Skip to main content
SpringerLink
Log in

Column generation based solution for bi-objective gate assignment problems

  • Original Article
  • Published:
Mathematical Methods of Operations Research Aims and scope Submit manuscript

Abstract

In this paper, we present a column generation-based algorithm for the bi-objective gate assignment problem (GAP) to generate gate schedules that minimize squared slack time at the gates while satisfying passenger expectations by minimizing their walking distance. While most of the literature focuses on heuristic or metaheuristic solutions for the bi-objective GAP, we propose flow-based and column-based models that lead to exact or near optimal solution approaches. The developed algorithm calculates a set of solutions to approximate the Pareto front. The algorithm is applied to the over-constrained GAP where gates are a limited resource and it is not possible to serve every flight using a gate. Our test cases are based on real data from an international airport and include various instances with flight-to-gate ratios between 23.9 and 34.7. Numerical results reveal that a set of solutions representing a compromise between the passenger-oriented and robustness-oriented objectives may be obtained with a tight optimality gap and within reasonable computational time even for these difficult problems.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Algorithm 1
Fig. 2
Fig. 3

Similar content being viewed by others

References

  • Barnhart C, Boland NL, Clarke LW, Johnson EL, Nemhauser GL, Shenoi RG (1998) Flight string models for aircraft fleeting and routing. Transp Sci 32(3):208–220

    Article  Google Scholar 

  • Benlic U, Burke EK, Woodward JR (2017) Breakout local search for the multi-objective gate allocation problem. Comput Oper Res 78:80–93

    Article  MathSciNet  Google Scholar 

  • Bihr RA (1990) A conceptual solution to the aircraft gate assignment problem using 0, 1 linear programming. Comput Ind Eng 19(1):280–284

    Article  Google Scholar 

  • Braaksma JP, Shortreed JH (1971) Improving airport gate usage with critical path. Transp Eng J ASCE 97(2):187–203

    Article  Google Scholar 

  • Cai X, Sun W, Misir M, Tan KC, Li X, Xu T, Fan Z (2019) A bi-objective constrained robust gate assignment problem: formulation, instances and algorithm. IEEE Trans Cybern 51(9):4488–4500

    Article  Google Scholar 

  • Cecen RK (2021) Multi-objective optimization model for airport gate assignment problem. Aircraft Eng Aerosp Technol 93:311

    Article  Google Scholar 

  • Cheng Y (1997) A knowledge-based airport gate assignment system integrated with mathematical programming. Comput Ind Eng 32(4):837–852

    Article  Google Scholar 

  • Daş GS (2017) New multi objective models for the gate assignment problem. Comput Ind Eng 109:347–356

    Article  Google Scholar 

  • Daş GS, Gzara F, Stützle T (2020) A review on airport gate assignment problems: single versus multi objective approaches. Omega 92:102146

    Article  Google Scholar 

  • Dell’Orco M, Marinelli M, Altieri MG (2017) Solving the gate assignment problem through the fuzzy bee colony optimization. Transp Res Part C Emerg Technol 80:424–438

    Article  Google Scholar 

  • Deng W, Zhao H, Yang X, Xiong J, Sun M, Li B (2017) Study on an improved adaptive PSO algorithm for solving multi-objective gate assignment. Appl Soft Comput 59:288–302

    Article  Google Scholar 

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

    Article  MathSciNet  Google Scholar 

  • Ding H, Lim A, Rodrigues B, Zhu Y (2005) The over-constrained airport gate assignment problem. Comput Oper Res 32(7):1867–1880

    Article  Google Scholar 

  • Dorndorf U, Jaehn F, Pesch E (2008) Modelling robust flight-gate scheduling as a clique partitioning problem. Transp Sci 42(3):292–301

    Article  Google Scholar 

  • Drexl A, Nikulin Y (2008) Multicriteria airport gate assignment and pareto simulated annealing. IIE Trans 40(4):385–397

    Article  Google Scholar 

  • Ehrgott M (2005) Multicriteria optimization, vol 491. Springer, New York

    Google Scholar 

  • Ehrgott M, Gandibleux X, Przybylski A (2016) Exact methods for multi-objective combinatorial optimisation. In: Figueira J, Greco S, Ehrgott M (eds) Multiple criteria decision analysis, vol 233. Springer, New York, pp 817–850

    Chapter  Google Scholar 

  • Emmerich MT, Deutz AH (2018) A tutorial on multiobjective optimization: fundamentals and evolutionary methods. Nat Comput 17:585–609

    Article  MathSciNet  Google Scholar 

  • Glize E, Jozefowiez N, Ngueveu SU (2018) An exact column generation-based algorithm for bi-objective vehicle routing problems. In: Mahjoub A, Lee J, Rinaldi G (eds) Combinatorial optimization. ISCO 2018, vol 10856. LNCS. Springer, Cham, pp 208–218

    Google Scholar 

  • Grönkvist M (2006) Accelerating column generation for aircraft scheduling using constraint propagation. Comput Oper Res 33(10):2918–2934

    Article  Google Scholar 

  • Haghani A, Chen M-C (1998) Optimizing gate assignments at airport terminals. Transp Res Part A Policy Pract 32(6):437–454

    Article  Google Scholar 

  • Hu XB, Di Paolo E (2009) An efficient genetic algorithm with uniform crossover for the multi-objective airport gate assignment problem. Stud Comput Intell 171:71–89

    Article  Google Scholar 

  • Kaliszewski I, Miroforidis J, Stańczak JT (2017) Multiobjective optimization in the airport gate assignment problem, exact versus evolutionary multiobjective optimization. Comput Sci 18(1):41

    Article  Google Scholar 

  • Kaliszewski I, Miroforidis J (2019) Lower and upper bounds for the general multiobjective optimization problem. In: AIP conference proceedings, vol 2070. AIP Publishing LLC, p 020038

