Abstract
In this paper, we study the problem of planning a timetable for passenger trains considering that possible delays might occur due to unpredictable circumstances. If a delay occurs, a timetable could not be able to manage it unless some extra time has been scheduled in advance. Delays might be managed in several ways and the usual objective function considered for such purpose is the minimization of the overall waiting time caused to passengers.
We analyze the timetable planning problem in terms of the recoverable robustness model, where a timetable is said to be recoverable robust if it is able to absorb small delays by possibly applying given limited recovery capabilities. The quality of a robust timetable is measured by the price of robustness that is the ratio between the cost of the recoverable robust timetable and that of a non-robust optimal one.
We consider the problem of designing recoverable robust timetables subject to bounded delays. We show that finding an optimal solution for this problem is NP-hard. Then, we propose robust algorithms, evaluate their prices of robustness, and show that such algorithms are optimal in some important cases.
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References
Bayer HG, Sendhoff B (2007) Robust optimization—a comprehensive survey. Comput Methods Appl Mech Eng 196(33–34):3190–3218
Ben-Tal A, El Ghaoui L, Nemirovski A (2006) Mathematical programming: special issue on robust optimization, vol 107. Springer, Berlin
Bertsimas D, Sim M (2004) The price of robustness. Oper Res 52(1):35–53
Cicerone S, D’Angelo G, Di Stefano G, Frigioni D, Navarra A (2007) Robust algorithms and price of robustness in shunting problems. In: Proc of the 7th workshop on algorithmic approaches for transportation modeling, optimization, and systems (ATMOS’07), pp 175–190
Cicerone S, D’Angelo G, Di Stefano G, Frigioni D, Navarra A (2008) Delay management problem: Complexity results and robust algorithms. In: Proc of 2nd annual international conference on combinatorial optimization and applications (COCOA’08). Lecture notes in computer science, vol 5165. Springer, Berlin, pp 458–468
De Giovanni L, Heilporn G, Labbé M (2007) Optimization models for the delay management problem in public transportation. Eur J Oper Res 189(3):762–774
Fischetti M, Monaci M (2006) Robust optimization through branch-and-price. In: Proceedings of the 37th annual conference of the Italian operations research society (AIRO)
Garey MR, Johnson DS (1979) Computers and intractability, a guide to the theory of NP-completeness. Freeman, New York
Gatto M, Glaus B, Jacob R, Peeters L, Widmayer P (2004) Railway delay management: Exploring its algorithmic complexity. In: Proc of the 9th Scandinavian workshop on algorithm theory (SWAT). Lecture notes in computer science, vol 3111. Springer, Berlin, pp 199–211
Gatto M, Jacob R, Peeters L, Schöbel A (2005) The computational complexity of delay management. In: Proc of the 31st international workshop on graph-theoretic concepts in computer science (WG). Lecture notes in computer science, vol 3787. Springer, Berlin, pp 227–238
Gatto M, Jacob R, Peeters L, Widmayer P (2007) Online delay management on a single train line. In: Proc. of the algorithmic methods for railway optimization (ATMOS’04). Lecture notes in computer science, vol 4359. Springer, Berlin, pp 306–320
Ginkel A, Schöbel A (2007) The bicriteria delay management problem. Transp Sci 41(4):527–538
Levy F, Thompson G, Wies J (1963) The ABCs of the critical path method. Graduate School of Business Administration, Harvard University
Liebchen C, Lüebbecke M, Möhring RH, Stiller S (2007) Recoverable robustness. Tech Rep ARRIVAL-TR-0066, ARRIVAL Project
Liebchen C, Stiller S (2008) Delay resistant timetabling. Public Transp 1(1):55–72
Schöbel A (2004) A model for the delay management problem based on mixed integer programming. Electron Notes Theor Comput Sci 50(1):1–10
Schöbel A (2007) Integer programming approaches for solving the delay management problem. In: Proc of the algorithmic methods for railway optimization (ATMOS’04). Lecture notes in computer science, vol 4359. Springer, Berlin, pp 145–170
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This work was partially supported by the Future and Emerging Technologies Unit of EC (IST priority–6th FP), under contract no. FP6-021235-2 (project ARRIVAL). An extended abstract of this paper appeared in the proceedings of the 2nd Annual International Conference on Combinatorial Optimization and Applications (COCOA’08) (Cicerone et al. 2008).
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Cicerone, S., D’Angelo, G., Di Stefano, G. et al. Recoverable robust timetabling for single delay: Complexity and polynomial algorithms for special cases. J Comb Optim 18, 229–257 (2009). https://doi.org/10.1007/s10878-009-9247-4
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DOI: https://doi.org/10.1007/s10878-009-9247-4