Graduate Seminar: Nonlinear Road Pricing

GAINESVILLE, FL: Dr. Siriphong (Toi) Lawphongpanich, Associate Professor of Industrial and Systems Engineering, will deliver the ISE Graduate Seminar on Thursday, August 25 at 4:05 p.m. on the topic of Nonlinear Road Pricing.

Under nonlinear road pricing (or tolling), the price charged is not strictly proportional to the distance travelled inside a tolling area, the generalized travel cost is not link-wise additive, and finding a user equilibrium distribution is typically formulated as a complementarity problem, a difficult problem to solve in mathematical programming.  In this paper, we use piecewise linear functions to determine tolls andshow that finding a user equilibrium distribution with such functionscan be formulated as a convex optimization problem that is based on path flows and solvable by traditional algorithms such as simplicial decomposition.  In the case of two-part tariffs and area-based pricing,the tolling function consists of only one linear piece and the problem offending a user equilibrium distribution reduces to a convex optimization problem formulated in terms of link flows and solvable by any softwarefor linearly constrained convex programs.

To find an optimal pricing scheme, e.g., one that maximizes the social benefit, we formulate the problem as a mathematical program with equilibrium constraints, an optimization problem that is generally non-convex and difficult to solve.  However, the number of parameters in our piecewise linear schemes is typically small.  Thus, it is possible to use search algorithms to find an optimal pricing scheme.  To illustrate,we use a coordinate search algorithm to find an optimal two-part tariff for a small network with randomly generated data.

Dr. Siriphong Lawphongpanich is an associate professor in theDepartment of Industrial and Systems Engineering at the University of Florida.  His main research interests are in transportation science, large-scale optimization, and logistics.  He has published widely in these areas. Recently, he is a co-editor of a recent booktitled “Mathematical and Computational Models for CongestionCharging.”  Dr. Lawphongpanich is an associate editor of Computational Optimization and Applications, a past associate editor of Naval Research Logistics, and a referee for journals such as Transportation Research, Transportation Science, Mathematical Programming, Operations Research, Networks, Journal of Global Optimization, and European Journal of Operations Research. Recently,Dr. Lawphongpanich has been a co-principal investigator of projects funded by the Center of Multimodal Solutions for Congestion Mitigation,Volvo Research and Educational Foundations, and the National Science Foundation.