Journal of Global Optimization

, Volume 63, Issue 3, pp 597–629 | Cite as

PILOT, GRASP, and VNS approaches for the static balancing of bicycle sharing systems

  • Marian Rainer-Harbach
  • Petrina Papazek
  • Günther R. RaidlEmail author
  • Bin Hu
  • Christian Kloimüllner


We consider a transportation problem arising in public bicycle sharing systems: To avoid rental stations to run entirely empty or full, a fleet of vehicles continuously performs tours moving bikes among stations. In the static problem variant considered in this paper, we are given initial and target fill levels for all stations, and the goal is primarily to find vehicle tours including corresponding loading instructions in order to minimize the deviations from the target fill levels. As secondary objectives we are further interested in minimizing the tours’ total duration and the overall number of loading actions. For this purpose we first propose a fast greedy construction heuristic and extend it to a PILOT method that evaluates each candidate station considered for addition to the current partial tour in a refined way by looking forward via a recursive call. Next we describe a Variable Neighborhood Descent (VND) that exploits a set of specifically designed neighborhood structures in a deterministic way to locally improve the solutions. While the VND is processing the search space of candidate routes to determine the stops for vehicles at unbalanced rental stations, the number of bikes to be loaded or unloaded at each stop is derived by an efficient method. Four alternatives are considered for this embedded procedure based on a greedy heuristic, two variants of maximum flow calculations, and linear programming. Last but not least, we investigate a general Variable Neighborhood Search (VNS) and variants of a Greedy Randomized Adaptive Search Procedure (GRASP) for further diversification and extended runs. Rigorous experiments using benchmark instances derived from a real-world scenario in Vienna with up to 700 stations document the performance of the suggested approaches and individual pros and cons. While the VNS yields the best results on instances of moderate size, a PILOT/GRASP hybrid turns out to be superior on very large instances. If solutions are required in short time, the construction heuristic or PILOT method optionally followed by VND still yield reasonable results.


Bicycle sharing systems Vehicle routing PILOT method Variable Neighborhood Search GRASP 



This work is supported by the Austrian Research Promotion Agency (FFG) under contract 831740. We thank Matthias Prandtstetter, Andrea Rendl, Christian Rudloff, and Markus Straub from the Austrian Institute of Technology (AIT) for the collaboration in this project, constructive comments and for providing the data used in our test instances. In addition, we thank Citybike Wien for providing information about practical aspects of their bicycle sharing system and additional data incorporated into the test instances.


