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

TLDR

The authors propose an integer programming model to address large‑scale air traffic flow management. The model jointly optimizes ground‑holding, rerouting, speed control, and airborne holding across takeoff, en‑route, and landing phases, using compact local constraints for rerouting and strengthening inequalities to improve the relaxation. Computational experiments show the model solves quickly on U.S.‑scale instances, enabling daily identification of effective flow‑management interventions at national or continental levels.

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.