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Journal of Applied Mathematics
Volume 2013, Article ID 535878, 11 pages
http://dx.doi.org/10.1155/2013/535878
Research Article

The Optimal Taxi Fleet Size Structure under Various Market Regimes When Charging Taxis with Link-Based Toll

1School of Transportation and Logistics, Southwest Jiaotong University, Chengdu 610031, China
2School of Transportation, Southeast University, Nanjing 210096, China
3School of Management and Economics, University of Electronic Science and Technology of China, Chengdu 610054, China

Received 27 August 2013; Accepted 25 October 2013

Academic Editor: Guiomar Martín-Herrán

Copyright © 2013 Jincheng Zhu et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

This paper investigates the optimal taxi fleet size structure under monopoly and oligopoly market regimes when taxis are charged with the link-based toll. We proposed a bilevel programming model to take account of the interaction between taxi fleet size and different traffic modes in the network. The upper level is to determine the optimal taxi fleet structure so as to maximize the profit of each taxi firm. The lower-level is a combined network equilibrium model (CNEM) representing the travelers’ response to the equilibrium taxi fleet size structure when congestion toll is imposed on taxis. We show that the lower level problem can be formulated as an equivalent variational inequality formulation, which considers the hierarchical logit-based mode split, route choice, elastic demand, and vacant taxi distributions. The bilevel problem can be solved by an iterative heuristic solution algorithm, whereas the lower level model is solved by the block Gauss-Seidel decomposition approach together with method of successive averages. An application with numerical examples is presented to illustrate the effectiveness of the proposed model and algorithm, and some interesting findings are also provided.