Valid inequalities and Branch-and-Cut for the Clique Pricing Problem

Motivated by an application in highway pricing, we consider the problem that consists in setting profit-maximizing tolls on a clique subset of a multicommodity transportation network. Following a proof that clique pricing is NP-hard, we propose strong valid inequalities, some of which define facets of the 2-commodity polyhedron. The numerical efficiency of these inequalities is … Read more

A parallel between two classes of pricing problems in transportation and economics

In this work, we establish a parallel between two classes of pricing problems that have attracted the attention of researchers in economics, theoretical computer science and operations research, each community addressing issues from its own vantage point. More precisely, we contrast the problems of pricing a network or a product line, in order to achieve … Read more

A polyhedral study of the Network Pricing Problem with Connected Toll Arcs

Consider the problem that consists in maximizing the revenue generated by tolls set on a subset of arcs of a transportation network, and where origin-destination flows are assigned to shortest paths with respect to the sum of tolls and initial costs. In this work, we address the instance where toll arcs must be connected, as … Read more

Design and analysis of an approximation algorithm for Stackelberg network pricing

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 $\frac{1}{2}\log m_T+1$, where … Read more