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Network pricing problem with unit toll
Author(s) -
Castelli Lorenzo,
Labbé Martine,
Violin Alessia
Publication year - 2017
Publication title -
networks
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.977
H-Index - 64
eISSN - 1097-0037
pISSN - 0028-3045
DOI - 10.1002/net.21701
Subject(s) - toll , computer science , mathematical optimization , shortest path problem , interval (graph theory) , polynomial , path (computing) , parametric statistics , representation (politics) , class (philosophy) , mathematics , theoretical computer science , combinatorics , graph , computer network , artificial intelligence , mathematical analysis , statistics , genetics , politics , political science , law , biology
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. © 2016 Wiley Periodicals, Inc. NETWORKS, Vol. 69(1), 83–93 2017