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

Abstract

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.

Increasing airport capacity utilisation through optimum slot scheduling: review of current developments and identification of future needs

“…Apart from assigning departure and arrival slots to each flight, the proposed model aims at determining the corresponding flight route. The proposed model is based on the mathematical formulation proposed in Bertsimas et al (2011) for the ATFM problem and aims to allocate a departure and an arrival slot for each flight, while simultaneously determining the corresponding route between departure and arrival airports. Each route involves a sequence of neighbouring airspace sectors connecting the origin and destination airports.…”

“…Constraint (15) states that the total duration of a flight should not exceed a maximum value (end f ). Finally, constraint (16) implies that if a flight has arrived at a sector ( j) by time t (w f j,t = 1), then w f j,t = 1for any t > t. The model is further enhanced with a set of valid inequalities proposed in Bertsimas et al (2011) in order to strengthen its linear relaxation. The proposed slot scheduling model belongs to the category of resource-constrained scheduling problems, and thus, it is rather unlikely to find a solution algorithm with polynomial computational complexity.…”

Single European Sky and Single European Railway Area: A system level analysis of air and rail transportation

“…This problem is recognized to be very critical in Europe: the density of flights in the sky is often very high, and hence en-route congestion is a major constraint to the increase of air traffic. As for the ground holding problem, several algorithms have been proposed for solving the air traffic flow management problem, tackling networks of different complexities, and adopting either exact or heuristic strategies (Bertsimas et al, 2011;Patterson, 1998, 2000;Helme, 1992;Lindsay et al, 1993;Lulli and Odoni, 2007;Sherali et al, 2003Sherali et al, , 2006. Most of these algorithms are based, at least in some part, on integer programming models.…”

A review of the impact of noise restrictions at airports

“…Other options that are in use today are sound insulation of buildings or land use procedures (Ganic et al, 2015). However, in order to reconcile system resource constraints with economic and environmental priorities, all the involved stakeholders (governments, aircraft manufacturers, ATC) are requested to collaborate (Bertsimas et al, 2011).…”