An equivalent optimization formulation for the traffic assignment problem with asymmetric linear costs

<title>A<sc>bstract</sc> </title> In this paper, we present a general formulation for the deterministic traffic assignment problem, using an equivalent optimization problem applicable to the case of asymmetric linear cost functions. We present a resolution approach for this problem in such a way that in equilibrium Wardrop's first principle or Nash equilibrium is satisfied. We conclude that many deterministic traffic assignment problems with asymmetric linear costs can be formulated as an optimization problem whose objective is defined by a line integral, and whose constraints correspond to non-negativity and flows conservation. By adequately defining the integration path, it is feasible to resolve the problem, obtaining Wardrop's equilibrium. This approach can be applied in other economic contexts, including microeconomic theory and consumer surplus analysis.