The purpose of the traffic assignment problem is to obtain a traffic flowpattern given a set of origin-destination travel demands and flow dependent link performance functions of a road network. In the general case, the traffic assignmentproblem can be formulated as a variational inequality, and several algorithms havebeen devised for its efficient solution. In this work we propose a new approach thatcombines two existing procedures: the master problem of a simplicial decompositionalgorithm is solved through the analytic center cutting plane method. Four variantsare considered for solving the master problem. The third and fourth ones, whichheuristically compute an appropriate initial point, provided the best results. The computational experience reported in the solution of real large-scale diagonal and difficult asymmetric problems—including a subset of the transportation networks of Madrid and Barcelona—show the effectiveness of the approach.