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    Mathematical Optimization models for Air Traffic Flow Management: A review
    (2010-02-10) Agustín, Alba; Alonso-Ayuso, Antonio; Escudero, Laureano F.; Pizarro, Celeste
    Congestion problems are becoming increasingly acute in many European and American airports and air sectors. To protect Air Traffic Control (ATC) from overload a planning activity called Air Traffic Flow Management (ATFM) tries to anticipate and prevent overload and limit resulting delays. When the traffic expects to exceed the airport arrival and departure capacities or the airsector capacity a delay in the flight arrival (so called-congestion) occurs. The casuistry to be considered in this field is very extensive. In general, most references to be found in the literature written some years ago refer to the simplest models, those which do not take into account airsector. This is so because this work was first studied in USA, where only the problems of congestion in airports basically occur. In the paper we present a state-of-the-art survey on the main optimization models encountered in the literature. They are classified as follows: (1) Single-Airport Ground-Holding Problem (SAGHP). The simplest of the methodologies of planning modelling studied proposes solutions to the problem of deciding the optimal planning for an arrival airport. (2) Multi-Airport Ground-Holding Problem (MAGHP). In this methodology the field of work is extended and the inter-relationship which exists between different airports is included. (3) Air Traffic Flow Management Problem (ATFMP). This methodology attempts to solve real situations that are much more complex than those which can be dealt with using the previous methodologies, since the air sector capacity is also considered. (4) Air Traffic Flow Management Rerouting Problem (ATFMRP). This methodology considers the more realistic situation where the flights can be diverted to alternative routes. (5) Air Traffic Flow Management Rerouting Problem (ATFMRP) with uncertainty. The ATFM problem is especially sensitive to changes in capacity. This leads to generalize the previous methodologies and to include generic uncertainty for these possible unforeseen changes in the parameters of the model, making way for stochastic methodologies. This type of problems are the most difficult ones, but alas the realistic ones.