM-9158118Dimitris Bertsimas

The achievable region method in the optimal control of queueing systems : formulations, bounds and policies

Cover title.Includes bibliographical references (p. 44-48).Supported in part by a Presidential Young Investigator Award, with matching funds from Draper Laboratory. DDM-9158118Dimitris Bertsimas