The spatial price equilibrium problem with path variables

Most of the recent literature dealing with the solution of the spatial price equilibrium model has dealt with the arc variable formulation; that is, the situation where the flows on the paths connecting an origin-destination pair in a network with trans-shipment nodes are not explicitly considered. This paper presents a clarification of the main assumption underlying this arc formulation and presents an argument for the need for using a model with path variables in certain applications. After this discussion, a new solution algorithm for the model with path variables is stated and compared against the linear approximation algorithm first proposed by Florian and Los 1] for this problem. Numerical examples are presented which illustrate the features of this new algorithm.