Advertisement

Models and Algorithms for the Airport Capacity Allocation Problem

  • Paolo Dell’Olmo
  • Guglielmo Lulli
Part of the Applied Optimization book series (APOP, volume 79)

Abstract

In this chapter, we present the airport capacity allocation problem, i.e., the problem of finding for each time unit the optimal balance between the number of arrivals and departures in order to reduce the total economic loss over a given decision horizon. In this class of problem, airport capacity is represented by an arrival-departure capacity curve or envelope. Therefore, arrival and departure capacities are considered as interdependent variables whose values depend on the arrival/departure ratio of total airport operations.

We formalise both the single-airport and the multi-airport version of the problem. In particular, for the single-airport capacity allocation problem, we present a dynamic programming formulation solved by using a customised algorithm. For the multi-airport version we propose a integer programming formulation, since some of the properties of the single-airport capacity allocation problem break down when dealing with a network structure. We solve this version of the problem using the CPLEX branch and bound. Computational results are given for both versions of the problem.

Keywords

capacity allocation problem air traffic flow management dynamic programming mathematical programming 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. [1]
    Adams M., Kolitz S., Milner J., Odoni A.R., Evolutionary concepts for Decentralized Air Traffic Flow Management. Air Traffic Control Quarterly, 4: 281–306, 1997.Google Scholar
  2. [2]
    Andreatta G., Brunetta L., Multiairport Ground Holding Problem: A Computational Evaluation of Exact Algorithm. Operation Research, 46: 57–64, 1998.zbMATHCrossRefGoogle Scholar
  3. [3]
    Andreatta G., Odoni A.R., Richetta O., Models for the Ground Holding Problem. In Large Scale Computation and Information Processing in ATC, L. Bianco, A.R.Odoni (eds.), Heidelberg: Springer Verlag, 1995.Google Scholar
  4. [4]
    Beasly J.E., Krishnamoorthy M., Sharaiha Y.M., Abramson A., Scheduling aircraft landings — the static case. Transportation Science, 34: 180–197, 2000.CrossRefGoogle Scholar
  5. [5]
    Beasly J. E., Krishnamoorthy M., Sharaiha Y. M., Abramson A. The displacement problem and dynamically scheduling aircraft landings, http://www.ms.ic.ac.uk/jeb/jeb.html.
  6. [6]
    Bertsimas D.J., Stock Patterson S. The Air Traffic Management Problem with Enroute Capacities. Operation Research, 46 406–422, 1998.zbMATHCrossRefGoogle Scholar
  7. [7]
    Bertsimas D. J., Stock Patterson S. The Air Traffic Management Problem in Air Traffic Control: A Dynamic Network Approach. Transportation Science, 34 239–255, 1999.CrossRefGoogle Scholar
  8. [8]
    Bianco L., Bielli M., System Aspects and Optimization Models in ATC Planning. In Large Scale Computation and Information Processing in ATC, L. Bianco, A.R. Odoni (eds.), Heidelberg: Springer Verlag, 1995.Google Scholar
  9. [9]
    Bianco L., Dell’Olmo P., Giordani S., Scheduling Models and Algorithm for TMA traffic management. In Modelling and Simulation in Air Traffic Management, L. Bianco, P. Dell’Olmo, A.R. Odoni (eds.), Heidelberg: Springer Verlag, 1997.CrossRefGoogle Scholar
  10. [10]
    Bianco L., Dell’Olmo P., Giordani S. Coordination of Traffic Flows in the TMA. In New Concepts and Methods in Air Traffic Management, L. Bianco, P. Dell’Olmo, A.R. Odoni (eds.), Heidelberg: Springer Verlag, 2002.Google Scholar
  11. [11]
    Blumstein A. The landing capacity of a runway. Operations Research, 7 752–763, 1959.CrossRefGoogle Scholar
  12. [12]
    Collaborative Decision Making in Aviation Transportation, http://www.metsci.com/, October 2000.
  13. [13]
    Dell’Olmo P., Lulli G., The airport capacity allocation problem: a dynamic programming approach. Technical Report 16/2001, Dept. of Statistics, Probability and Applied Statistics, University of Rome “LaSapienza”, 2001.Google Scholar
  14. [14]
    Gilbo E.P., Airport Capacity: Representation, Estimation Optimization. IEEE Transaction on Control Systems Technology, 1 144–154, 1993.CrossRefGoogle Scholar
  15. [15]
    Gilbo E.P. Optimizing Airport Capacity Utilization in Air Traffic Flow Management Subject to Constraints at Arrival and Departure Fixes. IEEE Transaction on Control Systems Technology, 5 490–503, 1997.CrossRefGoogle Scholar
  16. [16]
    Hall W. D. Efficient Capacity Allocation in a Collaborative Air Transportation System. PhD dissertation, MIT, 1999.Google Scholar
  17. [17]
    Hoffman R. L. Integer Programming Models for Ground-Holding in Air Traffic Flow Management PhD dissertation, University of Maryland, 1997.Google Scholar
  18. [18]
    Hoffman R. L., Ball M.O. A Comparison of Formulations for the Single Airport Ground Holding Problem with Banking Constraints. Operations Research, 48 578–590, 2000.CrossRefGoogle Scholar
  19. [19]
    Odoni A.R., Bowman J., et. al. Existing and Required Modeling Capabilities for Evaluating ATM System and Concepts. Final Report International Centre for Air Transportation, MIT, March 1997.Google Scholar
  20. [20]
    Odoni A. R. Efficient operation of runways. In Analysis of Public Systems, A.W. Drake, R.L. Keeney and P.M. Morse (eds.), Cambridge, MA: MIT Press, 1972.Google Scholar
  21. [21]
    Odoni A. R., Rousseau J., Wilson N. H. M. Models in Urban Transportation. In Operations Research and the Public Sector, Pollock S.M., Rothkopf M. M., Barnett A. (eds.), Amsterdam: North Holland, 1994.Google Scholar
  22. [22]
    Vranas P.B., Bertsimas D.J., Odoni A.R. The Multi-Airport Ground Holding Problem in Air Traffic Control. Operations Research, 42 249–261, 1994.zbMATHCrossRefGoogle Scholar
  23. [23]
    Winer D.E. Models for the Ground Holding Problem. In Large Scale Computation and Information Processing in ATC, L. Bianco, A.R. Odoni (eds.), Heidelberg: Springer Verlag, 1995.Google Scholar
  24. [24]
    Zenios S.A. Network based models for air traffic control. European Journal of Operational Reserch, 50 166–178, 1991.CrossRefGoogle Scholar
  25. [25]
    Zografos K. G., Stamatopoulos M.A., Odoni A.R. An Analitical Model for Runway System Capacity Analysis. Proceedings of 8 th IF AC Symposium on Transportation System, Chania, 1997.Google Scholar

Copyright information

© Springer Science+Business Media Dordrecht 2003

Authors and Affiliations

  • Paolo Dell’Olmo
    • 1
  • Guglielmo Lulli
    • 2
  1. 1.Dept. of Statistics, Probability and Applied StatisticsUniversity of Rome “La Sapienza”RomeItaly
  2. 2.Dept. of Statistics, Probability and Applied StatisticsUniversity of Rome “La Sapienza”Italy

Personalised recommendations