IDEAS home Printed from https://ideas.repec.org/a/eee/ecotra/v2y2013i1p47-52.html
   My bibliography  Save this article

Beckmann's transportation network equilibrium model: Its history and relationship to the Kuhn–Tucker conditions

Author

Listed:
  • Boyce, David

Abstract

During 1952–54, Martin Beckmann, and his colleagues, formulated a nonlinear programming problem corresponding to behavioral assumptions from the viewpoint of an individual traveler concerning travel demand and cost-minimizing route choice over a congested road network. Their formulation was based on the conditions for a constrained maximum, recently derived by Kuhn and Tucker. This formulation was evidently the first time that economists used the Kuhn–Tucker conditions to formulate a new problem in economics, one of substantial practical importance and consequence, and quite possibly the first to use these conditions to formulate a new, large-scale problem in all fields of engineering. In this paper, an overview of the research leading to the formulation is offered. Then, the derivation presented in their monograph is described and explored in more detail. Finally, the impacts of this model on the field of transportation economics and the associated fields of transportation engineering and regional science are examined.

Suggested Citation

  • Boyce, David, 2013. "Beckmann's transportation network equilibrium model: Its history and relationship to the Kuhn–Tucker conditions," Economics of Transportation, Elsevier, vol. 2(1), pages 47-52.
    • Handle: RePEc:eee:ecotra:v:2:y:2013:i:1:p:47-52
    DOI: 10.1016/j.ecotra.2012.11.002
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S2212012212000111
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.ecotra.2012.11.002?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. Takayama,Akira, 1985. "Mathematical Economics," Cambridge Books, Cambridge University Press, number 9780521314985, October.
    2. W. S. Dorn, 1963. "Non-Linear Programming--A Survey," Management Science, INFORMS, vol. 9(2), pages 171-208, January.
    3. Bar-Gera, Hillel & Boyce, David & Nie, Yu (Marco), 2012. "User-equilibrium route flows and the condition of proportionality," Transportation Research Part B: Methodological, Elsevier, vol. 46(3), pages 440-462.
    4. Anna Nagurney, 2000. "Sustainable Transportation Networks," Books, Edward Elgar Publishing, number 2069.
    5. David Boyce, 2007. "Forecasting Travel on Congested Urban Transportation Networks: Review and Prospects for Network Equilibrium Models," Networks and Spatial Economics, Springer, vol. 7(2), pages 99-128, June.
    6. Boyce, David, 2007. "Future research on urban transportation network modeling," Regional Science and Urban Economics, Elsevier, vol. 37(4), pages 472-481, July.
    7. David E. Boyce & Hani S. Mahmassani & Anna Nagurney, 2005. "A retrospective on Beckmann, McGuire and Winsten's Studies in the Economics of Transportation," Papers in Regional Science, Wiley Blackwell, vol. 84(1), pages 85-103, March.
    8. Carlos F. Daganzo & Yosef Sheffi, 1977. "On Stochastic Models of Traffic Assignment," Transportation Science, INFORMS, vol. 11(3), pages 253-274, August.
    9. Boyce, David & Mattsson, Lars-Göran, 1999. "Modeling residential location choice in relation to housing location and road tolls on congested urban highway networks," Transportation Research Part B: Methodological, Elsevier, vol. 33(8), pages 581-591, November.
    10. F. H. Knight, 1924. "Some Fallacies in the Interpretation of Social Cost," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 38(4), pages 582-606.
    11. F. Virginia Rohde, 1957. "Bibliography on Linear Programming," Operations Research, INFORMS, vol. 5(1), pages 45-62, February.
    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. Jansuwan, Sarawut & Chen, Anthony & Xu, Xiangdong, 2021. "Analysis of freight transportation network redundancy: An application to Utah’s bi-modal network for transporting coal," Transportation Research Part A: Policy and Practice, Elsevier, vol. 151(C), pages 154-171.
    2. Amirgholy, Mahyar & Gonzales, Eric J., 2017. "Efficient frontier of route choice for modeling the equilibrium under travel time variability with heterogeneous traveler preferences," Economics of Transportation, Elsevier, vol. 11, pages 1-14.
    3. Chen, Daqiang & Ignatius, Joshua & Sun, Danzhi & Goh, Mark & Zhan, Shalei, 2018. "Impact of congestion pricing schemes on emissions and temporal shift of freight transport," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 118(C), pages 77-105.
    4. David Boyce & Anna Nagurney, 2019. "In Memoriam: Martin Beckmann (1924–2017)," Transportation Science, INFORMS, vol. 53(6), pages 1798-1799, November.
    5. Kitthamkesorn, Songyot & Chen, Anthony, 2017. "Alternate weibit-based model for assessing green transport systems with combined mode and route travel choices," Transportation Research Part B: Methodological, Elsevier, vol. 103(C), pages 291-310.

