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A branch and cut heuristic for a runway scheduling problem

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. 1.

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

  2. 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.

  3. 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.

  4. 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.

  5. 5.

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

  6. 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.

  7. 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.

  8. 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.

  9. 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.

  10. 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.

  11. 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.

  12. 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.

  13. 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.

  14. 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.

  15. 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.

  16. 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.

  17. 17.

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

  18. 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.

  19. 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.

  20. 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.

  21. 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.

  22. 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.

  23. 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.

  24. 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.

  25. 25.

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

  26. 26.

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

  27. 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.

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Correspondence to I. L. Vasilyev.

Additional information

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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