  • Karsu Ö, Azizoğlu M, Alanlı K (2021) Exact and heuristic solution approaches for the airport gate assignment problem. Omega 103:102422

    Article  Google Scholar 

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

    Article  Google Scholar 

  • Kim SH, Feron E, Clarke JP, Marzuoli A, Delahaye D (2017) Airport gate scheduling for passengers, aircraft, and operation. J Air Transp 25:1–6

    Article  Google Scholar 

  • Li Y, Clarke JP, Dey SS (2021) Using submodularity within column generation to solve the flight-to-gate assignment problem. Transp Res Part C Emerg Technol 129:103217

    Article  Google Scholar 

  • Lim A, Wang F (2005) Robust airport gate assignment. In: 17th IEEE international conference on tools with artificial intelligence, 2005. ICTAI. IEEE, pp 74–81

  • Lin KM, Ehrgott M, Raith A (2017) Integrating column generation in a method to compute a discrete representation of the nondominated set of multi-objective linear programmes. 4OR 15(4):331–357

    Article  MathSciNet  Google Scholar 

  • Liu S, Chen WH, Liu J (2016) Robust assignment of airport gates with operational safety constraints. Int J Autom Comput 13(1):31–41

    Article  Google Scholar 

  • Maharjan B, Matis TI (2012) Multi-commodity flow network model of the flight gate assignment problem. Comput Ind Eng 63(4):1135–1144

    Article  Google Scholar 

  • Mangoubi RS, Mathaisel DFX (1985) Optimizing gate assignments at airport terminals. Transp Sci 19(2):173–188

    Article  Google Scholar 

  • Mavrotas G, Florios K (2013) An improved version of the augmented εconstraint method (AUGMECON2) for finding the exact pareto set in multi-objective integer programming problems. Appl Math Comput 219(18):9652–9669

    MathSciNet  Google Scholar 

  • Mokhtarimousavi S, Talebi D, Asgari H (2018) A nondominated sorting genetic algorithm approach for optimization of multi-objective airport gate assignment problem. Transp Res Rec 2672:1–12

    Article  Google Scholar 

  • Moradi S, Raith A, Ehrgott M (2015) A bi-objective column generation algorithm for the multi-commodity minimum cost flow problem. Eur J Oper Res 244(2):369–378

    Article  MathSciNet  Google Scholar 

  • Neuman UM, Atkin JA (2013) Airport gate assignment considering ground movement. In: International conference on computational logistics, pp 184–198

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

    Article  MathSciNet  Google Scholar 

  • Nourmohammadzadeh A, Voß S (2021) Robust multi-objective gate scheduling at hub airports considering flight delays: a hybrid metaheuristic approach. In: International conference on computational logistics. Springer, pp 594–610

  • Pintea C-M, Pop PC, Chira C, Dumitrescu D (2008) A hybrid ant-based system for gate assignment problem. In: Hybrid artificial intelligence systems, pp 273–280

  • Prem 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 

  • Ruzika S, Wiecek MM (2005) Approximation methods in multiobjective programming. J Optim Theory Appl 126(3):473–501

    Article  MathSciNet  Google Scholar 

  • 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 

  • Tang C-H, Wang W-C (2013) Airport gate assignments for airlinespecific gates. J Air Transp Manag 30:10–16

    Article  Google Scholar 

  • Xu J, Bailey G (2001) The airport gate assignment problem: mathematical model and a tabu search algorithm. In: Proceedings of the 34th annual hawaii international conference on system sciences. IEEE

  • Yan S, Chang CM (1998) A network model for gate assignment. J Adv Transp 32(2):176–189

    Article  Google Scholar 

  • Yan S, Huo CM (2001) Optimization of multiple objective gate assignments. Transp Res Part A Policy Pract 35(5):413–432

    Article  Google Scholar 

  • Yildiz BC, Gzara F, Elhedhli S (2017) Airline crew pairing with fatigue: modeling and analysis. Transp Res Part C Emerg Technol 74:99–112

    Article  Google Scholar 

  • Yu C, Zhang D, Lau HYK (2016) MIP-based heuristics for solving robust gate assignment problems. Comput Ind Eng 93:171–191

    Article  Google Scholar 

  • Yu C, Zhang D, Lau HYK (2017) An adaptive large neighborhood search heuristic for solving a robust gate assignment problem. Expert Syst Appl 84:143–154

    Article  Google Scholar 

  • Yuan Y, Yan P, Zhao L (2020) Continuous time formulation and Lagrangian relaxation algorithm for the gate assignment problem. Math Probl Eng 2020:1–11

    MathSciNet  Google Scholar 

Download references

Funding

The first author is supported by Scientific and Technological Research Council of Turkey (TUBITAK) (Grant No. 1059B191700275) 2219 Post Doctoral Research Fellowship Program during her research at WAnOpt Lab, University of Waterloo.

Author information

Authors and Affiliations

  1. Department of Industrial Engineering, Kırıkkale University, Kırıkkale, Turkey

    Gülesin Sena Daş

  2. Leicester Castle Business School, De Montfort University, Leicester, UK

    Gülesin Sena Daş

  3. Department of Management Science and Engineering, University of Waterloo, Waterloo, ON, Canada

    Fatma Gzara

Authors
  1. Gülesin Sena Daş
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Fatma Gzara
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Gülesin Sena Daş.

Additional information

Publisher's Note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Daş, G.S., Gzara, F. Column generation based solution for bi-objective gate assignment problems. Math Meth Oper Res (2024). https://doi.org/10.1007/s00186-024-00856-1

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • DOI: https://doi.org/10.1007/s00186-024-00856-1

Keywords

Search

Navigation