The Static Bicycle Repositioning Problem - Literature Survey and New Formulation

  • Hans Martin Espegren
  • Johannes Kristianslund
  • Henrik AnderssonEmail author
  • Kjetil Fagerholt
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 9855)


This paper considers the static bicycle repositioning problem (SBRP), which deals with optimally re-balancing bike sharing systems (BSS) overnight, i.e. using service vehicles to move bikes from (nearly) full stations to (nearly) empty stations. An exhaustive literature survey comparing existing models is presented, and a new and improved mathematical formulation for the SBRP is proposed. The model is tested on a number of instances generated based on data from a real BSS.


Valid Inequality Bender Decomposition Vehicle Capacity Large Neighborhood Search Delivery Station 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


  1. 1.
    Angeloudis, P., Hu, J., Bell, M.G.: A strategic repositioning algorithm for bicycle-sharing schemes. Transportmetrica A Transp. Sci. 10(8), 759–774 (2014)CrossRefGoogle Scholar
  2. 2.
    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)CrossRefzbMATHGoogle Scholar
  3. 3.
    Berbeglia, G., Cordeau, J.F., Gribkovskaia, I., Laporte, G.: Static pickup and delivery problems: a classification scheme and survey. Top 15(1), 1–31 (2007)CrossRefzbMATHMathSciNetGoogle Scholar
  4. 4.
    Brinkmann, J., Ulmer, M.W., Mattfeld, D.C.: Short-term strategies for stochastic inventory routing in bike sharing systems. Transp. Res. Procedia 10, 364–373 (2015)CrossRefGoogle Scholar
  5. 5.
    Caggiani, L., Ottomanelli, M.: A modular soft computing based method for vehicles repositioning in bike-sharing systems. Procedia Soc. Behav. Sci. 54, 675–684 (2012)CrossRefGoogle Scholar
  6. 6.
    Chemla, D., Meunier, F., Calvo, R.W.: Bike sharing systems: solving the static rebalancing problem. Discrete Optim. 10(2), 120–146 (2013)CrossRefzbMATHMathSciNetGoogle Scholar
  7. 7.
    Contardo, C., Morency, C., Rousseau, L.M.: Balancing a dynamic public bike-sharing system. Technical report CIRRELT-2012-09, Universitè de Montrèal, Montrèal, Canada (2012).
  8. 8.
    Dell’Amico, M., Hadjicostantinou, E., Iori, M., Novellani, S.: The bike sharing rebalancing problem: mathematical formulations and benchmark instances. Omega 45, 7–19 (2014)CrossRefGoogle Scholar
  9. 9.
    DeMaio, P.: Bike-sharing: history, impacts, models of provision, and future. J. Public Transp. 12(4), 3 (2009)CrossRefMathSciNetGoogle Scholar
  10. 10.
    DeMaio, P., Meddin, R.: The bike-sharing world map (2015). Accessed 06 Oct 2015
  11. 11.
    Desrochers, M., Laporte, G.: Improvements and extensions to the Miller-Tucker-Zemlin subtour elimination constraints. Oper. Res. Lett. 10(1), 27–36 (1991)CrossRefzbMATHMathSciNetGoogle Scholar
  12. 12.
    Erdoğan, G., Battarra, M., Calvo, R.: An exact algorithm for the static rebalancing problem arising in bicycle sharing systems. Eur. J. Oper. Res. 245(3), 667–679 (2015)CrossRefMathSciNetGoogle Scholar
  13. 13.
    Erdoğan, G., Laporte, G., Calvo, R.W.: The static bicycle relocation problem with demand intervals. Eur. J. Oper. Res. 238(2), 451–457 (2014)CrossRefzbMATHMathSciNetGoogle Scholar
  14. 14.
    Forma, I.A., Raviv, T., Tzur, M.: A 3-step math heuristic for the static repositioning problem in bike-sharing systems. Transp. Res. Part B Methodol. 71, 230–247 (2015)CrossRefGoogle Scholar
  15. 15.
    Fricker, C., Gast, N.: Incentives and redistribution in homogeneous bike-sharing systems with stations of finite capacity. EURO J. Transp. Logistics 3, 1–31 (2014)CrossRefGoogle Scholar
  16. 16.
    García-Palomares, J.C., Gutiérrez, J., Latorre, M.: Optimizing the location of stations in bike-sharing programs: a GIS approach. Appl. Geogr. 35(1), 235–246 (2012)CrossRefGoogle Scholar
  17. 17.
    Gaspero, L., Rendl, A., Urli, T.: Balancing bike sharing systems with constraint programming. Constraints 21(2), 318–348 (2016)CrossRefzbMATHMathSciNetGoogle Scholar
  18. 18.
    Hernández-Pérez, H., Salazar-González, J.J.: The one-commodity pickup-and-delivery traveling salesman problem: Inequalities and algorithms. Networks 50(4), 258–272 (2007)CrossRefzbMATHMathSciNetGoogle Scholar
  19. 19.
    Ho, S.C., Szeto, W.: Solving a static repositioning problem in bike-sharing systems using iterated tabu search. Transp. Res. Part E: Logistics and Transp. Rev. 69, 180–198 (2014)CrossRefGoogle Scholar
  20. 20.
