IDEAS home Printed from https://ideas.repec.org/a/eee/transb/v100y2017icp1-19.html
   My bibliography  Save this article

Deficit function related to public transport: 50 year retrospective, new developments, and prospects

Author

Listed:
  • Liu, Tao
  • (Avi) Ceder, Avishai

Abstract

The Deficit Function (DF), with its graphical concept and modelling, was introduced 50 years ago by Linis and Maksim (1967) under the title of “On the problem of constructing routes.” Since then, there have been many developments in the understanding of the theoretical, methodological and application aspects of the DF concept. This work, for the first time, makes a comprehensive and thorough retrospective examination of the major developments of DF modelling and applications in public transport (PT) planning and operations over the past 50 years, introduces some new developments, and offers future research directions. It is shown and proven that the graphical DF concept helps in creating efficient PT vehicle schedules, timetables, crew duties, networks of routes, bus rapid transit systems, and operational parking spaces. For instance, in one large bus company the total number of vehicles and crew duties were reduced by 6% to 12% and 8% to 15%, respectively. This work intends to stimulate further use of the DF concept as a bridge between the world of researchers and the world of practitioners.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:transb:v:100:y:2017:i:c:p:1-19
    DOI: 10.1016/j.trb.2017.01.015
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0191261516306956
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.trb.2017.01.015?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. I. Gertsbach & Yu. Gurevich, 1977. "Constructing an Optimal Fleet for a Transportation Schedule," Transportation Science, INFORMS, vol. 11(1), pages 20-36, February.
    2. Ilya Gertsbakh & Helman I. Stern, 1978. "Minimal Resources for Fixed and Variable Job Schedules," Operations Research, INFORMS, vol. 26(1), pages 68-85, February.
    3. Avishai Ceder & Helman I. Stern, 1981. "Deficit Function Bus Scheduling with Deadheading Trip Insertions for Fleet Size Reduction," Transportation Science, INFORMS, vol. 15(4), pages 338-363, November.
    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. Helman I. Stern & Avishai Ceder, 1983. "Technical Note---An Improved Lower Bound to the Minimum Fleet Size Problem," Transportation Science, INFORMS, vol. 17(4), pages 471-477, November.
    6. Gertsbakh, I. & Gurevich, Yuri, 1982. "Homogeneous optimal fleet," Transportation Research Part B: Methodological, Elsevier, vol. 16(6), pages 459-470, December.
    7. Gertsbakh, Ilya & Serafini, Paolo, 1991. "Periodic transportation schedules with flexible departure times : An interactive approach based on the periodic event scheduling problem and the deficit function approach," European Journal of Operational Research, Elsevier, vol. 50(3), pages 298-309, February.
    8. Miller, Mark A. & Yin, Yafeng & Balvanyos, Tunde & Ceder, Avishai, 2004. "Framework for Bus Rapid Transit Development and Deployment Planning," Institute of Transportation Studies, Research Reports, Working Papers, Proceedings qt8936v73j, Institute of Transportation Studies, UC Berkeley.
    9. Avishai (Avi) Ceder & Stephan Hassold & Christopher Dunlop & Iris Chen, 2013. "Improving urban public transport service using new timetabling strategies with different vehicle sizes," International Journal of Urban Sciences, Taylor & Francis Journals, vol. 17(2), pages 239-258, July.
    10. Hassold, Stephan & Ceder, Avishai (Avi), 2014. "Public transport vehicle scheduling featuring multiple vehicle types," Transportation Research Part B: Methodological, Elsevier, vol. 67(C), pages 129-143.
    11. Franz J. M. Salzborn, 1972. "Optimum Bus Scheduling," Transportation Science, INFORMS, vol. 6(2), pages 137-148, May.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Pei, Mingyang & Lin, Peiqun & Du, Jun & Li, Xiaopeng & Chen, Zhiwei, 2021. "Vehicle dispatching in modular transit networks: A mixed-integer nonlinear programming model," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 147(C).
    2. 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.
    3. Radislav Vaisman & Ilya B. Gertsbakh, 2023. "Optimal balanced chain decomposition of partially ordered sets with applications to operating cost minimization in aircraft routing problems," Public Transport, Springer, vol. 15(1), pages 199-225, March.
    4. Jiawei Gui & Qunqi Wu, 2020. "Multiple Utility Analyses for Sustainable Public Transport Planning and Management: Evidence from GPS-Equipped Taxi Data in Haikou," Sustainability, MDPI, vol. 12(19), pages 1-46, September.
    5. Kayhan Alamatsaz & Sadam Hussain & Chunyan Lai & Ursula Eicker, 2022. "Electric Bus Scheduling and Timetabling, Fast Charging Infrastructure Planning, and Their Impact on the Grid: A Review," Energies, MDPI, vol. 15(21), pages 1-39, October.
    6. Stern, Helman I. & Gertsbakh, Ilya B., 2019. "Using deficit functions for aircraft fleet routing," Operations Research Perspectives, Elsevier, vol. 6(C).
    7. Saltzman, Robert M. & Stern, Helman I., 2022. "The multi-day aircraft maintenance routing problem," Journal of Air Transport Management, Elsevier, vol. 102(C).

