IDEAS home Printed from https://ideas.repec.org/a/spr/pubtra/v11y2019i1d10.1007_s12469-018-0177-3.html
   My bibliography  Save this article

Aggregation techniques for frequency assignment in public transportation

Author

Listed:
  • Benjamin Otto

    (Friedrich-Schiller-Universität Jena)

Abstract

In public transportation, frequency assignment is a sub-problem of line planning which is responsible for assigning each route of a line a certain frequency with which they are serviced by vehicles. Frequency assignment is among the most important decision problems for optimizing the waiting times in a transportation network and is often a very complex matter. This paper focuses on different aggregation techniques for reducing the computational effort to obtain (near-)optimal line frequencies. In detail, the influence of different model formulations and strategies for customer input data aggregation are investigated. For this purpose, six models are provided, their computational complexity is investigated and suitable mixed-integer mathematical programs are developed. These models vary in the levels of line utilization detail and predict the resulting travel times. Both aggregation techniques are evaluated according to their influence on the solution quality, which is determined by the transport suppliers’ point of view as forecast accuracy of the weighted number of customers using the transport. This comprehensive computational study reveals that some model formulations reduce the computational effort considerably by only small losses in line frequency quality. Furthermore, dramatically compressed customer data lead to (near-)optimal line frequencies.

