Skip to main content

A Stochastic Maximal Covering Formulation for a Bike Sharing System

  • Conference paper
  • First Online:
Optimization and Decision Science: Methodologies and Applications (ODS 2017)

Part of the book series: Springer Proceedings in Mathematics & Statistics ((PROMS,volume 217))

Included in the following conference series:


This paper discusses a maximal covering approach for bike sharing systems under deterministic and stochastic demand. Bike sharing is constantly becoming a more popular and sustainable alternative transportation system. One of the most important elements for the design of a successful bike sharing system is given by the location of stations and bikes. The demands in each zone for each period is however uncertain and can only be estimated. Therefore, it is necessary to address this problem by taking into account the stochastic features of the problem. The proposed model determines the optimal location of bike stations, and the number of bikes located initially in each station, considering an initial investment lower than a given predetermined budget. The objective of the model is to maximize the percentage of covered demand. Moreover, during the time horizon, it is possible to relocate a certain amount of bikes in different stations with a cost proportional to the traveled distance. Both deterministic and stochastic models are formulated as mixed integer linear programs.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Subscribe and save

Springer+ Basic
EUR 32.99 /Month
  • Get 10 units per month
  • Download Article/Chapter or eBook
  • 1 Unit = 1 Article or 1 Chapter
  • Cancel anytime
Subscribe now

Buy Now

USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
USD 129.00
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 169.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD 169.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Similar content being viewed by others


  1. Frade, I., Ribeiro, A.: Bicycle sharing systems demand. Procedia-Soc. Behav. Sci. 111, 518–527 (2014)

    Google Scholar 

  2. Alvarez-Valdes, R., Belenguer, J.M., Benavent, E., Bermudez, J.D., Muñoz, F., Vercher, E., Verdejo, F.: Optimizing the level of service quality of a bike-sharing system. Omega 62, 163–175 (2016)

    Google Scholar 

  3. Shu, J., Chou, M.C., Liu, Q., Teo, C.P., Wang, I.L.: Models for effective deployment and redistribution of bicycles within public bicycle-sharing systems. Oper. Res. 61(6), 1346–1359 (2013)

    Google Scholar 

  4. Lin, J.R., Yang, T.H.: Strategic design of public bicycle sharing systems with service level constraints. Transp. Res. Part E: Logist. Transp. Rev. 47(2), 284–294 (2011)

    Google Scholar 

  5. O’Mahony, E., Shmoys, D.B.: Data analysis and optimization for (Citi) bike sharing. In: AAAI, pp. 687–694. (2015)

    Google Scholar 

  6. Yan, S., Lin, J.R., Chen, Y.C., Xie, F.R.: Rental bike location and allocation under stochastic demands. Comput. Ind. Eng. 107, 1–11 (2017)

    Article  Google Scholar 

  7. Brinkmann, J., Ulmer, M.W., Mattfeld, D.C.: Inventory routing for bike sharing systems. Transp. Res. Procedia 19, 316–327 (2016)

    Article  Google Scholar 

  8. Kloimüllner, C., Papazek, P., Hu, B., Raidl, G.R.: A cluster-first route-second approach for balancing bicycle sharing systems. In: Computer Aided Systems Theory EUROCAST Lecture Notes in Computer Science, vol. 95(20), pp. 439–446. Springer (2015)

    Google Scholar 

  9. Martinez, L.M., Caetano, L., Eiró, T., Cruz, F.: An optimisation algorithm to establish the location of stations of a mixed fleet biking system: an application to the city of Lisbon. Procedia Soc. Behav. Sci. 54, 513–524 (2012)

    Google Scholar 

  10. Frade, I., Ribeiro, A.: Bike-sharing stations: a maximal covering location approach. Transp. Res. Part A: Policy Pract. 82, 216–227 (2015)

    Google Scholar 

Download references

Author information

Authors and Affiliations


Corresponding author

Correspondence to Claudio Ciancio .

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 2017 Springer International Publishing AG

About this paper

Check for updates. Verify currency and authenticity via CrossMark

Cite this paper

Ciancio, C., Ambrogio, G., Laganá, D. (2017). A Stochastic Maximal Covering Formulation for a Bike Sharing System. In: Sforza, A., Sterle, C. (eds) Optimization and Decision Science: Methodologies and Applications. ODS 2017. Springer Proceedings in Mathematics & Statistics, vol 217. Springer, Cham.

Download citation

Publish with us

Policies and ethics