    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. Stern, Helman I. & Gertsbakh, Ilya B., 2019. "Using deficit functions for aircraft fleet routing," Operations Research Perspectives, Elsevier, vol. 6(C).
    2. Kulkarni, Sarang & Krishnamoorthy, Mohan & Ranade, Abhiram & Ernst, Andreas T. & Patil, Rahul, 2018. "A new formulation and a column generation-based heuristic for the multiple depot vehicle scheduling problem," Transportation Research Part B: Methodological, Elsevier, vol. 118(C), pages 457-487.
    3. Saltzman, Robert M. & Stern, Helman I., 2022. "The multi-day aircraft maintenance routing problem," Journal of Air Transport Management, Elsevier, vol. 102(C).
    4. 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.
    5. Benjamin Otto, 2019. "Aggregation techniques for frequency assignment in public transportation," Public Transport, Springer, vol. 11(1), pages 51-87, June.
    6. Liang Gong & Yinzhen Li & Dejie Xu, 2019. "Combinational Scheduling Model Considering Multiple Vehicle Sizes," Sustainability, MDPI, vol. 11(19), pages 1-14, September.
    7. 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.
    8. Niu, Huimin & Zhou, Xuesong & Tian, Xiaopeng, 2018. "Coordinating assignment and routing decisions in transit vehicle schedules: A variable-splitting Lagrangian decomposition approach for solution symmetry breaking," Transportation Research Part B: Methodological, Elsevier, vol. 107(C), pages 70-101.
    9. 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.
    10. Arbex, Renato Oliveira & da Cunha, Claudio Barbieri, 2015. "Efficient transit network design and frequencies setting multi-objective optimization by alternating objective genetic algorithm," Transportation Research Part B: Methodological, Elsevier, vol. 81(P2), pages 355-376.
    11. Gkiotsalitis, K. & Schmidt, M.E. & van der Hurk, E., 2021. "Subline frequency setting for autonomous minibusses under demand uncertainty," ERIM Report Series Research in Management ERS-2021-008-LIS, Erasmus Research Institute of Management (ERIM), ERIM is the joint research institute of the Rotterdam School of Management, Erasmus University and the Erasmus School of Economics (ESE) at Erasmus University Rotterdam.
    12. Zhang, Wei & (Ato) Xu, Wangtu, 2017. "Simulation-based robust optimization for the schedule of single-direction bus transit route: The design of experiment," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 106(C), pages 203-230.
    13. José Carbajal & Alan Erera & Martin Savelsbergh, 2013. "Balancing fleet size and repositioning costs in LTL trucking," Annals of Operations Research, Springer, vol. 203(1), pages 235-254, March.
    14. 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.
    15. Kayhan Alamatsaz & Sadam Hussain & Chunyan Lai & Ursula Eicker, 2022. "Electric Bus Scheduling and Timetabling, Fast Charging Infrastructure Planning, and Their Impact on the Grid: A Review," Energies, MDPI, vol. 15(21), pages 1-39, October.
    16. Kallrath, J. & Klosterhalfen, S.T. & Walter, M. & Fischer, G. & Blackburn, R., 2017. "Payload-based fleet optimization for rail cars in the chemical industry," European Journal of Operational Research, Elsevier, vol. 259(1), pages 113-129.
    17. 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.
    18. Bojovic, Nebojsa J., 2002. "A general system theory approach to rail freight car fleet sizing," European Journal of Operational Research, Elsevier, vol. 136(1), pages 136-172, January.
    19. 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.
    20. 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).

    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:eee:transb:v:100:y:2017:i:c:p:1-19. 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: Catherine Liu (email available below). General contact details of provider: http://www.elsevier.com/wps/find/journaldescription.cws_home/548/description#description .

    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.