An Optimization Problem with an Equilibrium Constraint in Urban Transport

Abstract

The paper presents a study of transport in urban areas served by a public transport system, as well as by private vehicles on which road pricing is imposed. It is supposed that the road pricing fare, the ticket price and the frequency of the lines of public transport are established by the Public Administration in such a way that the surplus of users of both the transport modes is maximised, under the conditions that the system is in equilibrium, the budget constraint of the company managing public transport is satisfied, and the private transport demand does not exceed a given threshold for environmental reasons. The theoretical model that has been devised leads to a problem of nonlinear programming, with an equilibrium constraint formulated as a fixed point problem. From an application of the model to an urban area it emerges that, if the proceeds of road pricing are used for financing public transport, the results of road pricing essentially depend on the proportion of demand that is captive to public transport, and on the level of congestion existing on the urban road network before the imposition of road pricing.