An approximation algorithm for Stackelberg network pricing

Authors:
Sébastien Roch;Gilles Savard;Patrice Marcotte
Affiliations:
Department of Statistics, University of California, Berkeley, Berkeley, California (This work was done while the author was at École Polytechnique, Montréal);Département de mathématiques et de génie industriel, École Polytechnique de Montréal, Montréal, Québec, Canada;Département d'informatique et de recherche opérationnelle, Université de Montréal, Montréal, Québec, Canada
Venue:
Networks
Year:
2005

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Abstract

We consider the problem of maximizing the revenue raised from tolls set on the arcs of a transportation network, under the constraint that users are assigned to toll-compatible shortest paths. We first prove that this problem is strongly NP-hard. We then provide a polynomial time algorithm with a worst-case precision guarantee of ${{1 \over 2}\log_2 m_T+1}$, where mT denotes the number of toll arcs. Finally, we show that the approximation is tight with respect to a natural relaxation by constructing a family of instances for which the relaxation gap is reached. © 2005 Wiley Periodicals, Inc. NETWORKS, Vol. 46(1), 57–67 2005