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Valid inequalities for the synchronization bus timetabling problem

Author

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  • Fouilhoux, P.
  • Ibarra-Rojas, O.J.
  • Kedad-Sidhoum, S.
  • Rios-Solis, Y.A.

Abstract

Bus transit network planning is a complex process that is divided into several phases such as: line planning, timetable generation, vehicle scheduling, and crew scheduling. In this work, we address the timetable generation which consists in scheduling the departure times for all trips of each bus line. We focus on the Synchronization Bus Timetabling Problem (SBTP) that favors passenger transfers and avoids congestion of buses at common stops. A Mixed Integer Program (MIP) was proposed in the literature for the SBTP but it fails to solve real bus network instances. We develop in this paper four classes of valid inequalities for this MIP using combinatorial properties of the SBTP on the number of synchronizations. Experimental results show that large instances are solved within few minutes with a relative deviation from the optimal solution that is usually less than 3 percent.

Suggested Citation

  • Fouilhoux, P. & Ibarra-Rojas, O.J. & Kedad-Sidhoum, S. & Rios-Solis, Y.A., 2016. "Valid inequalities for the synchronization bus timetabling problem," European Journal of Operational Research, Elsevier, vol. 251(2), pages 442-450.
    • Handle: RePEc:eee:ejores:v:251:y:2016:i:2:p:442-450
    DOI: 10.1016/j.ejor.2015.12.006
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    References listed on IDEAS

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    1. Ibarra-Rojas, Omar J. & Rios-Solis, Yasmin A., 2012. "Synchronization of bus timetabling," Transportation Research Part B: Methodological, Elsevier, vol. 46(5), pages 599-614.
    2. Quadrifoglio, Luca & Dessouky, Maged M. & Ordonez, Fernando, 2008. "Mobility allowance shuttle transit (MAST) services: MIP formulation and strengthening with logic constraints," European Journal of Operational Research, Elsevier, vol. 185(2), pages 481-494, March.
    3. Cacchiani, Valentina & Toth, Paolo, 2012. "Nominal and robust train timetabling problems," European Journal of Operational Research, Elsevier, vol. 219(3), pages 727-737.
    4. Ibarra-Rojas, O.J. & Delgado, F. & Giesen, R. & Muñoz, J.C., 2015. "Planning, operation, and control of bus transport systems: A literature review," Transportation Research Part B: Methodological, Elsevier, vol. 77(C), pages 38-75.
    5. Ceder, A. & Golany, B. & Tal, O., 2001. "Creating bus timetables with maximal synchronization," Transportation Research Part A: Policy and Practice, Elsevier, vol. 35(10), pages 913-928, December.
    6. Christian Liebchen, 2007. "Periodic Timetable Optimization in Public Transport," Operations Research Proceedings, in: Karl-Heinz Waldmann & Ulrike M. Stocker (ed.), Operations Research Proceedings 2006, pages 29-36, Springer.
    7. Guihaire, Valérie & Hao, Jin-Kao, 2008. "Transit network design and scheduling: A global review," Transportation Research Part A: Policy and Practice, Elsevier, vol. 42(10), pages 1251-1273, December.
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    Cited by:

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    2. Yin, Jiateng & D’Ariano, Andrea & Wang, Yihui & Yang, Lixing & Tang, Tao, 2021. "Timetable coordination in a rail transit network with time-dependent passenger demand," European Journal of Operational Research, Elsevier, vol. 295(1), pages 183-202.
    3. Cortés, Cristián E. & Gil, Cristiam & Gschwender, Antonio & Rey, Pablo A., 2023. "The bus synchronization timetabling problem with dwelling times," Transportation Research Part B: Methodological, Elsevier, vol. 174(C).
    4. Dalong Li & Benxing Liu & Fangtong Jiao & Ziwen Song & Pengsheng Zhao & Xiaoqing Wang & Feng Sun, 2022. "Optimization Method of Combined Multi-Mode Bus Scheduling under Unbalanced Conditions," Sustainability, MDPI, vol. 14(23), pages 1-17, November.
    5. Liu, Tao & Ceder, Avishai (Avi), 2018. "Integrated public transport timetable synchronization and vehicle scheduling with demand assignment: A bi-objective bi-level model using deficit function approach," Transportation Research Part B: Methodological, Elsevier, vol. 117(PB), pages 935-955.
    6. Yuan, Yin & Li, Shukai & Yang, Lixing & Gao, Ziyou, 2022. "Real-time optimization of train regulation and passenger flow control for urban rail transit network under frequent disturbances," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 168(C).

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