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

Mike Benchimol; Pascal Benchimol; Benoît Chappert; Arnaud de la Taille; Fabien Laroche; Frédéric Meunier; Ludovic Robinet

RAIRO - Operations Research (2011)

  • Volume: 45, Issue: 1, page 37-61
  • ISSN: 0399-0559

Abstract

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This paper is motivated by operating self service transport systems that flourish nowadays. In cities where such systems have been set up with bikes, trucks travel to maintain a suitable number of bikes per station. It is natural to study a version of the C-delivery TSP defined by Chalasani and Motwani in which, unlike their definition, C is part of the input: each vertex v of a graph G=(V,E) has a certain amount xv of a commodity and wishes to have an amount equal to yv (we assume that v V x v = v V y v and all quantities are assumed to be integers); given a vehicle of capacity C, find a minimal route that balances all vertices, that is, that allows to have an amount yv of the commodity on each vertex v. This paper presents among other things complexity results, lower bounds, approximation algorithms, and a polynomial algorithm when G is a tree.

How to cite

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Benchimol, Mike, et al. "Balancing the stations of a self service “bike hire” system." RAIRO - Operations Research 45.1 (2011): 37-61. <http://eudml.org/doc/276363>.

@article{Benchimol2011,
abstract = { This paper is motivated by operating self service transport systems that flourish nowadays. In cities where such systems have been set up with bikes, trucks travel to maintain a suitable number of bikes per station. It is natural to study a version of the C-delivery TSP defined by Chalasani and Motwani in which, unlike their definition, C is part of the input: each vertex v of a graph G=(V,E) has a certain amount xv of a commodity and wishes to have an amount equal to yv (we assume that $\sum_\{v\in V\}x_v=\sum_\{v\in V\}y_v$ and all quantities are assumed to be integers); given a vehicle of capacity C, find a minimal route that balances all vertices, that is, that allows to have an amount yv of the commodity on each vertex v. This paper presents among other things complexity results, lower bounds, approximation algorithms, and a polynomial algorithm when G is a tree. },
author = {Benchimol, Mike, Benchimol, Pascal, Chappert, Benoît, de la Taille, Arnaud, Laroche, Fabien, Meunier, Frédéric, Robinet, Ludovic},
journal = {RAIRO - Operations Research},
keywords = {Approximation algorithm; routing problem; self service transport system; approximation algorithm},
language = {eng},
month = {5},
number = {1},
pages = {37-61},
publisher = {EDP Sciences},
title = {Balancing the stations of a self service “bike hire” system},
url = {http://eudml.org/doc/276363},
volume = {45},
year = {2011},
}

TY - JOUR
AU - Benchimol, Mike
AU - Benchimol, Pascal
AU - Chappert, Benoît
AU - de la Taille, Arnaud
AU - Laroche, Fabien
AU - Meunier, Frédéric
AU - Robinet, Ludovic
TI - Balancing the stations of a self service “bike hire” system
JO - RAIRO - Operations Research
DA - 2011/5//
PB - EDP Sciences
VL - 45
IS - 1
SP - 37
EP - 61
AB - This paper is motivated by operating self service transport systems that flourish nowadays. In cities where such systems have been set up with bikes, trucks travel to maintain a suitable number of bikes per station. It is natural to study a version of the C-delivery TSP defined by Chalasani and Motwani in which, unlike their definition, C is part of the input: each vertex v of a graph G=(V,E) has a certain amount xv of a commodity and wishes to have an amount equal to yv (we assume that $\sum_{v\in V}x_v=\sum_{v\in V}y_v$ and all quantities are assumed to be integers); given a vehicle of capacity C, find a minimal route that balances all vertices, that is, that allows to have an amount yv of the commodity on each vertex v. This paper presents among other things complexity results, lower bounds, approximation algorithms, and a polynomial algorithm when G is a tree.
LA - eng
KW - Approximation algorithm; routing problem; self service transport system; approximation algorithm
UR - http://eudml.org/doc/276363
ER -

References

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  9. H. Hernández-Pérz and J.-J. Salazar-González, A branch-and-cut algorithm for a traveling salesman problem with pickup and delivery. Discr. Appl. Math.145 (2004) 126–139.  Zbl1058.90054
  10. J.A. Hoogeveen, Analysis of christofides'heuristic: some paths are more difficult than cycles. Oper. Res. Lett.10 (1991) 291–295.  Zbl0748.90071
  11. D. König, Uber Graphen und ihre Anwendung auf Determinantentheorie une Mengenlehre. Math. Ann.77 (1916) 453–465.  Zbl46.0146.03
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