Abstract
We present a new robust formulation for the crew pairing problem where flight and connection times are random and vary within an interval. The model protects against infeasibility with a specified level of uncertainty and minimizes crew cost in the worst case. The resulting robust terms in the objective function and in the resource constraints are nonlinear. We apply Lagrangian relaxation to separate the nonlinear terms in the subproblem leading to a new robust formulation of the shortest path problem with resource constraints. We show that the nonlinear subproblem can be solved as a series of linear auxiliary problems. The proposed solution methodology was successful to solve industry instances in very competitive times and led to more robust crew pairing solutions as shown by simulation experiments.
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A4A. Annual and per-minute cost of delays to U.S. airlines. http://www.airlines.org/Pages/Annual-and-Per-Minute-Cost-of-Delays-to-U.S.-Airlines.aspx, May (2012). Accessed 06 May 2014
Ball, M., Barnhart, C., Dresner, M., Hansen, M., Neels, K., Odoni, A., Peterson, E., Sherry, L., Trani, A., Zou, B.: Total delay impact study: a comprehensive assessment of the costs and impacts of flight delay in the united states. http://www.nextor.org/pubs/TDI_Report_Final_11_03_10.pdf (2010). Accessed 06 May 2014
Ball, M.O., Magnanti, T.L., Monma, G.L.: Network Routing, 1st edn. Elsevier, Amsterdam (1995)
Barnhart, C., Hatay, L., Johnson, E.: Deadhead selection for the long-haul crew pairing problem. Oper. Res. 43(3), 491–499 (1995)
Barnhart, C., Cohn, A., Johnson, E., Klabjan, D., Nemhauser, G.L., Vance, P.H.: Airline crew scheduling. In: Hall, R.W. (ed.) Handbook of Transportation Science. International Series in Operations Research & Management Science, vol. 56, pp. 517–560. Springer, US (2003). doi:10.1007/0-306-48058-1_14
Ben-Tal, A., Nemirovski, A.: Robust convex optimization. Math. Oper. Res. 23(4), 769–805 (1998)
Ben-Tal, A., Nemirovski, A.: Robust solutions of uncertain linear programs. OR Lett. 25(1), 1–13 (1999)
Ben-Tal, A., Nemirovski, A.: Robust solutions of linear programming problems contaminated with uncertain data. Math. Program. 88(3), 414–424 (2000)
Bertsimas, D., Sim, M.: Robust discrete optimization and network flows. Math. Program. 98(1), 49–71 (2003)
Bertsimas, D., Sim, M.: The price of robustness. Oper. Res. 52(1), 35–53 (2004)
Birge, J., Louveaux, F.: Introduction to Stochastic Programming, 1st edn. Springer, New York (1997)
Clarke, M.D.D., Ryan, D.M.: Airline industry operations research, In: Encyclopedia of Operations Research and Management Science, pp. 10–16. Springer, US (2011). doi:10.1007/1-4020-0611-X_24
Desaulniers, G., Desrosiers, J., Dumas, Y., Marc, S., Rioux, B., Solomon, M., Soumis, F.: Crew pairing at air france. Eur. J. Oper. Res. 97(2), 245–259 (1997)
Desaulniers, G., Desrosiers, J., Loachim, I., Solomon, M.M., Soumis, F., Villeneuve, D.: A unified framework for deterministic time constrained vehicle routing and crew scheduling problems. In: Crainic, T., Laporte, G. (eds.) Fleet Management and Logistics. Centre for Research on Transportation, pp. 57–93. Springer, US (1998). doi:10.1007/978-1-4615-5755-5_3
Deshpande, V., Arkan, M.: The impact of airline flight schedules on flight delays. Manuf. Serv. Oper. Manag. 14(3), 423–440 (2012)
Desrosiers, J., Dumas, Y., Desrochers, M., Soumis, F., Sanso, B., Trudeau, P.: A breakthrough in airline crew scheduling. Technical Report G-91-11, Cahiers du GERAD (1991).
