Network pricing problem with unit toll - Inria - Institut national de recherche en sciences et technologies du numérique Access content directly
Journal Articles Networks Year : 2017

Network pricing problem with unit toll

Abstract

In the so-called network pricing problem an authority owns some arcs of the network and tolls them, while users travel between their origin and destination choosing their minimum cost path. In this article, we consider a unit toll scheme, and in particular the cases where the authority is imposing either the same toll on all of its arcs, or a toll proportional to a given parameter particular to each arc (for instance a per kilometer toll). We show that if tolls are all equal then the complexity of the problem is polynomial, whereas in case of proportional tolls it is pseudo-polynomial, proposing ad-hoc solution algorithms and relating these problems to the parametric shortest path problem. We then address a robust approach using an interval representation to take into consideration uncertainty on parameters. We show how to modify the algorithms for the deterministic case to solve the robust counterparts, maintaining their complexity class.
No file

Dates and versions

hal-01419552 , version 1 (19-12-2016)

Identifiers

Cite

Lorenzo Castelli, Martine Labbé, Alessia Violin. Network pricing problem with unit toll. Networks, 2017, 69 (1), pp.83--93. ⟨10.1002/net.21701⟩. ⟨hal-01419552⟩
71 View
0 Download

Altmetric

Share

Gmail Facebook X LinkedIn More