26: Determination of Optimal Toll Levels and Toll Locations of Alternative Congestion Pricing Schemes

The well-known first-best pricing scheme assumes a marginal cost is charged on each link of a transportation network so that the optimal traffic condition can be obtained. However, this assumption is not practical in spite of its perfect theoretical basis. Therefore, the second-best pricing schemes have received more and more attention in recent years. This paper deals with the second-best link-based and cordon-based pricing schemes that involve optimal selection of both toll levels and toll locations. Social welfare maximization with or without inclusion of implementation cost of toll charge is sought subject to elastic travel demand in general networks. Optimization models with mixed (integer and continuous) variables are formulated for determining toll levels and toll locations simultaneously. A binary genetic algorithm is employed to search optimal toll locations dynamically and a simulated annealing method to search optimal toll levels. In the analysis of the cordon-based toll scheme, transportation network is viewed as a directed graph, and the concept of cutset in graph theory is introduced to describe the mathematical properties of a toll cordon by examining the incidence matrix of the network.