Bike Sharing

  • Daniel FreundEmail author
  • Shane G. Henderson
  • David B. Shmoys
Part of the Springer Series in Supply Chain Management book series (SSSCM, volume 6)


We discuss planning methods for bike-sharing systems that operate a set of stations consisting of docks. Specific questions include decisions related to the number of docks to allocate to each station, how to rebalance the system by moving bikes to match demand, and expansion planning. We describe linear integer programming models, specially tailored optimization algorithms, and simulation methods. All of these methods rely on careful statistical analysis of bike-sharing data, which we also briefly review. Our discussion of the issues is informed by our 4-year collaboration with Citi Bike in New York City, and its parent company Motivate.



We thank our colleagues at Citi Bike, and its parent company Motivate, for our strong and ongoing collaboration. We also thank the many contributors to the work described herein, especially the students, both undergraduate and graduate, at Cornell University. This work was partially supported by National Science Foundation grants CCF-1526067, CMMI-1537394, CCF-1522054, and CCF-1740822, and Army Research Office grant W911NF-17-1-0094.


  1. Banerjee S, Freund D, Lykouris T (2017) Pricing and optimization in shared vehicle systems: an approximation framework. In: Proceedings of the 2017 ACM conference on economics and computation. ACM, p 517. arXiv preprint:1608.06819Google Scholar
  2. Benchimol M, Benchimol P, Chappert B, De La Taille A, Laroche F, Meunier F, Robinet L (2011) Balancing the stations of a self service “bike hire” system. RAIRO-Oper Res 45(1):37–61CrossRefGoogle Scholar
  3. Bulhões T, Subramanian A, Erdoğan G, Laporte G (2018) The static bike relocation problem with multiple vehicles and visits. Eur J Oper Res 264:508–523CrossRefGoogle Scholar
  4. Casazza M, Ceselli A, Calvo RW (2017) Inventory rebalancing in bike-sharing systems. In: Proceedings of the 15th cologne-twente workshop on graphs and combinatorial optimization, pp 35–38Google Scholar
  5. Chemla D, Meunier F, Calvo RW (2013) Bike sharing systems: solving the static rebalancing problem. Discret Optim 10(2):120–146CrossRefGoogle Scholar
  6. Chen L, Zhang D, Wang L, Yang D, Ma X, Li S, Wu Z, Pan G, Thi-Mai-Trang Nguyen JJ (2016) Dynamic cluster-based over-demand prediction in bike sharing systems. In: Proceedings of the 2016 ACM international joint conference on pervasive and ubiquitous computing. ACM, pp 841–852Google Scholar
  7. Chung H, Freund D, Shmoys DB (2018) Bike angels: an analysis of Citi Bike’s incentive program. In: Proceedings of the 1st ACM SIGCAS conference on computing and sustainable societies. ACM, pp 5:1–5:9Google Scholar
  8. Çinlar E (1972) Superposition of point processes. In: Lewis PAW (ed) Stochastic point processes: statistical analysis, theory, and applications. Wiley Interscience, New York, pp 549–606Google Scholar
  9. Contardo C, Morency C, Rousseau L-M (2012) Balancing a dynamic public bike-sharing system. Technical report, CIRRELT, Sept 2012. Accessed in Mar 2018
  10. Datner S, Raviv T, Tzur M, Chemla D (2017) Setting inventory levels in a bike sharing network. Transp Sci. Articles in Advance. CrossRefGoogle Scholar
  11. de Chardon CM, Caruso G, Thomas I (2016) Bike-share rebalancing strategies, patterns, and purpose. J Transp Geogr 55:22–39CrossRefGoogle Scholar
  12. Dell’Amico M, Hadjicostantinou E, Iori M, Novellani S (2014) The bike sharing rebalancing problem: mathematical formulations and benchmark instances. Omega 45:7–19CrossRefGoogle Scholar
  13. Di Gaspero L, Rendl A, Urli T (2013) Constraint-based approaches for balancing bike sharing systems. In: Schulte C (ed) Proceedings of the 19th international conference on principles and practice of constraint programming. Springer, pp 758–773Google Scholar
  14. Erdoğan G, Laporte G, Calvo RW (2014) The static bicycle relocation problem with demand intervals. Eur J Oper Res 238(2):451–457CrossRefGoogle Scholar
  15. Erdoğan G, Battarra M, Calvo RW (2015) An exact algorithm for the static rebalancing problem arising in bicycle sharing systems. Eur J Oper Res 245(3):667–679CrossRefGoogle Scholar
  16. Forma IA, Raviv T, Tzur M (2015) A 3-step math heuristic for the static repositioning problem in bike-sharing systems. Transp Res B Methodol 71:230–247CrossRefGoogle Scholar
