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Optimum Bus Scheduling

Author

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  • Franz J. M. Salzborn

    (Department of Applied Mathematics, University of Adelaide, Adelaide, South Australia)

Abstract

The paper presents a mathematical investigation into bus scheduling. The passenger arrival rate is supposed to be given; the problem is to determine the bus departure rate as a function of time. The primary objective is to minimize the number of buses that is needed. A secondary criterion is the minimization of the passenger waiting time, for which a calculus of variation technique is used. Although the paper deals mainly with a single busroute, it is also shown how the theory can be extended to the case of a pair of linked busroutes. The practical implications are illustrated by an example. The fleetsize formula that is used here is thought to be applicable to many transportation systems.

Suggested Citation

  • Franz J. M. Salzborn, 1972. "Optimum Bus Scheduling," Transportation Science, INFORMS, vol. 6(2), pages 137-148, May.
    • Handle: RePEc:inm:ortrsc:v:6:y:1972:i:2:p:137-148
    DOI: 10.1287/trsc.6.2.137
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    Cited by:

    1. Cong, Yuan & Bie, Yiming & Liu, Ziyan & Zhu, Aoze, 2024. "Collaborative vehicle-crew scheduling for multiple routes with a mixed fleet of electric and fuel buses," Energy, Elsevier, vol. 298(C).
    2. Liu, Tao & (Avi) Ceder, Avishai, 2017. "Deficit function related to public transport: 50 year retrospective, new developments, and prospects," Transportation Research Part B: Methodological, Elsevier, vol. 100(C), pages 1-19.
    3. Qingyun Tian & Yun Hui Lin & David Z. W. Wang, 2021. "Autonomous and conventional bus fleet optimization for fixed-route operations considering demand uncertainty," Transportation, Springer, vol. 48(5), pages 2735-2763, October.
    4. Herbon, Avi & Hadas, Yuval, 2015. "Determining optimal frequency and vehicle capacity for public transit routes: A generalized newsvendor model," Transportation Research Part B: Methodological, Elsevier, vol. 71(C), pages 85-99.
    5. 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.
    6. Dwi Novirani & Hari Adianto, 2020. "Relation of Service Quality, Load Factors and Tariff on Bus City of Bandung," International Review of Management and Marketing, Econjournals, vol. 10(4), pages 152-160.
    7. Loder, Allister & Bliemer, Michiel C.J. & Axhausen, Kay W., 2022. "Optimal pricing and investment in a multi-modal city — Introducing a macroscopic network design problem based on the MFD," Transportation Research Part A: Policy and Practice, Elsevier, vol. 156(C), pages 113-132.
    8. Asplund, Disa, 2021. "Optimal frequency of public transport in a small city: examination of a simple method," Working Papers 2021:9, Swedish National Road & Transport Research Institute (VTI).
    9. Hatzenbühler, Jonas & Cats, Oded & Jenelius, Erik, 2020. "Transitioning towards the deployment of line-based autonomous buses: Consequences for service frequency and vehicle capacity," Transportation Research Part A: Policy and Practice, Elsevier, vol. 138(C), pages 491-507.
    10. Chen, Zhiwei & Li, Xiaopeng & Zhou, Xuesong, 2020. "Operational design for shuttle systems with modular vehicles under oversaturated traffic: Continuous modeling method," Transportation Research Part B: Methodological, Elsevier, vol. 132(C), pages 76-100.
    11. Verbas, İ. Ömer & Mahmassani, Hani S., 2015. "Exploring trade-offs in frequency allocation in a transit network using bus route patterns: Methodology and application to large-scale urban systems," Transportation Research Part B: Methodological, Elsevier, vol. 81(P2), pages 577-595.
    12. Benjamin Otto, 2019. "Aggregation techniques for frequency assignment in public transportation," Public Transport, Springer, vol. 11(1), pages 51-87, June.
    13. Yan, Shangyao & Chen, Hao-Lei, 2002. "A scheduling model and a solution algorithm for inter-city bus carriers," Transportation Research Part A: Policy and Practice, Elsevier, vol. 36(9), pages 805-825, November.
    14. 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.
    15. Suman, Hemant & Larrain, Homero & Muñoz, Juan Carlos, 2021. "The impact of using a naïve approach in the limited-stop bus service design problem," Transportation Research Part A: Policy and Practice, Elsevier, vol. 149(C), pages 45-61.
    16. Dakic, Igor & Yang, Kaidi & Menendez, Monica & Chow, Joseph Y.J., 2021. "On the design of an optimal flexible bus dispatching system with modular bus units: Using the three-dimensional macroscopic fundamental diagram," Transportation Research Part B: Methodological, Elsevier, vol. 148(C), pages 38-59.
    17. David Schmaranzer & Roland Braune & Karl F. Doerner, 2020. "Population-based simulation optimization for urban mass rapid transit networks," Flexible Services and Manufacturing Journal, Springer, vol. 32(4), pages 767-805, December.
    18. David Schmaranzer & Roland Braune & Karl F. Doerner, 2021. "Multi-objective simulation optimization for complex urban mass rapid transit systems," Annals of Operations Research, Springer, vol. 305(1), pages 449-486, October.
    19. Hemant Kumar Suman & Nomesh B. Bolia, 2019. "Mitigation of overcrowding in buses through bus planning," Public Transport, Springer, vol. 11(1), pages 159-187, June.
    20. Langevin, André & Mbaraga, Pontien & Campbell, James F., 1996. "Continuous approximation models in freight distribution: An overview," Transportation Research Part B: Methodological, Elsevier, vol. 30(3), pages 163-188, June.

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