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

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  • 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.

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  • 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
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    References listed on IDEAS

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    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.

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