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Flight gate assignment and recovery strategies with stochastic arrival and departure times


We consider the problem of assigning flights to airport gates. We examine the general case in which an aircraft serving a flight may be assigned to different gates for arrival, parking, and departure processing. The objectives can be divided into deterministic and stochastic goals. The former include maximization of the total assignment preference score, a minimal number of unassigned flights during overload periods, and minimization of the number of tows. A special focus lies on the stochastic objectives, which aim at minimizing the expected number of any kind of constraint violations, i.e. not respecting gate closures, violation of shadow restrictions (a situation in which gate assignments may cause blocking of neighboring gates) or of tow time restrictions and classical gate conflicts in which two aircraft are assigned to the same gate and are at the airport at the same time. We show that the minimization of expected gate conflicts can be modeled in a graph theoretical approach using the clique partitioning problem (CPP). We furthermore show that the classical (deterministic) flight gate assignment problem, which can also be modeled using a CPP, can be integrated such that a simple though powerful model emerges, which no longer needs including a dummy gate, which is often used in practical gate assignment models. As constraint violations cannot fully be prevented, recovery strategies become necessary. We present a procedure for recovery planning that has proved its practical relevance at numerous airports. Finally, in an extensive numerical study we test our results on practical data, which contain a statistical analysis of flight arrival and departure times. The tests include a detailed comparison of current robustness measures and state-of-the-art approaches found in literature.

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  1. We assume that the time for parking includes a possible towing procedure. That is, \(C_j-S_j\) is the available time for towing and parking the aircraft.

  2. For convenience we do not consider gate setup times. They can easily be regarded when calculating the overlapping probabilities. In fact, in the computational tests gate setup times are included.


  • Bolat A (2000) Procedures for providing robust gate assignments for arriving aircraft. Eur J Oper Res 120:63–80

    Article  Google Scholar 

  • Castaing J, Mukherjee I, Cohn A, Hurwitz L, Nguyen A, Müller JJ (2016) Reducing airport gate blockage in passenger aviation: models and analysis. Comput Oper Res 65:189–199

    Article  Google Scholar 

  • Diepen G, Akker J, Hoogeveen J, Smeltink J (2012) Finding a robust assignment of flights to gates at Amsterdam Airport Schiphol. J Sched 15(6):703–715

    Article  Google Scholar 

  • Ding H, Lim A, Rodrigues B, Zhu Y (2004) New heuristics for the overconstrained airport gate assignment problem. J Oper Res Soc 55:760–768

    Article  Google Scholar 

  • Dorndorf U (2002) Project scheduling with time windows: from theory to application. Physica, Heidelberg

    Book  Google Scholar 

  • Dorndorf U, Pesch E (1994) Fast clustering algorithms. ORSA J Comput 6:141–153

    Article  Google Scholar 

  • Dorndorf U, Pesch E, Phan-Huy T (2000) A time-oriented branch-and-bound algorithm for resource constrained project scheduling with generalised precedence constraints. Manag Sci 46:1365–1384

    Article  Google Scholar 

  • Dorndorf U, Drexl A, Nikulin Y, Pesch E (2007) Flight gate scheduling: state-of-the-art and recent developments. Omega 35:326–334

    Article  Google Scholar 

  • Dorndorf U, Jaehn F, Pesch E (2008) Modelling robust flight gate scheduling as a clique partitioning problem. Transp Sci 42:292–301

    Article  Google Scholar 

  • Dorndorf U, Jaehn F, Pesch E (2012) Flight gate scheduling with respect to a reference schedule. Ann Oper Res 194:177–187

    Article  Google Scholar 

  • Drexl A, Nikulin Y (2006) Fuzzy multicriteria flight gate assignment. Working paper no. 605, University of Kiel

  • Grötschel M, Wakabayashi Y (1989) A cutting plane algorithm for a clustering problem. Math Program B 45:52–96

    Article  Google Scholar 

  • Grötschel M, Wakabayashi Y (1990) Facets of the clique partitioning polytope. Math Program A 47:367–387

    Article  Google Scholar 

  • Guépet J, Acuna-Agost R, Briant O, Gayon J-P (2015) Exact and heuristic approaches to the airport stand allocation problem. Eur J Oper Res 246(2):597–608

    Article  Google Scholar 

  • Hassounah M, Steuart G (1993) Demand for aircraft gates. Transp Res Rec 1423:26–33

    Google Scholar 

  • Jaehn F, Pesch E (2013) New bounds and constraint propagation techniques for the clique partitioning problem. Discrete Appl Math 161(13):2025–2037

    Article  Google Scholar 

  • Kim SH, Feron E, Clarke J-P (2013) Gate assignment to minimize passenger transit time and aircraft taxi time. J Guid Control Dyn 36(2):467–475

    Article  Google Scholar 

  • Kumar V, Bierlaire M (2014) Multi-objective airport gate assignment problem in planning and operations. J Adv Transp 48(7):902–926

    Article  Google Scholar 

  • Lim A, Wang F (2005) Robust airport gate assignment. In: ICTAI ’05: proceedings of the 17th IEEE international conference on tools with artificial intelligence, Washington, DC, USA. IEEE Computer Society, pp 74–81

  • List GF, Wood B, Nozick LK, Turnquist MA, Jones DA, Kjeldgaard EA, Lawton CR (2003) Robust optimization for fleet planning under uncertainty. Transp Res Part E: Logist Transp Rev 39(3):209–227

    Article  Google Scholar 

  • Mulvey JM, Vanderbei RJ, Zenios SA (1995) Robust optimization of large-scale systems. Oper Res 43(2):264–281

    Article  Google Scholar 

  • Neuman UM, Atkin JA (2013) Airport gate assignment considering ground movement. Lect Notes Comput Sci 8197:184–198

    Article  Google Scholar 

  • Nikulin Y (2006) Robustness in combinatorial optimization and scheduling theory: an extended annotated bibliography. Working paper no. 606, University of Kiel

  • Nikulin Y, Drexl A (2010) Theoretical aspects of multicriteria flight gate scheduling: deterministic and fuzzy models. J Sched 13(3):261–280

    Article  Google Scholar 

  • Ravizza S, Atkin J, Burke E (2014) A more realistic approach for airport ground movement optimisation with stand holding. J Sched 17(5):507–520

    Article  Google Scholar 

  • Richter U (2005) Analyse und Simulation von FlugverspStungen zur robusten Schichtplanung von Abfertigungsdiensten auf FlughSfen. Master’s thesis, Department of Mathematics, RWTH Aachen University

  • Şeker M, Noyan N (2012) Stochastic optimization models for the airport gate assignment problem. Transp Res Part E: Logist Transp Rev 48(2):438–459

    Article  Google Scholar 

  • Yan S, Tang C (2007) A heuristic approach for airport gate assignments for stochastic flight delays. Eur J Oper Res 180:547–567

    Article  Google Scholar 

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Correspondence to Florian Jaehn.

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This work has been supported by the German Science Foundation (DFG) through the grant “Planung der Bodenabfertigung an Flughäfen” (PE 514/10-1).

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Dorndorf, U., Jaehn, F. & Pesch, E. Flight gate assignment and recovery strategies with stochastic arrival and departure times. OR Spectrum 39, 65–93 (2017).

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  • Gate assignment
  • Clique partitioning
  • Robustness