  17. Freund D, Norouzi-Fard A, Paul A, Wang C, Henderson SG, Shmoys DB (2016) Data-driven rebalancing methods for bike-share systems. Working paperGoogle Scholar
  18. Freund D, Henderson SG, Shmoys DB (2017) Minimizing multimodular functions and allocating capacity in bike-sharing systems. In: Eisenbrand F, Koenemann J (eds) Integer programming and combinatorial optimization proceedings. Lecture notes in computer science, vol 10328. Springer, pp 186–198. arXiv preprint arXiv:1611.09304Google Scholar
  19. George DK, Xia CH, Squillante MS (2012) Exact-order asymptotic analysis for closed queueing networks. J Appl Probab 49(2):503–520CrossRefGoogle Scholar
  20. Ghosh S, Trick M, Varakantham P (2016) Robust repositioning to counter unpredictable demand in bike sharing systems. In: Kambhampati S (ed) Proceedings of the twenty-fifth international joint conference on artificial intelligence. IJCAI/AAAI Press, pp 3096–3102Google Scholar
  21. Ghosh S, Varakantham P, Adulyasak Y, Jaillet P (2017) Dynamic repositioning to reduce lost demand in bike sharing systems. J Artif Intell Res 58:387–430CrossRefGoogle Scholar
  22. Ho SC, Szeto W (2014) Solving a static repositioning problem in bike-sharing systems using iterated tabu search. Transp Res E Logist Transp Rev 69:180–198CrossRefGoogle Scholar
  23. Hsu YT, Kang L, Wu YH (2016) User behavior of bikesharing systems under demand–supply imbalance. Transp Res Rec J Transp Res Board (2587):117–124CrossRefGoogle Scholar
  24. Jian N, Henderson SG (2015) An introduction to simulation optimization. In: Yilmaz L, Chan WKV, Roeder TMK, Macal C, Rosetti M (eds) Proceedings of the 2015 winter simulation conference. IEEE, pp 1780–1794Google Scholar
  25. Jian N, Freund D, Wiberg H, Henderson SG (2016) Simulation optimization for a large-scale bike-sharing system. In: Roeder TMK, Frazier PI, Szechtman R, Zhou E (eds) Proceedings of the 2016 winter simulation conference. IEEE, Piscataway, pp 602–613CrossRefGoogle Scholar
  26. Kabra A, Girotra K, Belavina E (2015) Bike-share systems: accessibility and availability. Working paperGoogle Scholar
  27. Karlin S, Taylor HM (1975) A first course in stochastic processes, 2nd edn. Academic, BostonGoogle Scholar
  28. Kaspi M, Raviv T, Tzur M (2016) Detection of unusable bicycles in bike-sharing systems. Omega 65:10–16CrossRefGoogle Scholar
  29. Kaspi M, Raviv T, Tzur M (2017) Bike-sharing systems: user dissatisfaction in the presence of unusable bicycles. IISE Trans 49(2):144–158CrossRefGoogle Scholar
  30. Kloimüllner C, Papazek P, Hu B, Raidl GR (2014) Balancing bicycle sharing systems: an approach for the dynamic case. In: Blum C, Ochoa G (eds) European conference on evolutionary computation in combinatorial optimization. Springer, pp 73–84Google Scholar
  31. Li Y, Zheng Y, Zhang H, Chen L (2015) Traffic prediction in a bike-sharing system. In: Bao J, Sengstock C, Ali ME, Huang Y, Gertz M, Renz M, Sankaranarayanan J (eds) Proceedings of the 23rd SIGSPATIAL international conference on advances in geographic information systems. ACM, pp 33:1–33:10Google Scholar
  32. Liu J, Sun L, Chen W, Xiong H (2016) Rebalancing bike sharing systems: a multi-source data smart optimization. In: Krishnapuram B, Shah M, Smola AJ, Aggarwal CC, Shen D, Rastogi R (eds) Proceedings of the 22nd ACM SIGKDD international conference on knowledge discovery and data mining. ACM, pp 1005–1014Google Scholar
  33. Lowalekar M, Varakantham P, Ghosh S, Jena SD, Jaillet P (2017) Online repositioning in bike sharing systems. In: Barbulescu L, Frank J, Mausam, Smith SF (eds) Proceedings of the 27th international conference on automated planning and scheduling (ICAPS). AAAI Press, pp 200–208Google Scholar
  34. Murota K (2003) Discrete convex analysis. SIAM monographs on discrete mathematics and applications. Society for Industrial and Applied Mathematics, PhiladelphiaCrossRefGoogle Scholar
  35. Nair R, Miller-Hooks E, Hampshire RC, Bušić A (2013) Large-scale vehicle sharing systems: analysis of Vélib’. Int J Sustain Transp 7(1):85–106CrossRefGoogle Scholar
  36. Nelson BL (2013) Foundations and methods of stochastic simulation. International series in operations research & management science, vol 187. Springer, New YorkGoogle Scholar
  37. O’Mahony E (2015) Smarter tools for (Citi) bike sharing. Ph.D. thesis, Cornell University, IthacaGoogle Scholar