  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 Oper. Res. 45(1), 37–61 (2011)zbMATHCrossRefGoogle Scholar
  2. 2.
    Chemla, D., Meunier, F., Pradeau, T., Calvo, R.W., Yahiaoui, H.: Self-service bike sharing systems: simulation, repositioning, pricing. Tech. Rep. hal-00824078, Centre d’Enseignement et de Recherche en Mathématiques et Calcul Scientifique (CERMICS) (2013)Google Scholar
  3. 3.
    Chemla, D., Meunier, F., Calvo, R.W.: Bike sharing systems: solving the static rebalancing problem. Discret. Optim. 10(2), 120–146 (2013)zbMATHCrossRefGoogle Scholar
  4. 4.
    Cherkassky, B.V., Goldberg, A.V.: On implementing the push-relabel method for the maximum flow problem. Algorithmica 19(4), 390–410 (1997)zbMATHMathSciNetCrossRefGoogle Scholar
  5. 5.
    Contardo, C., Morency, C., Rousseau, L.M.: Balancing a dynamic public bike-sharing system. Tech. Rep. CIRRELT-2012-09, CIRRELT, Montreal, Canada (2012)Google Scholar
  6. 6.
    Dell’Amico, M., Maffioli, F., Värbrand, P.: On prize-collecting tours and the asymmetric travelling salesman problem. Int. Trans. Oper. Res. 2(3), 297–308 (1995)zbMATHCrossRefGoogle Scholar
  7. 7.
    DeMaio, P.: Bike-sharing: history, impacts, models of provision, and future. J. Public Transp. 12(4), 41–56 (2009)MathSciNetCrossRefGoogle Scholar
  8. 8.
    Di Gaspero, L., Rendl, A., Urli, T.: A hybrid ACO+CP for balancing bicycle sharing systems. In: Blesa, M., Blum, C., Festa, P., Roli, A., Sampels, M. (eds.) Hybrid Metaheuristics, Lecture Notes in Computer Science, vol. 7919, pp. 198–212. Springer, Berlin (2013)Google Scholar
  9. 9.
    Di Gaspero, L., Rendl, A., Urli, T.: Constraint-based approaches for balancing bike sharing systems. In: Schulte, C. (ed.) Principles and Practice of Constraint Programming. Lecture Notes in Computer Science, vol. 8124, pp. 758–773. Springer, Berlin (2013)Google Scholar
  10. 10.
    Golden, B., Raghavan, S., Wasil, E.A. (eds.): The Vehicle Routing Problem: Latest Advances and New Challenges, Operations Research/Computer Science Interfaces, vol. 43. Springer, Berlin (2008)Google Scholar
  11. 11.
    Hernández-Pérez, H., Salazar-González, J.J.: A branch-and-cut algorithm for a traveling salesman problem with pickup and delivery. Discret. Appl. Math. 145(1), 126–139 (2004)zbMATHCrossRefGoogle Scholar
  12. 12.
    Laporte, G., Martello, S.: The selective travelling salesman problem. Discret. Appl. Math. 26(2–3), 193–207 (1990)zbMATHMathSciNetCrossRefGoogle Scholar
  13. 13.
    Lin, J.H., Chou, T.C.: A geo-aware and VRP-based public bicycle redistribution system. Int. J. Veh. Technol. (2012)Google Scholar
  14. 14.
    Lin, J.R., Yang, T.H., Chang, Y.C.: A hub location inventory model for bicycle sharing system design: formulation and solution. Comput. Ind. Eng. 65(1), 77–86 (2013)CrossRefGoogle Scholar
  15. 15.
    Mladenović, N., Hansen, P.: Variable neighborhood search. Comput. Oper. Res. 24(11), 1097–1100 (1997)zbMATHMathSciNetCrossRefGoogle Scholar
  16. 16.
    Nair, R., Miller-Hooks, E., Hampshire, R.C., Bušić, A.: Large-scale vehicle sharing systems: analysis of vélib’. Int. J. Sustain. Transp. 7(1), 85–106 (2013)CrossRefGoogle Scholar
  17. 17.
    Pfrommer, J., Warrington, J., Schildbach, G., Morari, M.: Dynamic vehicle redistribution and online price incentives in shared mobility systems. Tech. Rep. arXiv:1304.3949, Cornell University, NY (2013)
  18. 18.
    Pirkwieser, S., Raidl, G.R.: A variable neighborhood search for the periodic vehicle routing problem with time windows. In: Prodhon, C., et al. (eds.) Proceedings of the 9th EU/MEeting on Metaheuristics for Logistics and Vehicle Routing. Troyes, France (2008)Google Scholar
  19. 19.
    Raidl, G.R., Hu, B., Rainer-Harbach, M., Papazek, P.: Balancing bicycle sharing systems: Improving a VNS by efficiently determining optimal loading operations. In: Blesa, M.J. et al. (eds.) Hybrid Metaheuristics, 8th International Workshop, HM 2013, LNCS, vol. 7919, pp. 130–143. Springer, Berlin (2013)Google Scholar
  20. 20.
    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.) Evolutionary Computation in Combinatorial Optimization. Lecture Notes in Computer Science, vol. 7832, pp. 121–132. Springer, Berlin (2013)Google Scholar
  21. 21.
    Raviv, T., Tzur, M., Forma, I.A.: Static repositioning in a bike-sharing system: models and solution approaches. EURO J. Transp. Logist. pp. 1–43 (2013)Google Scholar
  22. 22.
    Resende, M., Ribeiro, C.: Greedy randomized adaptive search procedures. In: Glover, F., Kochenberger, G. (eds.) Handbook of Metaheuristics, pp. 219–249. Kluwer, Dordrecht (2003)Google Scholar
  23. 23.
    Rudloff, C., Lackner, B.: Modeling demand for bicycle sharing system—neighboring stations as a source for demand and a reason for structural breaks. Tech. rep, Austrian Institute of Technology, Vienna, Austria (2013)Google Scholar
  24. 24.
    Savelsbergh, M.: Preprocessing and probing techniques for mixed integer programming problems. ORSA J. Comput. 6(4), 445–454 (1994)zbMATHMathSciNetCrossRefGoogle Scholar
  25. 25.
    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
  26. 26.
    Vansteenwegen, P., Souffriau, W., Oudheusden, D.V.: The orienteering problem: a survey. Eur. J. Oper. Res. 209, 1–10 (2011)zbMATHCrossRefGoogle Scholar
  27. 27.
    Voß, S., Fink, A., Duin, C.: Looking ahead with the pilot method. Ann. Oper. Res. 136, 285–302 (2005)zbMATHMathSciNetCrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media New York 2014

Authors and Affiliations

  • Marian Rainer-Harbach
    • 1
  • Petrina Papazek
    • 1
  • Günther R. Raidl
    • 1
    Email author
  • Bin Hu
    • 1
  • Christian Kloimüllner
    • 1
  1. 1.Institute of Computer Graphics and AlgorithmsVienna University of TechnologyViennaAustria

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