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

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.