Dual-Based Heuristic for Optimal Cordon Pricing Design

Abstract

This paper formulates the cordon pricing design problem with elastic demand as a mathematical program with complementarity constraints (MPCC) to simultaneously optimize the cordon locations and cordon-specific toll levels, thus maximizing total social welfare. The formulation is flexible so that various charging requirements, such as those on cordon numbers, cordon size, and cordon types, can be easily satisfied by slightly modifying the formulation. A dual-based heuristic algorithm is proposed to handle the problem by sequentially solving a relaxed cordon pricing design problem and an updating problem. To avoid directly dealing with the complementarity constraints contained in the two problems, the paper adopts alternative approaches by solving a series of subproblems. These subproblems can be easily handled by using available commercial solvers. Numerical tests are performed to generate different cordon designs for one single-layered cordon, multilayered cordons, and multicentered cordons. The results demonstrate that the proposed model and solution algorithm are able to efficiently produce optimal cordon pricing schemes on real-sized transportation networks.