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A branch and cut heuristic for a runway scheduling problem

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Abstract

The paper is focused on one of the major air traffic management problem that consists in sequencing and scheduling airplanes landing and taking off on a runway. This difficult practical task is still carried out by flight controllers manually with little help from decision support systems. In this paper we propose an approach based on a time indexed integer programming formulation. The formulation is solved with a branch and cut method combined with some heuristic rules for dimension reduction. The effectiveness of the proposed approach is illustrated by computational experiments on real-life problem instances for the Milano Linate airport.

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References

  1. Bennell, J.A., Mesgarpour, M., and Potts, C.N., Airport Runway Scheduling, 4OR, 2011, vol. 9, no. 2, pp. 115–138.

    Article  MathSciNet  MATH  Google Scholar 

  2. Furini, F., Kidd, M.P., Persiani, C.A., and Toth, P., Improved Rolling Horizon Approaches to the Aircraft Sequencing Problem, J. Sched., 2015, vol. 18, no. 5, pp. 435–447.

    Article  MathSciNet  MATH  Google Scholar 

  3. Nogueira, T.H., De Carvalho, C.R.V., and Ravetti, M.G., Analysis of Mixed Integer Programming Formulations for Single Machine Scheduling Problems with Sequence Dependent Setup Times and Release Dates, Optim. Online, 2014, submitted to 4OR.

    Google Scholar 

  4. Abela, J., Abramson, D., Krishnamoorthy, M., et al., Computing Optimal Schedules for Landing Aircraft, in Proc. 12 National Conf. Austral. Soc. Oper. Res. Adelaide, 1993, pp. 71–90.

    Google Scholar 

  5. Briskorn, D. and Stolletz, R., Aircraft Landing Problems with Aircraft Classes, J. Sched., 2014, vol. 17, no. 1, pp. 31–45.

    Article  MathSciNet  MATH  Google Scholar 

  6. Furini, F., Persiani, C., and Toth, P., Aircraft Sequencing Problems via a Rolling Horizon Algorithm, in Proc. Second Int. Sympos. Combinat. Optim., Athens, 2012, pp. 273–284.

    Google Scholar 

  7. Samà, M., D’Ariano, A., and Pacciarelli, D., Rolling Horizon Approach for Aircraft Scheduling in the Terminal Control Area of Busy Airports, Transp. Res. Pt. e-Logist. Transp. Rev., 2013, vol. 60, pp. 140–155.

    Article  Google Scholar 

  8. Heidt, A., Helmke, H., Liers, F., and Martin, A., Robust Runway Scheduling Using a Time-Indexed Model, in Proc. 4 SESAR Innovat. Days, Madrid, 2014.

    Google Scholar 

  9. Kjenstad, D., Mannino, C., Nordlander, T.E., et al., Optimizing AMAN-SMAN-DMAN at Hamburg and Arlanda airport, in Proc. the Third SESAR Innovat. Days, Stockholm, 2013.

    Google Scholar 

  10. Kjenstad, D., Mannino, C., Schittekat, P., and Smedsrud, M., Integrated Surface and Departure Management at Airports by Optimization, in Proc. 5 Int. Conf. Model., Simulat. App. Optim., Hammamet, 2013, pp. 1–5.

    Google Scholar 

  11. Masin, M. and Raviv, T., Linear Programming-Based Algorithms for the Minimum Makespan High Multiplicity Jobshop Problem, J. Sched., 2014, vol. 17, no. 4, pp. 321–338.

    Article  MathSciNet  MATH  Google Scholar 

  12. Savelsbergh, M.W.P., Uma, R.N., and Wein, J., An Experimental Study of LP-Based Approximation Algorithms for Scheduling Problems, INFORMS J. Comput., 2005, vol. 17, no. 1, pp. 123–136.

    Article  MathSciNet  MATH  Google Scholar 

  13. Uma, R.N., Wein, J., and Williamson, D.P., On the Relationship between Combinatorial and LP-Based Approaches to NP-Hard Scheduling Problems, Theor. Comput. Sci., 2006, vol. 361, nos. 2–3, pp. 241–256.

