Network pricing problem with unit toll

Lorenzo Castelli 1 Martine Labbé 2, 3 Alessia Violin 1, 3
2 INOCS - Integrated Optimization with Complex Structure
ULB - Université Libre de Bruxelles [Bruxelles], Inria Lille - Nord Europe, CRIStAL - Centre de Recherche en Informatique, Signal et Automatique de Lille (CRIStAL) - UMR 9189
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.
Type de document :
Article dans une revue
Networks, Wiley, 2017, 69 (1), pp.83--93. 〈10.1002/net.21701〉
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Soumis le : lundi 19 décembre 2016 - 16:13:55
Dernière modification le : mercredi 25 avril 2018 - 15:43:55

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Lorenzo Castelli, Martine Labbé, Alessia Violin. Network pricing problem with unit toll. Networks, Wiley, 2017, 69 (1), pp.83--93. 〈10.1002/net.21701〉. 〈hal-01419552〉



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