    Kaspi, M., Raviv, T., Tzur, M.: Detection of unusable bicycles in bike-sharing systems (2015)., working paper. Tel-Aviv University. Accessed 08 Nov 2015
  21. 21.
    Kloimüllner, C., Papazek, P., Hu, B., Raidl, G.R.: Balancing bicycle sharing systems: an approach for the dynamic case. In: Blum, C., Ochoa, G. (eds.) EvoCOP 2014. LNCS, vol. 8600, pp. 73–84. Springer, Heidelberg (2014)Google Scholar
  22. 22.
    Laporte, G., Meunier, F., Calvo, W.R.: Shared mobility systems. 4OR 13(4), 341–360 (2015)CrossRefzbMATHMathSciNetGoogle Scholar
  23. 23.
    Lin, J.R., Yang, T.H.: Strategic design of public bicycle sharing systems with service level constraints. Transp. Res. Part E Logistics Transp. Rev. 47(2), 284–294 (2011)CrossRefGoogle Scholar
  24. 24.
    Midgley, P.: Bicycle-sharing schemes: enhancing sustainable mobility in urban areas. In: 19th Session of the Commission on Sustainable Development, 02 May 2011. United Nations, Department of Economic and Social Affairs, Background Paper No. 8, May 2011Google Scholar
  25. 25.
    Miller, C.E., Tucker, A.W., Zemlin, R.A.: Integer programming formulation of traveling salesman problems. J. ACM (JACM) 7(4), 326–329 (1960)CrossRefzbMATHMathSciNetGoogle Scholar
  26. 26.
    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
  27. 27.
    O’Mahony, E., Shmoys, D.B.: Data analysis and optimization for (citi) bike sharing. In: Twenty-Ninth AAAI Conference on Artificial Intelligence, 25 January 2015. Association for the Advancement of Artificial Intelligence, January 2015Google Scholar
  28. 28.
    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
  29. 29.
    Rainer-Harbach, M., Papazek, P., Raidl, G.R., Hu, B., Kloimüllner, C.: PILOT, GRASP, and VNS approaches for the static balancing of bicycle sharing systems. J. Global Optim. 63(3), 597–629 (2015)CrossRefzbMATHMathSciNetGoogle Scholar
  30. 30.
    Raviv, T., Kolka, O.: Optimal inventory management of a bike-sharing station. IIE Trans. 45(10), 1077–1093 (2013)CrossRefGoogle Scholar
  31. 31.
    Raviv, T., Tzur, M., Forma, I.A.: Static repositioning in a bike-sharing system: models and solution approaches. EURO J. Transp. Logistics 2(3), 187–229 (2013)CrossRefGoogle Scholar
  32. 32.
    Regue, R., Recker, W.: Proactive vehicle routing with inferred demand to solve the bikesharing rebalancing problem. Transp. Res. Part E: Logistics Transp. Rev. 72, 192–209 (2014)CrossRefGoogle Scholar
  33. 33.
    Romero, J.P., Ibeas, A., Moura, J.L., Benavente, J., Alonso, B.: A simulation-optimization approach to design efficient systems of bike-sharing. Procedia Soc. Behav. Sci. 54, 646–655 (2012)CrossRefGoogle Scholar
  34. 34.
    Schuijbroek, J., Hampshire, R., van Hoeve, W.J.: Inventory rebalancing and vehicle routing in bike sharing systems (2013)., working paper. Tepper School of Business. Accessed Feb 2013–01 Dec 2015
  35. 35.
    Shaheen, S., Guzman, S., Zhang, H.: Bikesharing in Europe, the Americas, and Asia: past, present, and future. Transp. Res. Rec. J. Transp. Res. Board 2143, 159–167 (2010)CrossRefGoogle Scholar
  36. 36.
    Sörensen, K., Dilip, D.: The (city) bike request scheduling problem-a novel approach to solve the city bike repositioning problem. In: Toklu, Y.C., Bekdas, G. (eds.) Metaheuristics and Engineering, Workshop of the EURO Working Group, vol. 15, pp. 157–161. Bilecik Şeyh Edebali University (2014)Google Scholar
  37. 37.
    Vogel, P., Ehmke, J.F., Mattfeld, D.C.: Service network design of bike sharing systems (2015). publications/service_network_design_of_bike_sharing_systems.pdf, working paper. Technische Unversität Braunschweig. Accessed 24 Mar 2015–24 Sep 2015
  38. 38.
    Vogel, P., Greiser, T., Mattfeld, D.C.: Understanding bike-sharing systems using data mining: exploring activity patterns. Procedia Soc. Behav. Sci. 20, 514–523 (2011)CrossRefGoogle Scholar
  39. 39.
    Vogel, P., Neumann Saavedra, B.A., Mattfeld, D.C.: A hybrid metaheuristic to solve the resource allocation problem in bike sharing systems. In: Blesa, M.J., Blum, C., Voß, S. (eds.) HM 2014. LNCS, vol. 8457, pp. 16–29. Springer, Heidelberg (2014)Google Scholar

Copyright information

© Springer International Publishing Switzerland 2016

Authors and Affiliations

  • Hans Martin Espegren
    • 1
  • Johannes Kristianslund
    • 1
  • Henrik Andersson
    • 1
    Email author
  • Kjetil Fagerholt
    • 1
  1. 1.Department of Industrial Economics and Technology ManagementNorwegian University of Science and TechnologyTrondheimNorway

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