Desrosiers, J., Dumas, Y., Solomon, M.M., Soumis, F. : Chapter 2 Time constrained routing and scheduling. In: Ball M.O., Magnanti, T.L., Monma, C.L., Nemhauser, G.L. (eds.) Network Routing. Handbook in Operations Research and Management Science, vol. 8, pp. 35–139. Elsevier (1995). doi:10.1016/S0927-0507(05)80106-9
Dunbar, M., Froyland, G., Wu, C.: Robust airline schedule planning: minimizing propagated delay in an integrated routing and crewing framework. Transp. Sci. 46(2), 204–216 (2012)
Eggenberg, N. : Combining robustness and recovery for airline schedules. PhD thesis, École Polytechnique Fédérale de Lausanne, Suisse, Swiss (2009)
Ehrgott, M., Ryan, D.: Constructing robust crew scheduleswith bicriteria optimization. J. Multi-Criteria Decis. Anal. 11(3), 139–150 (2002)
Ferguson, J., Kara, A.Q., Hoffman, K., Sherry, L.: Estimating domestic U.S. airline cost of delay based on European model. Transp. Res. C Emerg. Technol. 33, 311–323 (2013)
Gao, C., Johnson, E., Smith, B.: Integrated airline fleet and crew robust planning. Transp. Sci. 43(1), 2–16 (2009)
Herroelen, W., Leus, R.: Project scheduling under uncertainty: survey and research potentials. Eur. J. Oper. Res. 165(2), 289–306 (2005)
Klabjan, D., Johnson, E.L., Nemhauser, G.L., Gelman, E., Ramaswamy, S.: Airline crew scheduling with regularity. Transp. Sci. 35(4), 359–374 (2001a)
Klabjan, D., Johnson, E.L., Nemhauser, G.L., Gelman, E., Ramaswamy, S.: Solving large airline crew scheduling problems: random pairing generation and strong branching. Comput. Optim. Appl. 20(1), 73–91 (2001b)
Kohl, N., Larsen, A., Larsen, J., Ross, A., Tiourine, S.: Airline disruption management—perspectives, experiences and outlook. J. Air Transp. Manag. 13(3), 149–162 (2007)
Lan, S., Clarke, J., Barnhart, C.: Planning for robust airline operations: optimizing aircraft routings and flight departure times to minimize passenger disruptions. Transp. Sci. 40(1), 15–28 (2006)
Lavoie, S., Minoux, M., Odier, E.: A new approach for crew pairing problems by column generation with an application to air transportation. Eur. J. Oper. Res. 35(1), 45–58 (1988)
Makri, A., Klabjan, D.: A new pricing scheme for airline crew scheduling. INFORMS J. Comput. 16(1), 56–67 (2004)
Minoux, M. : Column generation techniques in combinatorial optimization: a new application to crew pairing problems. In: XXIVth AGIFORS Symposium (1984)
Sahinidis, N.: Optimization under uncertainty: state-of-the-art and opportunities. Comput. Chem. Eng. 28(6–7), 971–983 (2004)
Schaefer, A., Johnson, E., Kleywegt, A., Nemhauser, G. : Airline crew scheduling under uncertainty. Technical Report TLI-01-01, Georgia Institute of Technology (2000)
Shebalov, S., Klabjan, D.: Robust airline crew pairing: move-up crews. Transp. Sci. 40(3), 300–312 (2006)
Silver, N.: Fly early, arrive on-time. http://www.airlines.org/Pages/Annual-and-Per-Minute-Cost-of-Delays-to-U.S.-Airlines.aspx, April (2013). Accessed 06 May 2014
Smith, B., Johnson, E.: Robust airline fleet assignment: imposing station purity using station decomposition. Transp. Sci. 40(4), 497–516 (2006)
Sohoni, M., Lee, Y., Klabjan, D.: Robust airline scheduling under block time uncertainty. Transp. Sci. 45(4), 451–464 (2011)
Soyster, A.: Convex programming with set-inclusive constraints and application to inexact linear programming. Oper. Res. 21(5), 1154–1157 (1973)
Tam, B., Ehrgott, M., Ryan, D., Zakeri, G.: A comparison of stochastic programming and bi-objective optimisation approaches to robust airline crew scheduling. OR Spectr. 33(1), 49–75 (2011)
Tekiner, H., Birbil, S., Bulbul, K.: Robust crew pairing for managing extra flights. Comput. Oper. Res. 36(6), 2031–2048 (2009)
Weide, O., Ryan, D., Ehrgott, M.: An iterative approach to robust and integrated aircraft routing and crew scheduling. Comput. Oper. Res. 37(5), 833–844 (2010)
Yen, J., Birge, J.: A stochastic programming approach to the airline crew scheduling problem. Technical report, University of Washington, WA (2000)
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Lu, D., Gzara, F. The robust crew pairing problem: model and solution methodology. J Glob Optim 62, 29–54 (2015). https://doi.org/10.1007/s10898-014-0222-y
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DOI: https://doi.org/10.1007/s10898-014-0222-y