Journal of the Operational Research Society

, Volume 55, Issue 1, pp 54–64

Displacement problem and dynamically scheduling aircraft landings

  • J E Beasley
  • M Krishnamoorthy
  • Y M Sharaiha
  • D Abramson
Theoretical Paper


In this paper we define a generic decision problem — the displacement problem. The displacement problem arises when we have to make a sequence of decisions and each new decision that must be made has an explicit link back to the previous decision that was made. This link is quantified by means of the displacement function. One situation where the displacement problem arises is that of dynamically scheduling aircraft landings at an airport. Here decisions about the landing times for aircraft (and the runways they land on) must be taken in a dynamic fashion as time passes and the operational environment changes. We illustrate the application of the displacement problem to the dynamic aircraft landing problem. Computational results are presented for a number of publicly available test problems involving up to 500 aircraft and five runways.


displacement problem air traffic control runway operations scheduling 


  1. Beasley JE, Krishnamoorthy M, Sharaiha YM and Abramson D (2000). Scheduling aircraft landings — the static case. Transport Sci 34: 180–197.CrossRefGoogle Scholar
  2. Beasley JE, Sonander J and Havelock P (2001). Scheduling aircraft landings at London Heathrow using a population heuristic. J Opl Res Soc 52: 483–493.CrossRefGoogle Scholar
  3. Odoni AR, Rousseau J-M and Wilson NHM (1994). Models in urban and air transportation. In: Pollock SM, Rothkopf MH and Barnett A (eds) Operations Research and the Public Sector: Handbooks in Operations Research and Management Science, Vol 6. North-Holland: Amsterdam, The Netherlands, pp 107–150.CrossRefGoogle Scholar
  4. Erzberger H (1995). Design principles and algorithms for automated air traffic management: In: Knowledge-based Functions in Aerospace Systems. AGARD Lecture Series no. 200. NATO Neuilly-Sur-Seine, France, 7:1–7:31.Google Scholar
  5. Milan J (1997). The flow management problem in air traffic control: a model of assigning priorities for landings at a congested airport. Transport Plann Technol 20: 131–162.CrossRefGoogle Scholar
  6. Andreussi A, Bianco L and Ricciardelli S (1981). A simulation model for aircraft sequencing in the near terminal area. Eur J Opl Res 8: 345–354.CrossRefGoogle Scholar
  7. Dear RG and Sherif YS (1989). The dynamic scheduling of aircraft in high density terminal areas. Microelectron Reliab 29: 743–749.CrossRefGoogle Scholar
  8. Dear RG and Sherif YS (1991). An algorithm for computer assisted sequencing and scheduling of terminal area operations. Transport Res A 25A: 129–139.CrossRefGoogle Scholar
  9. Dear RG (1976). The dynamic scheduling of aircraft in the near terminal area, Report R76-9 Flight Transportation Laboratory, MIT, Cambridge, MA, USA.Google Scholar
  10. Brinton CR (1992). An implicit enumeration algorithm for arrival aircraft scheduling. In: Proceedings of the 11th IEEE/AIAA Digital Avionics Systems Conference Seattle, WA. IEEE, NY, USA, pp 268–274.Google Scholar
  11. Venkatakrishnan CS, Barnett A and Odoni AR (1993). Landings at Logan Airport: describing and increasing airport capacity. Transport Sci 27: 211–227.CrossRefGoogle Scholar
  12. Psaraftis HN (1978). A dynamic programming approach to the aircraft sequencing problem, Report R78-4 Flight Transportation Laboratory, MIT, Cambridge MA, USA.Google Scholar
  13. Psaraftis HN (1980). A dynamic programming approach for sequencing groups of identical jobs. Opns Res 28: 1347–1359.CrossRefGoogle Scholar
  14. Ciesielski V and Scerri P (1997). An anytime algorithm for scheduling of aircraft landing times using genetic algorithms. Aust J Intell Inf Process Systems 4: 206–213.Google Scholar
  15. Ciesielski V and Scerri P (1998). Real time genetic scheduling of aircraft landing times. In: Fogel D (ed) Proceedings of the 1998 IEEE International Conference on Evolutionary Computation (ICEC98). IEEE, NY, USA, pp 360–364.Google Scholar
  16. Carr GC, Erzberger H and Neuman F (1998). Airline arrival prioritization in sequencing and scheduling. Paper presented at the second USA/Europe Air Traffic Management R&D Seminar, Orlando. Available from.
  17. Carr GC, Erzberger H and Neuman F (1999). Delay exchanges in arrival sequencing and scheduling. J Aircraft 36: 785–791.CrossRefGoogle Scholar
  18. Carr GC, Erzberger H and Neuman F (2000). Fast-time study of airline-influenced arrival sequencing and scheduling. J Guidance Control Dyn 23: 526–531.CrossRefGoogle Scholar
  19. Bolender MA and Slater GL (2000). Evaluation of scheduling methods for multiple runways. J Aircraft 37: 410–416.CrossRefGoogle Scholar
  20. Wong GL (2000). The dynamic planner: the sequencer, scheduler, and runway allocator for air traffic control automation, Report NASA/TM-2000-209586, NASA Ames Research Center, Moffett Field, CA, USA, Available from. Scholar
  21. ILOG Inc (1999). ILOG CPLEX 6.5 User's Manual. ILOG Inc.: Mountain View, CA, USA.Google Scholar
  22. Beasley JE (1990). OR-Library: distributing test problems by electronic mail. J Opl Res Soc 41: 1069–1072.CrossRefGoogle Scholar
  23. Beasley JE (1996). Obtaining test problems via Internet. J Global Optim 8: 429–433.CrossRefGoogle Scholar

Copyright information

© Palgrave Macmillan Ltd 2004

Authors and Affiliations

  • J E Beasley
    • 1
  • M Krishnamoorthy
    • 2
  • Y M Sharaiha
    • 1
  • D Abramson
    • 3
  1. 1.Imperial CollegeLondonUK
  2. 2.CSIRO Mathematical and Information Sciences, Clayton South MDCVictoriaAustralia
  3. 3.Monash UniversityVictoriaAustralia

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