A Comparison of Formulations for the Single-Airport Ground Holding Problem with Banking Constraints

Both the single-airport ground-holding problem (GH) and the multi-airport ground-holding problem can be extended by the addition of banking constraints to accommodate the hubbing operations of major airlines. These constraints enforce the desire of airlines to land certain groups of flights, called banks, within fixed time windows, thus preventing the propagation of delays throughout their entire operation. GH can be formulated as a transportation problem and readily solved. But in the presence of banking constraints, GH becomes a difficult integer programming problem. In this paper, we construct five different models of the single-airport ground holding problem with banking constraints (GHB). The models are evaluated both computationally and analytically. For two of the models, we show that the banking constraints induce facets of the convex hull of the set of integer solutions. In addition, we explore a linear transformation of variables and a branching technique

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

Allocating Air Traffic Flow Management Slots

In Europe, when an imbalance between demand and capacity is detected for air traffic network resources, Air Traffic Flow Management slots are allocated to flights on the basis of a First Planned First Served principle. We propose a market mechanism to allocate such slots in the case of a single constrained en-route sector or airport. We show that our mechanism provides a slot allocation which is economically preferable to the current one as it enables airlines to pay for delay reduction or receive compensations for delay increases. We also discuss the implementation of our mechanism through two alternative distributed approaches that spare airlines the disclosure of private information. Both these approaches have the additional advantage that they directly involve airlines in the decision making process. Two computational examples relying on real data illustrate our findings.Air Transportation, Market Mechanism Design, Air Traffic Flow Management slots, Collaborative Decision Making, SESAR.

Coordinated and robust aviation network resource allocation

In the United States, flight operators may schedule flights to most airports at whatever time best achieves their objectives. However, during some time periods, both at airports and in the airspace, these freely-developed schedules may become infeasible because weather or other factors reduce capacity. A plan must then be implemented to mitigate this congestion safely, efficiently, and equitably. Current planning processes treat each congested resource independently, applying various rules to increase interoperation times sufficiently to match the reduced capacity. However, several resources are occasionally congested simultaneously, and ignoring possible dependencies may yield infeasible allocations for flights using multiple resources. In this dissertation, this problem of developing coordinated flight-slot allocations for multiple congested resources is considered from several perspectives. First, a linear optimization model is developed. It is demonstrated that optimally minimizing flight arrival delays induces an increasing bias against flights using multiple resources. However, the resulting allocations reduce overall arrival delay, as compared to the infeasible independent allocations, and to current operational practice. The analytic properties of the model are used to develop a rule-based heuristic for allocating capacity that achieves comparable aggregate results. Alternatively, minimizing delay assigned at all resources is considered, and this objective is shown to mimic the flights' original schedule order. Recognizing that minimizing arrival delays is attractive because of its tangible impact on system performance, variations to the original optimization model are proposed that constrain the worst-case performance of any individual user. Several different constraints and cost-based approaches are considered, all of which are successful to varying degrees in limiting inequities. Finally, the model is reformulated to consider uncertainty in capacity. This adds considerable complexity to the formulation, and introduces practical difficulties in identifying joint probability distributions for the capacity outcomes at each resource. However, this new model is successful in developing more robust flight-slot allocations that enable quick responses to capacity variations. Each of the optimization models and heuristics presented here are tested on a realistic case study. The problem studied and the approaches employed represent an important middle ground in air traffic flow management research between single resource models and comprehensive ones

Resource Allocation in Air Traffic Flow-Constrained Areas with Stochastic Termination Times

In this dissertation we address a stochastic air traffic flow management problem. This problem arises when airspace congestion is predicted, usually because of a weather disturbance, so that the number of flights passing through a volume of airspace (flow constrained area - FCA) must be reduced. We formulate an optimization model for the assignment of dispositions to flights whose preferred flight plans passed through the FCA. For each flight, the disposition can be either to depart as scheduled but via a secondary route thereby avoiding the FCA, or to use the originally intended route but to depart with a controlled (adjusted) departure time and accompanying ground delay. We model the possibility that the capacity of the FCA may increase at some future time once the weather activity clears. The model is a two-stage stochastic program that represents the time of this capacity windfall as a random variable, and determines expected costs given a second-stage decision, conditioning on that time. We also allow the initial reroutes to vary from a conservative or pessimistic approach where all reroutes avoid the weather entirely to an optimistic or hedging strategy where some or all reroute trajectories can presume that the weather will clear by the time the FCA is reached, understanding that a drastic contingency may be necessary later if this turns out not to be true. We conduct experiments allowing a range of such trajectories and draw conclusions regarding appropriate strategies

