Rebalancing static bike-sharing systems: a two-period two-commodity multi-depot mathematical model

    S. Mohammad Arabzad Affiliation
    ; Hadi Shirouyehzad Affiliation
    ; Mahdi Bashiri Affiliation
    ; Reza Tavakkoli-Moghaddam Affiliation
    ; Esmaeil Najafi Affiliation


In this paper, an Integer Linear Programming (ILP) has been developed for rebalancing the stations of a Periodic Bike Relocation Problem (PBRP) in multiple periods. The objective function of the mathematical model is reducing costs of implementing trucks, transportation between stations and holding bikes on trucks during rebalancing. The variables we are following them in this model are conducting the optimal route in several periods, using the most appropriate trucks for these routes, and determining the best program for loading/unloading bikes for stations. The distinguishing features of the proposed model are considering several bike types, several exclusive trucks and several time periods. Finally, a numerical example confirms the applicability of the proposed model.

Keyword : bike-sharing systems (BSS), periodic bike relocation problem (PBRP), mathematical modelling

How to Cite
Arabzad, S. M., Shirouyehzad, H., Bashiri, M., Tavakkoli-Moghaddam, R., & Najafi, E. (2018). Rebalancing static bike-sharing systems: a two-period two-commodity multi-depot mathematical model. Transport, 33(3), 718-726.
Published in Issue
Aug 20, 2018
Abstract Views
PDF Downloads
Creative Commons License

This work is licensed under a Creative Commons Attribution 4.0 International License.


Ahmed, F.; Rose, G.; Jacob, C. 2010. Impact of weather on commuter cyclist behaviour and implications for climate change adaptation, in ATRF 2010: 33rd Australasian Transport Research Forum, 29 September – 1 October 2010, Canberra, Australia, 33: 1–19. Available from Internet:

Bachand-Marleau, J.; Lee, B.; El-Geneidy, A. 2012. Better understanding of factors influencing likelihood of using shared bicycle systems and frequency of use, Transportation Research Record: Journal of the Transportation Research Board 2314: 66–71.

Basch, C. H.; Ethan, D.; Rajan, S.; Samayoa-Kozlowsky, S.; Basch, C. E. 2014. Helmet use among users of the citi bike bicycle-sharing program: a pilot study in New York City, Journal of Community Health 39(3): 503–507.

Bektas, T. 2006. The multiple traveling salesman problem: an overview of formulations and solution procedures, Omega: the International Journal of Management Science 34(3): 209–219.

Brake, J.; Mulley, C.; Nelson, J. D.; Wright, S. 2007. Key lessons learned from recent experience with flexible transport services, Transport Policy 14(6): 458–466.

Buck, D.; Buehler, R.; Happ, P.; Rawls, B.; Chung, P.; Borecki, N. 2013. Are bikeshare users different from regular cyclists?: A first look at short-term users, annual members, and area cyclists in the Washington, D.C., Region, Transportation Research Record: Journal of the Transportation Research Board 2387: 112–119.

Chemla, D.; Meunier, F.; Wolfler Calvo, R. 2013. Bike sharing systems: solving the static rebalancing problem, Discrete Optimization 10(2): 120–146.

DeMaio, P. 2016. The Bike-Sharing World Map. MetroBike, LLC. Available from Internet:

Dell’Amico, M.; Hadjicostantinou, E.; Iori, M.; Novellani, S. 2014. The bike sharing rebalancing problem: Mathematical formulations and benchmark instances, Omega: the International Journal of Management Science 45: 7–19.

Dell’Amico, M.; Iori, M.; Novellani, S.; Stützle, T. 2016. A destroy and repair algorithm for the bike sharing rebalancing problem, Computers & Operations Research 71: 149–162.

Dikas, G.; Minis, I. 2014. Scheduled paratransit transport systems, Transportation Research Part B: Methodological 67: 18–34.

Fishman, E.; Washington, S.; Haworth, N. 2012a. Barriers and facilitators to public bicycle scheme use: a qualitative approach, Transportation Research Part F: Traffic Psychology and Behaviour 15(6): 686–698.

Fishman, E.; Washington, S.; Haworth, N. 2012b. Understanding the fear of bicycle riding in Australia, Journal of the Australasian College of Road Safety 23(3): 19–27.

Fishman, E.; Washington, S.; Haworth, N. 2013. Bike share: a synthesis of the literature, Transport Reviews 33(2): 148–165.

Fishman, E.; Washington, S.; Haworth, N.; Mazzei, A. 2014. Barriers to bikesharing: an analysis from Melbourne and Brisbane, Journal of Transport Geography 41: 325–337.

Fishman, E.; Washington, S.; Haworth, N.; Watson, A. 2015. Factors influencing bike share membership: an analysis of Melbourne and Brisbane, Transportation Research Part A: Policy and Practice 71: 17–30.

Fu, L. 2002. A simulation model for evaluating advanced diala-ride paratransit systems, Transportation Research Part A: Policy and Practice 36(4): 291–307.

Goodman, A.; Green, J.; Woodcock, J. 2014. The role of bicycle sharing systems in normalising the image of cycling: an observational study of London cyclists, Journal of Transport & Health 1(1): 5–8.

Gutin, G.; Punnen, A. P. 2007. The Traveling Salesman Problem and its Variations. Springer US. 830 p.

Horton, D.; Rosen, P.; Cox, P. 2012. Cycling and Society. Ashgate. 232 p.

LDA Consulting. 2013. 2013 Capital Bikeshare Member Survey Report. Washington, DC: Commissioned by Capital Bikeshare. Washington, DC, US. 114 p.

Martens, K. 2004. The bicycle as a feedering mode: experiences from three European countries, Transportation Research Part D: Transport and Environment 9(4): 281–294.

Pfrommer, J.; Warrington, J.; Schildbach, G.; Morari, M. 2014. Dynamic vehicle redistribution and online price incentives in shared mobility systems, IEEE Transactions on Intelligent Transportation Systems 15(4): 1567–1578.

Raviv, T.; Kolka, O. 2013. Optimal inventory management of a bike-sharing station, IIE Transactions 45(10): 1077–1093.

Raviv, T.; Tzur, M.; Forma, I. A. 2013. Static repositioning in a bike-sharing system: models and solution approaches, EURO Journal on Transportation and Logistics 2(3): 187–229.

Sayarshad, H.; Tavassoli, S.; Zhao, F. 2012. A multi-periodic optimization formulation for bike planning and bike utilization, Applied Mathematical Modelling 36(10): 4944–4951.

Schalekamp, H.; Behrens, R. 2013. Engaging the paratransit sector in Cape Town on public transport reform: progress, process and risks, Research in Transportation Economics 39(1): 185–190.

Shaheen, S.; Cohen, A.; Martin, E. 2013. Public bikesharing in North America: early operator understanding and emerging trends, Transportation Research Record: Journal of the Transportation Research Board 2387: 83–92.

Starke, L. (Ed.). 2002. Vital Signs 2002: the Trends that are Shaping Our Future. Worldwatch Institute. W. W. Norton & Co Inc. 215 p.

Woodcock, J.; Goodman, A. 2014. Hard Evidence: Do Bikeshare Schemes Lead to More Head Injuries Among Cyclists? Available from Internet:

Zhu, W.; Pang, Y.; Wang, D.; Timmermans, H. 2013. Travel behavior change after the introduction of public bicycle systems: case study in Minhang District, Shanghai, in TRB 92nd Annual Meeting Compendium of Papers, 13–17 January 2013, Washington, DC, US, 1–15.