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Recoverable robust timetabling for single delay: Complexity and polynomial algorithms for special cases

Author

Listed:
  • Serafino Cicerone

    (University of L’Aquila)

  • Gianlorenzo D’Angelo

    (University of L’Aquila)

  • Gabriele Stefano

    (University of L’Aquila)

  • Daniele Frigioni

    (University of L’Aquila)

  • Alfredo Navarra

    (University of Perugia)

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.

Suggested Citation

  • Serafino Cicerone & Gianlorenzo D’Angelo & Gabriele Stefano & Daniele Frigioni & Alfredo Navarra, 2009. "Recoverable robust timetabling for single delay: Complexity and polynomial algorithms for special cases," Journal of Combinatorial Optimization, Springer, vol. 18(3), pages 229-257, October.
    • Handle: RePEc:spr:jcomop:v:18:y:2009:i:3:d:10.1007_s10878-009-9247-4
    DOI: 10.1007/s10878-009-9247-4
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    References listed on IDEAS

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    1. Dimitris Bertsimas & Melvyn Sim, 2004. "The Price of Robustness," Operations Research, INFORMS, vol. 52(1), pages 35-53, February.
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    Cited by:

    1. Polinder, G.-J. & Breugem, T. & Dollevoet, T.A.B. & Maróti, G., 2019. "An Adjustable Robust Optimization Approach for Periodic Timetabling," Econometric Institute Research Papers EI2019-01, Erasmus University Rotterdam, Erasmus School of Economics (ESE), Econometric Institute.
    2. Carrizosa, Emilio & Goerigk, Marc & Schöbel, Anita, 2017. "A biobjective approach to recoverable robustness based on location planning," European Journal of Operational Research, Elsevier, vol. 261(2), pages 421-435.
    3. Bakker, Hannah & Dunke, Fabian & Nickel, Stefan, 2020. "A structuring review on multi-stage optimization under uncertainty: Aligning concepts from theory and practice," Omega, Elsevier, vol. 96(C).

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