    Article  MathSciNet  MATH  Google Scholar 

  14. Furini, F., Kidd, M.P., Persiani, C.A., and Toth, P., State Space Reduced Dynamic Programming for the Aircraft Sequencing Problem with Constrained Position Shifting, Proc. Third Int. Sympos. Combinat. Optim., Lisbon, 2014, pp. 267–279.

    Google Scholar 

  15. Gruzdeva, T.V., Solution of the Clique Problem by Reducing It to a Problem with a D.C. Constraint, Diskret. Anal. Issled. Oper., 2008, vol. 15, no. 6, pp. 17–22.

    MathSciNet  MATH  Google Scholar 

  16. Gruzdeva, T.V., On a Continuous Approach for the Maximum Weighted Clique Problem, J. Glob. Optim., 2013, vol. 56, no. 3, pp. 971–981.

    Article  MathSciNet  MATH  Google Scholar 

  17. Padberg, M.W., On the Facial Structure of the Set Packing Polyhedra, Math. Prog., 1973, vol. 5, no. 1, pp. 199–215.

    Article  MathSciNet  MATH  Google Scholar 

  18. Sousa, J.P. and Wolsey, L.A., A Time Indexed Formulation of Non-Preemptive Single Machine Scheduling Problems, Math. Prog., 1992, vol. 54, no. 1, pp. 353–367.

    Article  MathSciNet  MATH  Google Scholar 

  19. Avella, P., Boccia, M., Sforza, A., and Vasil’ev, I., A Branch-and-Cut Algorithm for the Median-Path Problem, Comput. Optim. Appl., 2005, vol. 32, no. 3, pp. 215–230.

    Article  MathSciNet  MATH  Google Scholar 

  20. Avella, P., Boccia, M., and Vasilyev, I., Computational Experience with General Cutting Planes for the Set Covering Problem, Oper. Res. Lett., 2009, vol. 37, no. 1, pp. 16–20, http://dx.doi.org/10.1016/j.orl.2008.09.009.

    Article  MathSciNet  MATH  Google Scholar 

  21. Avella, P., Boccia, M., and Vasilyev, I., Lifted and Local Reachability Cuts for the Vehicle Routing Problem with Time Windows, Comput. Oper. Res., 2013, vol. 40, no. 8, pp. 2004–2010.

    Article  MathSciNet  MATH  Google Scholar 

  22. Avella, P. and Vasil’ev, I., A Computational Study of a Cutting Plane Algorithm for University Course Timetabling, J. Sched., 2005, vol. 8, no. 6, pp. 497–514.

    Article  MathSciNet  MATH  Google Scholar 

  23. Vasilyev, I., Klimentova, K., and Boccia, M., Polyhedral Study of Simple Plant Location Problem with Order, Oper. Res. Lett., 2013, vol. 41, no. 2, pp. 153–158.

    Article  MathSciNet  MATH  Google Scholar 

  24. Vasilyev, I. and Klimentova, K., The Branch and Cut Method for the Facility Location Problem with Client’s Preferences, J. Appl. Industr. Math., 2010, vol. 4, pp. 441–454.

    Article  Google Scholar 

  25. Conforti, M., Cornuéjols, G., and Zambelli, G., Integer Programming, Cham: Springer, 2014.

    Book  MATH  Google Scholar 

  26. Wolsey, L., Integer Programming, New York: Wiley-Interscience, 1998.

    MATH  Google Scholar 

  27. Kochetov, Y.A. and Khmelev, A.V., Hybrid Local Search for the Heterogeneous Fixed Fleet Vehicle Routing Problem, Diskret. Anal. Issled. Oper., 2015, vol. 22, no. 5, pp. 5–29.

    MathSciNet  MATH  Google Scholar 

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Correspondence to I. L. Vasilyev.

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Original Russian Text © I.L. Vasilyev, P. Avella, M. Boccia, 2016, published in Avtomatika i Telemekhanika, 2016, No. 11, pp. 131–141.

This paper was recommended for publication by A.A. Lazarev, a member of the Editorial Board

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Vasilyev, I.L., Avella, P. & Boccia, M. A branch and cut heuristic for a runway scheduling problem. Autom Remote Control 77, 1985–1993 (2016). https://doi.org/10.1134/S0005117916110084

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  • DOI: https://doi.org/10.1134/S0005117916110084

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