Balancing the stations of a self-service bike hire system

Mike Benchimol (1) , Pascal Benchimol (1) , Benoît Chappert (1) , Arnaud de La Taille (1) , Fabien Laroche (1) , Frédéric Meunier (1) , Ludovic Robinet (1)

1 CERMICS - Centre d'Enseignement et de Recherche en Mathématiques, Informatique et Calcul Scientifique

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 $x_v$ of a commodity and wishes to have an amount equal to $y_v$ (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 {\em balances} all vertices, that is, that allows to have an amount $y_v$ 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.

Domaines: Mathématique discrète [cs.DM]

Mike Benchimol, Pascal Benchimol, Benoît Chappert, Arnaud de La Taille, Fabien Laroche, et al.. Balancing the stations of a self-service bike hire system. RAIRO - Operations Research, 2011, 45 (1), pp.37-61. ⟨10.1051/ro/2011102⟩. ⟨hal-00601443⟩