Soft Computing

, Volume 23, Issue 14, pp 5945–5966 | Cite as

Lower and upper bounds for scheduling multiple balancing vehicles in bicycle-sharing systems

  • Ahmed A. Kadri
  • Imed KacemEmail author
  • Karim Labadi
Methodologies and Application


Public bicycle-sharing systems have been implemented in many big cities around the world to face many public transport problems. The exploitation and the management of such transportation systems imply crucial operational challenges. The balancing of stations is the most crucial question for their operational efficiency and economic viability. In this paper, we study the balancing problem of stations with multiple vehicles by considering the static case. A mathematical formulation of the problem is proposed, and two lower bounds based on Eastman’s bound and SPT rule are developed. Moreover, we proposed four upper bounds based on a genetic algorithm, a greedy search algorithm and two hybrid methods that integrate a genetic algorithm, a local search method and a branch-and-bound algorithm. The developed lower and upper bounds are tested and compared on a large set of instances.


Bicycle-sharing systems Lower and upper bounds Greedy search Hybrid algorithms Branch-and-bound Vehicle routing problem 


Compliance with ethical standards

Conflict of interest

All authors declare that they have no conflict of interest.

Human and animal rights

This article does not contain any studies with human participants or animals performed by any of the authors.


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Copyright information

© Springer-Verlag GmbH Germany, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Université de Lorraine, LCOMS EA 7306, UFR MIMMetzFrance
  2. 2.ECAM-EPMICergy-PontoiseFrance

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