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Strengthened Formulations and Valid Inequalities for Single Delay Management in Public Transportation

Author

Listed:
  • Veronica Dal Sasso

    (Dipartimento di Matematica “Tullio Levi–Civita,” Università degli Studi di Padova, 35121 Padova, Italy)

  • Luigi De Giovanni

    (Dipartimento di Matematica “Tullio Levi–Civita,” Università degli Studi di Padova, 35121 Padova, Italy)

  • Martine Labbé

    (Graphes et Optimisation Mathématique, Université Libre de Bruxelles, 1050 Bruxelles, Belgium)

Abstract

The delay management problem arises in public transportation networks, often characterized by the necessity of connections between different vehicles. The attractiveness of public transportation networks is strongly related to the reliability of connections, which can be missed when delays or other unpredictable events occur. Given a single initial delay at one node of the network, the delay management problem is to determine which vehicles have to wait for the delayed ones, with the aim of minimizing the dissatisfaction of the passengers. In this paper, we present strengthened mixed integer linear programming formulations and new families of valid inequalities. The implementation of branch-and-cut methods and tests on a benchmark of instances taken from real networks show the potential of the proposed formulations and cuts.

Suggested Citation

  • Veronica Dal Sasso & Luigi De Giovanni & Martine Labbé, 2019. "Strengthened Formulations and Valid Inequalities for Single Delay Management in Public Transportation," Transportation Science, INFORMS, vol. 53(5), pages 1271-1286, September.
    • Handle: RePEc:inm:ortrsc:v:53:y:2019:i:5:p:1271-1286
    DOI: 10.1287/trsc.2018.0874
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    References listed on IDEAS

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    1. Michael Schachtebeck & Anita Schöbel, 2010. "To Wait or Not to Wait---And Who Goes First? Delay Management with Priority Decisions," Transportation Science, INFORMS, vol. 44(3), pages 307-321, August.
    2. Heilporn, Géraldine & De Giovanni, Luigi & Labbé, Martine, 2008. "Optimization models for the single delay management problem in public transportation," European Journal of Operational Research, Elsevier, vol. 189(3), pages 762-774, September.
    3. Twan Dollevoet & Dennis Huisman & Leo Kroon & Marie Schmidt & Anita Schöbel, 2015. "Delay Management Including Capacities of Stations," Transportation Science, INFORMS, vol. 49(2), pages 185-203, May.
    4. Dollevoet, T.A.B. & Huisman, D. & Schmidt, M.E. & Schöbel, A., 2010. "Delay Management with Re-Routing of Passengers," Econometric Institute Research Papers EI 2010-31, Erasmus University Rotterdam, Erasmus School of Economics (ESE), Econometric Institute.
    5. Corman, Francesco & D’Ariano, Andrea & Marra, Alessio D. & Pacciarelli, Dario & Samà, Marcella, 2017. "Integrating train scheduling and delay management in real-time railway traffic control," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 105(C), pages 213-239.
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    2. Nasini, Stefano & Labbé, Martine & Brotcorne, Luce, 2022. "Multi-market portfolio optimization with conditional value at risk," European Journal of Operational Research, Elsevier, vol. 300(1), pages 350-365.

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