Constraint-Based Approaches for Balancing Bike Sharing Systems

  • Luca Di Gaspero
  • Andrea Rendl
  • Tommaso Urli
Part of the Lecture Notes in Computer Science book series (LNCS, volume 8124)


In order to meet the users’ demand, bike sharing systems must be regularly rebalanced. The problem of balancing bike sharing systems (BBSS) is concerned with designing optimal tours and operating instructions for relocating bikes among stations to maximally comply with the expected future bike demands. In this paper, we tackle the BBSS by means of Constraint Programming: first, we introduce two novel constraint models for the BBSS including a smart branching strategy that focusses on the most promising routes. Second, in order to speed-up the search process, we incorporate both models in a Large Neighborhood Search (LNS) approach that is adapted to the respective CP model. Third, we perform a computational evaluation on instances based on real-world data, where we see that the LNS approach outperforms the Branch & Bound approach and is competitive with other existing approaches.


Mixed Integer Linear Programming Variable Neighborhood Search Vehicle Rout Problem Time Budget Step Model 
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  1. 1.
    Benchimol, M., Benchimol, P., Chappert, B., De la Taille, A., Laroche, F., Meunier, F., Robinet, L.: Balancing the stations of a self service bike hire system. RAIRO – Operations Research 45(1), 37–61 (2011)CrossRefzbMATHGoogle Scholar
  2. 2.
    Bent, R., Van Hentenryck, P.: A two-stage hybrid local search for the vehicle routing problem with time windows. Transportation Science 38(4), 515–530 (2004)CrossRefGoogle Scholar
  3. 3.
    Birattari, M., Yuan, Z., Balaprakash, P., Stützle, T.: F-race and iterated F-race: an overview. In: Experimental Methods for the Analysis of Optimization Algorithms, pp. 311–336 (2010)Google Scholar
  4. 4.
    Chemla, D., Meunier, F., Calvo, R.W.: Bike sharing systems: Solving the static rebalancing problem. To Appear in Discrete Optimization (2012)Google Scholar
  5. 5.
    Contardo, C., Morency, C., Rousseau, L.M.: Balancing a Dynamic Public Bike-Sharing System. Tech. Rep. CIRRELT-2012-09, Montreal, Canada (2012)Google Scholar
  6. 6.
    Di Gaspero, L., Rendl, A., Urli, T.: A hybrid ACO+CP for balancing bicycle sharing systems. In: Blesa, M.J., Blum, C., Festa, P., Roli, A., Sampels, M. (eds.) HM 2013. LNCS, vol. 7919, pp. 198–212. Springer, Heidelberg (2013)CrossRefGoogle Scholar
  7. 7.
    Gecode Team: Gecode: Generic constraint development environment (2006),
  8. 8.
    Kilby, P., Shaw, P.: Vehicle routing. In: Rossi, F., Beek, P. (eds.) Handbook of Constraint Programming, ch. 23, pp. 799–834. Elsevier Science Inc., New York (2006)Google Scholar
  9. 9.
    Rainer-Harbach, M., Papazek, P., Hu, B., Raidl, G.R.: Balancing bicycle sharing systems: A variable neighborhood search approach. In: Middendorf, M., Blum, C. (eds.) EvoCOP 2013. LNCS, vol. 7832, pp. 121–132. Springer, Heidelberg (2013)CrossRefGoogle Scholar
  10. 10.
    Raviv, T., Tzur, M., Forma, I.A.: Static repositioning in a bike-sharing system: models and solution approaches. To Appear in EURO Journal on Transportation and Logistics (2012)Google Scholar
  11. 11.
    Rousseau, L.M., Gendreau, M., Pesant, G.: Using constraint-based operators to solve the vehicle routing problem with time windows. Journal of Heuristics 8(1), 43–58 (2002)CrossRefzbMATHGoogle Scholar
  12. 12.
    Schuijbroek, J., Hampshire, R., van Hoeve, W.J.: Inventory rebalancing and vehicle routing in bike sharing systems. Tech. Rep. 2013-E1, Tepper School of Business, Carnegie Mellon University (2013)Google Scholar
  13. 13.
    Shaw, P.: Using constraint programming and local search methods to solve vehicle routing problems. In: Maher, M.J., Puget, J.-F. (eds.) CP 1998. LNCS, vol. 1520, pp. 417–431. Springer, Heidelberg (1998)CrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2013

Authors and Affiliations

  • Luca Di Gaspero
    • 1
  • Andrea Rendl
    • 2
  • Tommaso Urli
    • 1
  1. 1.DIEGMUniversity of UdineUdineItaly
  2. 2.Dynamic Transportation Systems, Mobility DepartmentAustrian Institute of TechnologyViennaAustria

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