This paper analyses both the cordon and area pricings from the perspective of travel demand management. Sensitivity analysis of various performance measures with respect to the toll rate and demand elastic parameter is performed on a virtual grid network. The analysis shows that cordon pricing mainly affects those trips with origins outside of the Central Business District and destinations inside, while area pricing imposes additional cost on the trips with either origins or destinations in the Central Business District. Though both pricing strategies are able to alleviate traffic congestion in the charging area, area pricing seems more effective, however, area pricing owns the risk to detour too much traffic and thus cause severe congestion to the network outside of the Central Business District. Following the sensitivity analysis, a unified framework is proposed to optimize the designs of the both pricing strategies, which is flexible to account for various practical concerns. The optimization models are formulated as mixed-integer nonlinear programs with complementarity constraints, and the solution procedure is composed of solving a series of nonlinear programs and mixed-integer linear programs. Results from the numerical examples are in line with the findings in the sensitivity analysis. Under the specific network settings, cordon pricing achieves the best system performance when the toll rate reaches the maximum allowed, while area pricing finds the optimal design scheme when the toll rate equals half of the maximum allowed.
A projection-based reformulation and decomposition algorithm for global optimization of a class of mixed integer bilevel linear programs