    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. G. E. Cantarella & D. P. Watling, 2016. "Modelling road traffic assignment as a day-to-day dynamic, deterministic process: a unified approach to discrete- and continuous-time models," EURO Journal on Transportation and Logistics, Springer;EURO - The Association of European Operational Research Societies, vol. 5(1), pages 69-98, March.
    2. Wen-Long Jin, 2015. "Advances in Dynamic Traffic Assgmnt: TAC," Networks and Spatial Economics, Springer, vol. 15(3), pages 617-634, September.
    3. Kobayashi, Kiyoshi & Do, Myungsik, 2005. "The informational impacts of congestion tolls upon route traffic demands," Transportation Research Part A: Policy and Practice, Elsevier, vol. 39(7-9), pages 651-670.
    4. Honggang Zhang & Zhiyuan Liu & Yicheng Zhang & Weijie Chen & Chenyang Zhang, 2024. "A Distributed Computing Method Integrating Improved Gradient Projection for Solving Stochastic Traffic Equilibrium Problem," Networks and Spatial Economics, Springer, vol. 24(2), pages 361-381, June.
    5. Zhou, Zhong & Chen, Anthony & Wong, S.C., 2009. "Alternative formulations of a combined trip generation, trip distribution, modal split, and trip assignment model," European Journal of Operational Research, Elsevier, vol. 198(1), pages 129-138, October.
    6. Robin Lindsey, 2010. "Reforming Road User Charges: A Research Challenge For Regional Science," Journal of Regional Science, Wiley Blackwell, vol. 50(1), pages 471-492, February.
    7. Watling, David Paul & Rasmussen, Thomas Kjær & Prato, Carlo Giacomo & Nielsen, Otto Anker, 2015. "Stochastic user equilibrium with equilibrated choice sets: Part I – Model formulations under alternative distributions and restrictions," Transportation Research Part B: Methodological, Elsevier, vol. 77(C), pages 166-181.
    8. Bliemer, Michiel C.J. & Raadsen, Mark P.H. & Smits, Erik-Sander & Zhou, Bojian & Bell, Michael G.H., 2014. "Quasi-dynamic traffic assignment with residual point queues incorporating a first order node model," Transportation Research Part B: Methodological, Elsevier, vol. 68(C), pages 363-384.
    9. Idrisov, Georgy & Taganov, Boris, 2014. "Evaluation of the Competitiveness of Russian Transport Routes," Published Papers r902ad, Russian Presidential Academy of National Economy and Public Administration.
    10. Xu, Hongli & Lou, Yingyan & Yin, Yafeng & Zhou, Jing, 2011. "A prospect-based user equilibrium model with endogenous reference points and its application in congestion pricing," Transportation Research Part B: Methodological, Elsevier, vol. 45(2), pages 311-328, February.
    11. C. Robin Lindsey & Erik T. Verhoef, 2000. "Traffic Congestion and Congestion Pricing," Tinbergen Institute Discussion Papers 00-101/3, Tinbergen Institute.
    12. Akamatsu, Takashi, 1996. "Cyclic flows, Markov process and stochastic traffic assignment," Transportation Research Part B: Methodological, Elsevier, vol. 30(5), pages 369-386, October.
    13. David Boyce, 2007. "Forecasting Travel on Congested Urban Transportation Networks: Review and Prospects for Network Equilibrium Models," Networks and Spatial Economics, Springer, vol. 7(2), pages 99-128, June.
    14. Jiayang Li & Qianni Wang & Liyang Feng & Jun Xie & Yu Marco Nie, 2024. "A Day-to-Day Dynamical Approach to the Most Likely User Equilibrium Problem," Papers 2401.08013, arXiv.org.
    15. Robin Lindsey, 2006. "Do Economists Reach A Conclusion on Road Pricing? The Intellectual History of an Idea," Econ Journal Watch, Econ Journal Watch, vol. 3(2), pages 292-379, May.
    16. Senlai Zhu & Jie Ma & Tianpei Tang & Quan Shi, 2020. "A Combined Modal and Route Choice Behavioral Complementarity Equilibrium Model with Users of Vehicles and Electric Bicycles," IJERPH, MDPI, vol. 17(10), pages 1-18, May.
    17. Yitian Wang & Zixuan Peng & Keming Wang & Xiaolin Song & Baozhen Yao & Tao Feng, 2015. "Research on Urban Road Congestion Pricing Strategy Considering Carbon Dioxide Emissions," Sustainability, MDPI, vol. 7(8), pages 1-20, August.
    18. Maćkowiak, Piotr, 2009. "Adaptive Rolling Plans Are Good," MPRA Paper 42043, University Library of Munich, Germany.
    19. Terry E. Daniel & Eyran J. Gisches & Amnon Rapoport, 2009. "Departure Times in Y-Shaped Traffic Networks with Multiple Bottlenecks," American Economic Review, American Economic Association, vol. 99(5), pages 2149-2176, December.
    20. Moore, II, James E. & Kim, Geunyoung & Cho, Seongdil & Hu, Hsi-hwa & Xu, Rong, 1997. "Evaluating System ATMIS Technologies Via Rapid Estimation Of Network Flows: Final Report," Institute of Transportation Studies, Research Reports, Working Papers, Proceedings qt5c70f3d9, Institute of Transportation Studies, UC Berkeley.

    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:ecotra:v:2:y:2013:i:1:p:47-52. 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/locate/ecotra .

    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.