Massachusetts Institute of Technology, Cambridge, Massachusetts (Received August 1994; revision received October 1995; accepted May 1996) Throughout the United States and Europe, demand for airport use has been increasing rapidly, while airport capacity has been stagnating. Over the last ten years the number of passengers has increased by more than 50 percent and is expected to continue increasing at this rate. Acute congestion in many major airports has been the unfortunate result. For U.S. airlines, the expected yearly cost of the resulting delays is currently estimated at $3 billion. In order to put this number in perspective, the total reported losses of all U.S. airlines amounted to approximately $2 billion in 1991 and $2.5 billion in 1990. Furthermore, every day 700 to 1100 flights are delayed by 15 minutes or more. European airlines are in a similar plight. Optimally controlling the flow of aircraft either by adjusting their release times into the network (ground-holding) or their speed once they are airborne is a cost effective method to reduce the impact of congestion on the air traffic system. This paper makes the following contributions: (a) we build a model that takes into account the capacities of the National Airspace System (NAS) as well as the capacities at the airports, and we show that the resulting formulation is rather strong as some of the proposed inequalities are facet defining for the convex hull of solutions; (b) we address the complexity of the problem; (c) we extend that model to account for several variations of the basic problem, most notably, how to reroute flights and how to handle banks in the hub and spoke system; (d) we show that by relaxing some of our constraints we obtain a previously addressed problem and that the LP relaxation bound of our formulation is at least as strong when compared to all others proposed in the literature for this problem; and (e) we solve large scale, realistic size problems with several thousand flights.

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The Air Traffic Flow Management Problem with Enroute Capacities

We address the problem of determining how to reroute aircraft in the air traffic control system when faced with dynamically changing weather conditions. The overall objective of this problem is the minimization of delay costs. This problem is of primary concern in the European air traffic control system and in particular regions within the US air traffic control system. We present an integrated mathematical programming approach that consists of several methodologies. To address the high dimensionality, we begin by presenting an aggregate model, in which the problem is formulated as a dynamic, multicommodity, integer network flow problem with certain side constraints. Using Lagrangian relaxation, we generate aggregate flows. We decompose the aggregate flows into a collection of flight paths for individual aircraft using a randomized rounding heuristic. This collection of paths is then used in a packing integer programming formulation, the solution of which generates feasible and near-optimal routes for individual flights. The overall Lagrangian Generation Algorithm is used to solve real problems in the southwestern portion of United States. In computational experiments, the solutions returned by our algorithm are within 1% of the corresponding lower bounds.

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The Traffic Flow Management Rerouting Problem in Air Traffic Control: A Dynamic Network Flow Approach

This paper presents a new integer programming (IP) model for large-scale instances of the air traffic flow management (ATFM) problem. The model covers all the phases of each flight---i.e., takeoff, en route cruising, and landing---and solves for an optimal combination of flow management actions, including ground-holding, rerouting, speed control, and airborne holding on a flight-by-flight basis. A distinguishing feature of the model is that it allows for rerouting decisions. This is achieved through the imposition of sets of “local” conditions that make it possible to represent rerouting options in a compact way by only introducing some new constraints. Moreover, three classes of valid inequalities are incorporated into the model to strengthen the polyhedral structure of the underlying relaxation.

Computational times are short and reasonable for practical application on problem instances of size comparable to that of the entire U.S. air traffic management system. Thus, the proposed model has the potential of serving as the main engine for the preliminary identification, on a daily basis, of promising air traffic flow management interventions on a national scale in the United States or on a continental scale in Europe.

An Integer Optimization Approach to Large-Scale Air Traffic Flow Management

In this paper, we present a new Integer Program (IP) for the Air Traffic Flow Management (ATFM) problem. The model we propose provides a complete representation of all the phases of each flights, i.e., the phase of taking-off, of cruising and of landing; suggesting all the actions to be implemented to achieve the goal of safe, efficient, and expeditious aircraft movement. The distinctive feature of the model is that it allows rerouting decisions. These decisions are formulated by means of "local" conditions, which allow us to represent such decisions in a very compact way by only introducing new constraints. Moreover, to strengthen the polyhedral structure of the underlying relaxation, we also present three classes of valid inequalities.

We report short computational times (less than 15 minutes) on instances of the size of the US air traffic control system that make it realistic that our approach can be used as the main engine of managing air traffic in the US.

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The air traffic flow management problem: an integer optimization approach

Traffic flow management (TFM) allocates the various airport, airspace, and other resources to maintain an efficient traffic flow consistent with safety. TFM is a complex area of research involving the disciplines of operations research, guidance and control, human factors, and software engineering. Hundreds of human operators make TFM decisions that involve tens of thousands of aircraft, en route air traffic control centers, the Federal Aviation Administration's System Command Center, and many airline operation centers. This paper provides an overview of how TFM decisions are made today and challenges facing the system in the future, and reviews modeling and optimization approaches for facilitating system-wide modeling, performance assessments, and system-level optimization of the national airspace system in the presence of both en route and airport capacity constraints.

Modeling and Optimization in Traffic Flow Management

The author describes a formulation of National Airspace System (NAS) traffic management problem as a multicommodity minimum cost flow problem over a network in space-time. It is a formulation of the multidestination delay minimization problem of managing traffic in the NAS. The model's potential for improving over present practice is described in terms of six assumptions of present practice. The space-time network model can address uncertainty in capacity values, restrictive airways capacities, and hubbing. The minimum cost flow formulation further assumes that attempted entries into the system are deterministic, not Poisson, and that actual entries are controllable. The formulation specifically allows dynamic capacities and possesses good potential for short execution time. >

M.P. Helme

Papers

Reducing air traffic delay in a space-time network