Skip to main content

Aircraft landing problems with aircraft classes


This article focuses on the aircraft landing problem that is to assign landing times to aircraft approaching the airport under consideration. Each aircraft’s landing time must be in a time interval encompassing a target landing time. If the actual landing time deviates from the target landing time additional costs occur which depend on the amount of earliness and lateness, respectively. The objective is to minimize overall cost. We consider the set of aircraft being partitioned into aircraft classes such that two aircraft of the same class are equal with respect to wake turbulence. We develop algorithms to solve the corresponding problem. Analyzing the worst case run-time behavior, we show that our algorithms run in polynomial time for fairly general cases of the problem. Moreover, we present integer programming models. We show by means of a computational study how optimality properties can be used to increase efficiency of standard solvers.

This is a preview of subscription content, access via your institution.

Fig. 1
Fig. 2
Fig. 3


  • Balakrishnan, H., & Chandran, B. (2010). Algorithms for scheduling runway operations under constrained position shifting. Operations Research, 58(6), 1650–1665.

    Article  Google Scholar 

  • Baptiste, P. (2000). Scheduling equal-length jobs on identical parallel machines. Discrete Applied Mathematics, 103, 21–32.

    Article  Google Scholar 

  • Barnhart, C., Belobaba, P., & Odoni, A. R. (2003). Applications of operations research in the air transport industry. Transportation Science, 37(4), 368–391.

    Article  Google Scholar 

  • Beasley, J., Krishnamoorthy, M., Sharaiha, Y., & Abramson, D. (2000). Scheduling aircraft landings: The static case. Transportation Science, 34(2), 180–197.

    Article  Google Scholar 

  • Beasley, J. E., Krishnamoorthy, M., Sharaiha, Y. M., & Abramson, D. (2004). Displacement problem and dynamically scheduling aircraft landings. Journal of the Operational Research Society, 55, 54–64.

    Article  Google Scholar 

  • Bianco, L., Dell’Olmo, P., & Giordani, S. (1999). Minimizing total completion time subject to release dates and sequence-dependent processing times. Annals of Operations Research, 86, 393–415.

    Article  Google Scholar 

  • Bianco, L., Dell‘Olmo, P., & Giordani, S. (2006). Scheduling models for air traffic control in terminals areas. Journal of Scheduling, pp. 223–253.

  • Dear, R. G., & Sherif, Y. S. (1991). An algorithm for computer assisted sequencing and scheduling of terminal area operations. Transportation Research A, 25A(2/3), 129–139.

    Article  Google Scholar 

  • Ernst, A. T., Krishnamoorthy, M., & Storer, R. H. (1999). Heuristic and exact algorithms for scheduling aircraft landings. Networks, 34(3), 229–241.

    Article  Google Scholar 

  • Fahle, T., Feldmann, R., Gtz, S., Grothklags, S., & Monien, B. (2003). The aircraft sequencing problem. In R. Klein, H.-W. Six, & L. M. Wegner (Eds.), Computer Science in Perspective, Essays Dedicated to Thomas Ottmann, Lecture Notes in Computer Science (Vol. 2598, pp. 152–166). Springer: Berlin.

  • Harikiopoulo, D., & Neogi, N. (2011). Polynomial-time feasibility condition for multiclass aircraft sequencing on a single-runway airport. IEEE Transactions on Intelligent Transportation Systems, 12(1): 2–14.

    Google Scholar 

  • Pinedo, M. (2012). Scheduling: Theory, algorithms, and systems. Berlin: Springer.

    Book  Google Scholar 

  • Pinol, H., & Beasley, J. (2006). Scatter search and bionomic algorithms for the aircraft landing problem. European Journal of Operations Research, 171, 439–462.

    Article  Google Scholar 

  • Potts, C. N., & Kovalyov, M. Y. (2000). Scheduling with batching: A review. European Journal of Operational Research, 120, 228–249.

    Google Scholar 

  • Psaraftis, H. N. (1978). A dynamic programming approach to the aircraft sequencing problem. Flight Transportation Laboratory, Technical report, MIT.

  • Psaraftis, H. N. (1980). A dynamic programming approach for sequencing groups of identical jobs. Operations Research, 28(6), 1347–1359.

    Article  Google Scholar 

  • Soomer, M., & Koole, G. (2008). Fairness in the aircraft landing problem. Technical report, Department of Mathematics, Vrije Universiteit Amsterdam.

  • Soomer, M. J., & Franx, G. J. (2008). Scheduling aircraft landings using airlines’ preferences. European Journal of Operational Research, 190(1), 277–291.

    Google Scholar 

  • Venkatakrishnan, C., Barnett, A., & Odoni, A. R. (1993). Landings at logan airport: Describing and increasing airport capacity. Transportation Science, 27(3), 211–227.

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations


Corresponding author

Correspondence to Dirk Briskorn.

Rights and permissions

Reprints and Permissions

About this article

Cite this article

Briskorn, D., Stolletz, R. Aircraft landing problems with aircraft classes. J Sched 17, 31–45 (2014).

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: