Journal of Industrial and Management Optimization (JIMO)

A practical trial-and-error implementation of marginal-cost pricing on networks

Pages: 299 - 313, Volume 6, Issue 2, May 2010      doi:10.3934/jimo.2010.6.299

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Deren Han - School of Mathematics and Computer Sciences, Nanjing Normal University, Nanjing 210097, China (email)
Hai Yang - Department of Civil Engineering, The Hong Kong University of Science and Technology, Hong Kong, China (email)
Xiaoming Yuan - Department of Mathematics, Hong Kong Baptist University, Hong Kong, China (email)

Abstract: This paper proposes a trial-and-error implementation of marginal-cost pricing on transportation networks in the absence of both demand functions and travel time functions. Assuming that the corresponding link flows for given trial tolls are observable and that the approximations of the exact travel time functions are provided, the new trial is obtained via solving a system of equations. The new trial-and-error implementation is proved to be convergent globally under mild assumptions, and its improvements over existing methods are verified by some numerical experiments.

Keywords:  Network pricing problems, marginal cost, variational inequality, trial-and-error.
Mathematics Subject Classification:  Primary: 90B20, 49J20, 90B50, 90C33.

Received: December 2008;      Revised: November 2009;      Available Online: March 2010.