Document Type : Original Article


1 Department of Industrial engineering, Mazandaran University of Science and Technology, Babol, Iran.

2 Department of Mathematical Sciences, Sharif University of Technology, Tehran, Iran.

3 Department of Mathematics, Amirkabir University of Technology, Tehran, Iran.


Public Bicycle Sharing System (PBSS) is used as a way to reduce traffic and pollution in cities. Its performance is related to availability of bicycles for picking up and free docks to return them. Existence of different demand types leads to the emergence of imbalanced stations. Here, we try to balance inventory of stations via defining maximal response rates for each type of rental request. If the maximal response rate for a destination is lower than 100 percent, a part of the proposed destination requests is rejected in the hope of balancing the inventory. The goal is to minimize the mean extra inventory and the mean rejected requests by providing proper amounts of the maximal response rates. An approximation method named as Mean Value Analysis (MVA) is used to develop a genetic algorithm for solving the problem. Different examples are worked through to examine the applicability of the proposed method. The results show that the proposed policy leads to a significant improvement and reduces the users’ dissatisfaction. 


Alvarez-Valdes, R., Belenguer, J. M., Benavent, E., Bermudez, J. D., Muñoz, F., Vercher, E., & Verdejo, F., (2016). "Optimizing the level of service quality of a bike-sharing system", Omega, Vol. 62, pp. 163-175.
Bulhões, T., Subramanian, A., Erdoğan, G., & Laporte, G., (2018). "The static bike relocation problem with multiple vehicles and visits", European Journal of Operational Research, Vol. 264, No. 2, pp. 508-523.
Bruell, S. C., & Balbo, G., (1980). "Computational Algorithms for Closed Queueing Networks". Elsevier North-Holland, pp. 1-206.
Bryne, D. M., & Taguchi, S., (1987). "Taguchi approach to parameter design". Quality progress, 19-26.
Chemla, D., Meunier, F., Pradeau, T., Calvo, R. W., & Yahiaoui, H., (2013). "Self-service bike sharing systems: simulation, repositioning, pricing".
Contardo, C., Morency, C., & Rousseau, L. M., (2012). Balancing a dynamic public bike-sharing system (Vol. 4). Montreal: Cirrelt.
De Almeida Correia, G. H., & Antunes, A. P., (2012). "Optimization approach to depot location and trip selection in one-way carsharing systems", Transportation Research, Part E: Logistics and Transportation Review, Vol. 48, No. 1, pp. 233-247.
Dell'Amico, M., Hadjicostantinou, E., Iori, M., & Novellani, S., (2014). "The bike sharing rebalancing problem: Mathematical formulations and benchmark instances", Omega, Vol. 45, pp. 7-19.
Erdoğan, G., Laporte, G., & Calvo, R. W., (2014). "The static bicycle relocation problem with demand intervals", European Journal of Operational Research, Vol. 238, No. 2, pp. 451-457.
Fricker, C., & Gast, N., (2016). "Incentives and redistribution in homogeneous bike-sharing systems with stations of finite capacity", Euro Journal on Transportation and Logistics, Vol. 5, No. 3, pp. 261-291.
George, D. K., & Xia, C. H., (2011). "Fleet-sizing and service availability for a vehicle rental system via closed queueing networks", European Journal of Operational Research, Vol. 211, No. 1, pp. 198-207.
Ghosh, S., & Varakantham, P., (2017). Incentivizing the use of bike trailers for dynamic repositioning in bike sharing systems.
Goli, A., Aazami, A., & Jabbarzadeh, A., (2018). "Accelerated cuckoo optimization algorithm for capacitated vehicle routing problem in competitive conditions", Int J Artif Intell, Vol. 16, No. 1, pp. 88-112.
Goli, A., & Davoodi, S. M. R., (2018). "Coordination policy for production and delivery scheduling in the closed loop supply chain", Production Engineering, Vol. 12, No. 5, pp. 621-631.
Jian, N., Freund, D., Wiberg, H. M., & Henderson, S. G., (2016, December). "Simulation optimization for a large-scale bike-sharing system". In Proceedings of the 2016 Winter Simulation Conference. IEEE Press, pp. 603-613.
Kadri, A. A., Kacem, I., & Labadi, K., (2016). "A branch-and-bound algorithm for solving the static rebalancing problem in bicycle-sharing systems", Computers & Industrial Engineering, Vol. 95, pp. 41-52.
Lin, J. R., & Yang, T. H., (2011). "Strategic design of public bicycle sharing systems with service level constraints", Transportation Research, Part E: Logistics and Transportation Review, Vol. 47, No. 2, pp. 284-294.
Martinez, L. M., Caetano, L., Eiró, T., & Cruz, F., (2012). "An optimisation algorithm to establish the location of stations of a mixed fleet biking system: an application to the city of Lisbon", Procedia-Social and Behavioral Sciences, Vol. 54, pp. 513-524.
Nair, R., & Miller-Hooks, E., (2011). "Fleet management for vehicle sharing operations", Transportation Science, Vol. 45, No. 4, pp. 524-540.
Nair, R., & Miller-Hooks, E., (2014). "Equilibrium network design of shared-vehicle systems", European Journal of Operational Research, Vol. 235, No. 1, pp. 47-61.
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, Vol. 15, No. 4, pp. 1567-1578.
Raviv, T., & Kolka, O., (2013). "Optimal inventory management of a bike-sharing station", IIE Transactions, Vol. 45, No. 10, pp. 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, Vol. 2, No. 3, pp. 187-229.
Regue, R., & Recker, W., (2014). "Proactive vehicle routing with inferred demand to solve the bikesharing rebalancing problem", Transportation Research, Part E: Logistics and Transportation Review, Vol. 72, pp. 192-209.
Sangaiah, A. K., Tirkolaee, E. B., Goli, A., & Dehnavi-Arani, S., (2019). "Robust optimization and mixed-integer linear programming model for LNG supply chain planning problem", Soft Computing, pp. 1-21.
Tirkolaee, E. B., Goli, A., & Weber, G. W., (2019). "Multi-objective Aggregate Production Planning Model Considering Overtime and Outsourcing Options Under Fuzzy Seasonal Demand", In Advances in Manufacturing II (pp. 81-96). Springer, Cham.
Yan, S., Lin, J. R., Chen, Y. C., & Xie, F. R., (2017). "Rental bike location and allocation under stochastic demands", Computers & Industrial Engineering, Vol. 107, pp. 1-11.
Yang, X. H., Cheng, Z., Chen, G., Wang, L., Ruan, Z. Y., & Zheng, Y. J., (2018). "The impact of a public bicycle-sharing system on urban public transport networks", Transportation Research, Part A: Policy and Practice, 107, 246-256.
Zhang, D., Yu, C., Desai, J., Lau, H. Y. K., & Srivathsan, S., (2017). "A time-space network flow approach to dynamic repositioning in bicycle sharing systems", Transportation Research, Part B: Methodological, Vol. 103, pp. 188-207.