The Path&Cycle Formulation for the Hotspot Problem in Air Traffic Management

Authors Carlo Mannino, Giorgio Sartor

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Author Details

Carlo Mannino
  • SINTEF, Forskningsveien 1, Oslo, Norway
Giorgio Sartor
  • SINTEF, Forskningsveien 1, Oslo, Norway

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Carlo Mannino and Giorgio Sartor. The Path&Cycle Formulation for the Hotspot Problem in Air Traffic Management. In 18th Workshop on Algorithmic Approaches for Transportation Modelling, Optimization, and Systems (ATMOS 2018). Open Access Series in Informatics (OASIcs), Volume 65, pp. 14:1-14:11, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2018)


The Hotspot Problem in Air Traffic Management consists of optimally rescheduling a set of airplanes that are forecast to occupy an overcrowded region of the airspace, should they follow their original schedule. We first provide a MILP model for the Hotspot Problem using a standard big-M formulation. Then, we present a novel MILP model that gets rid of the big-M coefficients. The new formulation contains only simple combinatorial constraints, corresponding to paths and cycles in an associated disjunctive graph. We report computational results on a set of randomly generated instances. In the experiments, the new formulation consistently outperforms the big-M formulation, both in terms of running times and number of branching nodes.

Subject Classification

ACM Subject Classification
  • Applied computing → Transportation
  • Air Traffic Management
  • Hotspot Problem
  • Job-shop scheduling
  • Mixed Integer Linear Programming


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