Pricing bridges to cross a river

Mustapha Bouhtou, Alexander Grigoriev, Stan van Hoesel, Anton F. van der Kraaij, Frits C.R. Spieksma and Marc Uetz

Naval Research Logistics (NRL), 2007, vol. 54, issue 4, 411-420

Abstract: We consider a pricing problem in directed, uncapacitated networks. Tariffs must be defined by an operator, the leader, for a subset of m arcs, the tariff arcs. Costs of all other arcs in the network are assumed to be given. There are n clients, the followers, and after the tariffs have been determined, the clients route their demands independent of each other on paths with minimal total cost. The problem is to find tariffs that maximize the operator's revenue. Motivated by applications in telecommunication networks, we consider a restricted version of this problem, assuming that each client utilizes at most one of the operator's tariff arcs. The problem is equivalent to pricing bridges that clients can use in order to cross a river. We prove that this problem is APX‐hard. Moreover, we analyze the effect of uniform pricing, proving that it yields both an m approximation and a (1 + lnD)‐approximation. Here, D is upper bounded by the total demand of all clients. In addition, we consider the problem under the additional restriction that the operator must not reject any of the clients. We prove that this problem does not admit approximation algorithms with any reasonable performance guarantee, unless P = NP, and we prove the existence of an n‐approximation algorithm. © 2007 Wiley Periodicals, Inc. Naval Research Logistics, 2007

Date: 2007
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (5)

Downloads: (external link)
https://doi.org/10.1002/nav.20216

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:wly:navres:v:54:y:2007:i:4:p:411-420

Access Statistics for this article

More articles in Naval Research Logistics (NRL) from John Wiley & Sons
Bibliographic data for series maintained by Wiley Content Delivery ().