  38. O’Mahony E, Shmoys DB (2015) Data analysis and optimization for (Citi) bike sharing. In: Twenty-ninth AAAI conference on artificial intelligence, pp 687–694Google Scholar
  39. Parikh P, Ukkusuri S (2015) Estimation of optimal inventory levels at stations of a bicycle sharing system. In: Transportation Research Board 94th annual meeting. Transportation Research BoardGoogle Scholar
  40. Paul A, Freund D, Ferber A, Shmoys DB, Williamson DP (2017) Prize-collecting TSP with a budget constraint. In: Pruhs K, Sohler C (eds) 25th annual European symposium on algorithms (ESA 2017), Schloss Dagstuhl–Leibniz-Zentrum für Informatik, Dagstuhl, Germany, Leibniz International Proceedings in Informatics (LIPIcs), vol 87, pp 62:1–62:14.,
  41. Raidl GR, Hu B, Rainer-Harbach M, Papazek P (2013) Balancing bicycle sharing systems: improving a VNS by efficiently determining optimal loading operations. In: Middendorf M, Blum C (eds) International workshop on hybrid metaheuristics. Springer, pp 130–143Google Scholar
  42. Rainer-Harbach M, Papazek P, Hu B, Raidl GR (2013) Balancing bicycle sharing systems: a variable neighborhood search approach. In: European conference on evolutionary computation in combinatorial optimization. Springer, pp 121–132Google Scholar
  43. Raviv T, Kolka O (2013) Optimal inventory management of a bike-sharing station. IIE Trans 45(10):1077–1093CrossRefGoogle Scholar
  44. Raviv T, Tzur M, Forma IA (2013) Static repositioning in a bike-sharing system: models and solution approaches. EURO J Transp Logist 2(3):187–229CrossRefGoogle Scholar
  45. Riquelme C, Johari R, Zhang B (2017) Online active linear regression via thresholding. In: Singh SP, Markovitch S (eds) Proceedings of the thirty-first AAAI conference on artificial intelligence. AAAI Press, pp 2506–2512Google Scholar
  46. Rudloff C, Lackner B (2014) Modeling demand for bikesharing systems: neighboring stations as source for demand and reason for structural breaks. Transp Res Rec J Transp Res Board 2430:1–11CrossRefGoogle Scholar
  47. Salaken SM, Hosen MA, Khosravi A, Nahavandi S (2015) Forecasting bike sharing demand using fuzzy inference mechanism. In: Arik S, Huang T, Lai WK, Liu Q (eds) ICONIP 2015: proceedings of the 22nd international conference on neural information processing. Springer, pp 567–574Google Scholar
  48. Saltzman RM, Bradford RM (2016) Simulating a more efficient bike sharing system. J Supply Chain Oper Manag 14(2):36–47Google Scholar
  49. Schuijbroek J, Hampshire R, van Hoeve WJ (2017) Inventory rebalancing and vehicle routing in bike sharing systems. Eur J Oper Res 257(3):992–1004CrossRefGoogle Scholar
  50. Shu J, Chou MC, Liu Q, Teo CP, Wang IL (2013) Models for effective deployment and redistribution of bicycles within public bicycle-sharing systems. Oper Res 61(6):1346–1359CrossRefGoogle Scholar
  51. Singhvi D, Singhvi S, Frazier PI, Henderson SG, O’Mahony E, Shmoys DB, Woodard DB (2015) Predicting bike usage for New York City’s bike sharing system. In: Dilkina B, Ermon S, Hutchinson RA, Sheldon D (eds) AAAI workshop: computational sustainability. AAAI PressGoogle Scholar
  52. Singla A, Santoni M, Bartók G, Mukerji P, Meenen M, Krause A (2015) Incentivizing users for balancing bike sharing systems. In: Bonet B, Koenig S (eds) Proceedings of the twenty-ninth AAAI conference on artificial intelligence. AAAI Press, pp 723–729Google Scholar
  53. Szeto W, Liu Y, Ho SC (2016) Chemical reaction optimization for solving a static bike repositioning problem. Transp Res D Transp Env 47:104–135CrossRefGoogle Scholar
  54. Vogel P, Saavedra BAN, Mattfeld DC (2014) A hybrid metaheuristic to solve the resource allocation problem in bike sharing systems. In: Blesa MJ, Blum C, Voß S (eds) International workshop on hybrid metaheuristics. Springer, pp 16–29Google Scholar
  55. Waserhole A, Jost V (2016) Pricing in vehicle sharing systems: optimization in queuing networks with product forms. EURO J Transp Logist 5(3):293–320CrossRefGoogle Scholar
  56. Zhang J, Pan X, Li M, Philip SY (2016) Bicycle-sharing system analysis and trip prediction. In: Chow C, Jayaraman PP, Wu W (eds) 2016 17th IEEE international conference on mobile data management (MDM), vol 1. IEEE, pp 174–179Google Scholar

Copyright information

© Springer Nature Switzerland AG 2019

Authors and Affiliations

  • Daniel Freund
    • 1
    Email author
  • Shane G. Henderson
    • 1
  • David B. Shmoys
    • 1
  1. 1.Cornell UniversityIthacaUSA

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