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Balancing the stations of a self service “bike hire” system

Published online by Cambridge University Press:  10 May 2011

Mike Benchimol ,
Pascal Benchimol ,
Benoît Chappert ,
Arnaud de la Taille ,
Fabien Laroche ,
Frédéric Meunier  and
Ludovic Robinet
Mike Benchimol
Affiliation:
Université Paris Est, ENPC, 6-8 avenue Blaise Pascal, Cité Descartes Champs-sur-Marne, 77455 Marne-la-Vallée Cedex 2, France. mike.benchimol@eleves.enpc.fr; benoit.chappert@eleves.enpc.fr; de-la-ta@eleves.enpc.fr; frederic.meunier@enpc.fr; ludovic.robinet@eleves.enpc.fr
Pascal Benchimol
Affiliation:
École Polytechnique, 91128 Palaiseau Cedex, France. pascal.benchimol@polytechnique.edu; fabien.laroche@polytechnique.edu
Benoît Chappert
Affiliation:
Université Paris Est, ENPC, 6-8 avenue Blaise Pascal, Cité Descartes Champs-sur-Marne, 77455 Marne-la-Vallée Cedex 2, France. mike.benchimol@eleves.enpc.fr; benoit.chappert@eleves.enpc.fr; de-la-ta@eleves.enpc.fr; frederic.meunier@enpc.fr; ludovic.robinet@eleves.enpc.fr
Arnaud de la Taille
Affiliation:
Université Paris Est, ENPC, 6-8 avenue Blaise Pascal, Cité Descartes Champs-sur-Marne, 77455 Marne-la-Vallée Cedex 2, France. mike.benchimol@eleves.enpc.fr; benoit.chappert@eleves.enpc.fr; de-la-ta@eleves.enpc.fr; frederic.meunier@enpc.fr; ludovic.robinet@eleves.enpc.fr
Fabien Laroche
Affiliation:
École Polytechnique, 91128 Palaiseau Cedex, France. pascal.benchimol@polytechnique.edu; fabien.laroche@polytechnique.edu
Frédéric Meunier
Affiliation:
Université Paris Est, ENPC, 6-8 avenue Blaise Pascal, Cité Descartes Champs-sur-Marne, 77455 Marne-la-Vallée Cedex 2, France. mike.benchimol@eleves.enpc.fr; benoit.chappert@eleves.enpc.fr; de-la-ta@eleves.enpc.fr; frederic.meunier@enpc.fr; ludovic.robinet@eleves.enpc.fr
Ludovic Robinet
Affiliation:
Université Paris Est, ENPC, 6-8 avenue Blaise Pascal, Cité Descartes Champs-sur-Marne, 77455 Marne-la-Vallée Cedex 2, France. mike.benchimol@eleves.enpc.fr; benoit.chappert@eleves.enpc.fr; de-la-ta@eleves.enpc.fr; frederic.meunier@enpc.fr; ludovic.robinet@eleves.enpc.fr
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Abstract

This paper is motivated by operating self service transport systemsthat flourish nowadays. In cities where such systems have been setup with bikes, trucks travel to maintain a suitable number of bikesper station.It is natural to study a version of the C-delivery TSP defined byChalasani and Motwani in which, unlike their definition, C is partof the input: each vertex v of a graph G=(V,E) has a certainamount xv of a commodity and wishes to have an amount equal toyv (we assume that $\sum_{v\in V}x_v=\sum_{v\in V}y_v$ and allquantities are assumed to be integers); given a vehicle of capacityC, find a minimal route that balances all vertices, that is,that allows to have an amount yv of the commodity on each vertexv.This paper presents among other things complexity results, lowerbounds, approximation algorithms, and a polynomial algorithm whenG is a tree.

Keywords

Approximation algorithmrouting problemself service transport system
Type
Research Article
Information
RAIRO - Operations Research , Volume 45 , Issue 1 , January 2011 , pp. 37 - 61
Copyright
© EDP Sciences, ROADEF, SMAI, 2011

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