This paper investigates the cordon-based second-best congestion-pricing problems on road networks, including optimal selection of both toll levels and toll locations. A road network is viewed as a directed graph and the cutset concept in graph theory is used to describe the mathematical properties of a toll cordon by examining the incidence matrix of the network. Maximization of social welfare is sought subject to the elastic-demand traffic equilibrium constraint. A mathematical programming model with mixed (integer and continuous) variables is formulated and solved by a combined use of a binary genetic algorithm and a grid search method for simultaneous determination of the toll levels and cordon locations on the networks. The model and algorithm are demonstrated with a numerical example.