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.
@InProceedings{mannino_et_al:OASIcs.ATMOS.2018.14, author = {Mannino, Carlo and Sartor, Giorgio}, title = {{The Path\&Cycle Formulation for the Hotspot Problem in Air Traffic Management}}, booktitle = {18th Workshop on Algorithmic Approaches for Transportation Modelling, Optimization, and Systems (ATMOS 2018)}, pages = {14:1--14:11}, series = {Open Access Series in Informatics (OASIcs)}, ISBN = {978-3-95977-096-5}, ISSN = {2190-6807}, year = {2018}, volume = {65}, editor = {Bornd\"{o}rfer, Ralf and Storandt, Sabine}, publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik}, address = {Dagstuhl, Germany}, URL = {https://drops.dagstuhl.de/entities/document/10.4230/OASIcs.ATMOS.2018.14}, URN = {urn:nbn:de:0030-drops-97191}, doi = {10.4230/OASIcs.ATMOS.2018.14}, annote = {Keywords: Air Traffic Management, Hotspot Problem, Job-shop scheduling, Mixed Integer Linear Programming} }
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