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

Optimization Model with Fairness Objective for Air Traffic Management

With the ever-increasing congestion at airports around the world, studies into ways of minimizing delay costs on the ground while meeting the goals of the airlines are necessary. When arrival capacities are reduced at major airports, the Federal Aviation Administration (FAA) issues revised departure/arrival times to prevent congestion at restricted airports. This is referred to as the National Ground Delay Program Problem. A new approach to developing ground delay programs, called Collaborative Decision Making (CDM), is being developed. CDM goals include more information exchange and greater participation on the part of the airlines in determining landing slot allocations. This thesis develops a model specifically for the CDM setting. A key element is the inclusion of a fairness criterion within the underlying optimization model. The fairness criterion seeks to "pay back" an airline for time slots that it is owed but cannot make use of due to mechanical or other difficulties. It also attempts to provide incentives to the airlines to increase the exchange of information. This thesis investigates the Ground Delay Problem relative to a single airport. Different formulations of the integer programming model are given that take into account airport capacities and airline goals and experiments are conducted with realistic data to determine the solvability of the problem. Results for this model are compared with output from the Flight Schedule Monitor (FSM), the CDM decision support tool

Allocating banks of flights to arrivals slots in reduced-capacity situations

Thesis (M.S.)--Massachusetts Institute of Technology, Dept. of Civil and Environmental Engineering, 1997.Includes bibliographical references (leaves 57-59).by Paul M. Carlson.M.S

On modeling and optimisation of air Traffic flow management problem with en-route capacities.

Master of Science in Mathematics, Statistics and Computer Science. University of KwaZulu-Natal, Durban 2016.The air transportation industry in the past ten years witnessed an upsurge with the number of passengers swelling exponentially. This development has seen a high demand in airport and airspace usage, which consequently has an enormous strain on the aviation industry of a given country. Although increase in airport capacity would be logical to meet this demand, factors such as poor weather conditions and other unforeseen ones have made it difficult if not impossible to do such. In fact there is a high probability of capacity reduction in most of the airports and air sectors within these regions. It is no surprise therefore that, most countries experience congestion almost on a daily basis. Congestion interrupts activities in the air transportation network and this has dire consequences on the air traffic control system as well as the nation's economy due to the significant costs incurred by airlines and passengers. This is against a background where most air tra c managers are met with the challenge of finding optimal scheduling strategies that can minimise delay costs. Current practices and research has shown that there is a high possibility of reducing the effects of congestion problems on the air traffic control system as well as the total delay costs incurred to the nearest minimum through an optimal control of ights. Optimal control of these ights can either be achieved by assigning ground holding delays or air borne delays together with any other control actions to mitigate congestion. This exposes a need for adequate air traffic ow management given that it plays a crucial role in alleviating delay costs. Air Traffic Flow Management (ATFM) is defined as a set of strategic processes that reduce air traffic delays and congestion problems. More precisely, it is the regulation of air traffic in such a way that the available airport and airspace capacity are utilised efficiently without been exceeded when handling traffic. The problem of managing air traffic so as to ensure efficient and safe ow of aircraft throughout the airspace is often referred to as the Air Traffic Flow Management Problem (ATFMP). This thesis provides a detailed insight on the ATFMP wherein the existing approaches, methodologies and optimisation techniques that have been (and continue to be) used to address the ATFMP were critically examined. Particular attention to optimisation models on airport capacity and airspace allocation were also discussed extensively as they depict what is obtainable in the air transportation system. Furthermore, the thesis attempted a comprehensive and, up-to-date review which extensively fed off literature on ATFMP. The instances in this literature were mainly derived from North America, Europe and Africa. Having reviewed the current ATFM practices and existing optimisation models and approaches for solving the ATFMP, the generalised basic model was extended to account for additional modeling variations. Furthermore, deterministic integer programming formulations were developed for reducing the air traffic delays and congestion problems based on the sector and path-based approaches already proposed for incorporating rerouting options into the basic ATFMP model. The formulation does not only takes into account all the ight phases but it also solves for optimal synthesis of other ow management activities including rerouting decisions, ight cancellation and penalisation. The claims from the basic ATFMP model was validated on artificially constructed datasets and generated instances. The computational performance of the basic and modified ATFMP reveals that the resulting solutions are completely integral, and an optimal solution can be obtained within the shortest possible computational time. Thereby, affirming the fact that these models can be used in effective decision making and efficient management of the air traffic flow