Suggested Citation

  • Benjamin Otto, 2019. "Aggregation techniques for frequency assignment in public transportation," Public Transport, Springer, vol. 11(1), pages 51-87, June.
    • Handle: RePEc:spr:pubtra:v:11:y:2019:i:1:d:10.1007_s12469-018-0177-3
    DOI: 10.1007/s12469-018-0177-3
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s12469-018-0177-3
    File Function: Abstract
    Download Restriction: Access to the full text of the articles in this series is restricted.
    File URL: https://libkey.io/10.1007/s12469-018-0177-3?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. Dwi Groß & Horst Hamacher & Simone Horn & Anita Schöbel, 2009. "Stop location design in public transportation networks: covering and accessibility objectives," TOP: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 17(2), pages 335-346, December.
    2. Spiess, Heinz & Florian, Michael, 1989. "Optimal strategies: A new assignment model for transit networks," Transportation Research Part B: Methodological, Elsevier, vol. 23(2), pages 83-102, April.
    3. Dennis Huisman & Leo G. Kroon & Ramon M. Lentink & Michiel J. C. M. Vromans, 2005. "Operations Research in passenger railway transportation," Statistica Neerlandica, Netherlands Society for Statistics and Operations Research, vol. 59(4), pages 467-497, November.
    4. Han, Anthony F. & Wilson, Nigel H. M., 1982. "The allocation of buses in heavily utilized networks with overlapping routes," Transportation Research Part B: Methodological, Elsevier, vol. 16(3), pages 221-232, June.
    5. Bussieck, Michael R. & Kreuzer, Peter & Zimmermann, Uwe T., 1997. "Optimal lines for railway systems," European Journal of Operational Research, Elsevier, vol. 96(1), pages 54-63, January.
    6. LeBlanc, Larry J., 1988. "Transit system network design," Transportation Research Part B: Methodological, Elsevier, vol. 22(5), pages 383-390, October.
    7. Lawrence Frank & Mark Bradley & Sarah Kavage & James Chapman & T. Lawton, 2008. "Urban form, travel time, and cost relationships with tour complexity and mode choice," Transportation, Springer, vol. 35(1), pages 37-54, January.
    8. Gao, Ziyou & Sun, Huijun & Shan, Lian Long, 2004. "A continuous equilibrium network design model and algorithm for transit systems," Transportation Research Part B: Methodological, Elsevier, vol. 38(3), pages 235-250, March.
    9. 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.
    10. Martínez, Héctor & Mauttone, Antonio & Urquhart, María E., 2014. "Frequency optimization in public transportation systems: Formulation and metaheuristic approach," European Journal of Operational Research, Elsevier, vol. 236(1), pages 27-36.
    11. Ceder, Avishai & Wilson, Nigel H. M., 1986. "Bus network design," Transportation Research Part B: Methodological, Elsevier, vol. 20(4), pages 331-344, August.
    12. Jean-François Cordeau & Paolo Toth & Daniele Vigo, 1998. "A Survey of Optimization Models for Train Routing and Scheduling," Transportation Science, INFORMS, vol. 32(4), pages 380-404, November.
    13. David F. Rogers & Robert D. Plante & Richard T. Wong & James R. Evans, 1991. "Aggregation and Disaggregation Techniques and Methodology in Optimization," Operations Research, INFORMS, vol. 39(4), pages 553-582, August.
    14. Michael J. Klier & Knut Haase, 2008. "Line Optimization in Public Transport Systems," Operations Research Proceedings, in: Jörg Kalcsics & Stefan Nickel (ed.), Operations Research Proceedings 2007, pages 473-478, Springer.
    15. Jan-Willem Goossens & Stan van Hoesel & Leo Kroon, 2004. "A Branch-and-Cut Approach for Solving Railway Line-Planning Problems," Transportation Science, INFORMS, vol. 38(3), pages 379-393, August.
    16. Franz J. M. Salzborn, 1972. "Optimum Bus Scheduling," Transportation Science, INFORMS, vol. 6(2), pages 137-148, May.
    17. 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.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. 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.
    2. 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.
    3. Szeto, W.Y. & Jiang, Y., 2014. "Transit route and frequency design: Bi-level modeling and hybrid artificial bee colony algorithm approach," Transportation Research Part B: Methodological, Elsevier, vol. 67(C), pages 235-263.
    4. 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.
    5. 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.
    6. 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.
    7. David Canca & Belén Navarro-Carmona & Gabriel Villa & Alejandro Zarzo, 2023. "A Multilayer Network Approach for the Bimodal Bus–Pedestrian Line Planning Problem," Mathematics, MDPI, vol. 11(19), pages 1-36, October.
    8. Manser, Patrick & Becker, Henrik & Hörl, Sebastian & Axhausen, Kay W., 2020. "Designing a large-scale public transport network using agent-based microsimulation," Transportation Research Part A: Policy and Practice, Elsevier, vol. 137(C), pages 1-15.
    9. 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.
    10. Cancela, Héctor & Mauttone, Antonio & Urquhart, María E., 2015. "Mathematical programming formulations for transit network design," Transportation Research Part B: Methodological, Elsevier, vol. 77(C), pages 17-37.
    11. Elnaz Miandoabchi & Reza Farahani & Wout Dullaert & W. Szeto, 2012. "Hybrid Evolutionary Metaheuristics for Concurrent Multi-Objective Design of Urban Road and Public Transit Networks," Networks and Spatial Economics, Springer, vol. 12(3), pages 441-480, September.
    12. 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.
    13. Martínez, Héctor & Mauttone, Antonio & Urquhart, María E., 2014. "Frequency optimization in public transportation systems: Formulation and metaheuristic approach," European Journal of Operational Research, Elsevier, vol. 236(1), pages 27-36.
    14. Tian, Qingyun & Wang, David Z.W. & Lin, Yun Hui, 2021. "Service operation design in a transit network with congested common lines," Transportation Research Part B: Methodological, Elsevier, vol. 144(C), pages 81-102.
    15. 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.
    16. Javier Durán-Micco & Pieter Vansteenwegen, 2022. "A survey on the transit network design and frequency setting problem," Public Transport, Springer, vol. 14(1), pages 155-190, March.
    17. Chu, James C., 2018. "Mixed-integer programming model and branch-and-price-and-cut algorithm for urban bus network design and timetabling," Transportation Research Part B: Methodological, Elsevier, vol. 108(C), pages 188-216.
    18. 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.
    19. Schmid, Verena, 2014. "Hybrid large neighborhood search for the bus rapid transit route design problem," European Journal of Operational Research, Elsevier, vol. 238(2), pages 427-437.
    20. Amirali Zarrinmehr & Mahmoud Saffarzadeh & Seyedehsan Seyedabrishami & Yu Marco Nie, 2016. "A path-based greedy algorithm for multi-objective transit routes design with elastic demand," Public Transport, Springer, vol. 8(2), pages 261-293, September.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:spr:pubtra:v:11:y:2019:i:1:d:10.1007_s12469-018-0177-3. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Sonal Shukla or Springer Nature Abstracting and Indexing (email available below). General contact details of provider: http://www.springer.com .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.