Solving dynamic repositioning problem for bicycle sharing systems : model, heuristics, and decomposition

Bicycle sharing systems (BSS) have emerged as a powerful stimulus to non- motorized travel, especially for short-distance trips. However, the imbalances in the distribution of bicycles in BSS are widely observed. It is thus necessary to reposition bicycles to reduce the unmet demand due to such imbalances as much as possible. This paper formulates a new mixed-integer linear programming model considering the dynamic nature of the demand to solve the repositioning problem, which is later validated by an illustrative example. Due to the NP-Hard nature of this problem, we seek for two heuristics (greedy algorithm and rolling horizon approach) and one exact solution method (Benders’ decomposition) to get an acceptable solution for problems with large instances within a reasonable computation time. We create four datasets based on real world data with 12, 24, 36, and 48 stations respectively. Computational results show that our model and solution methods performed well. Finally, this paper gives some suggestions on extensions or modifications that might be added to our work in the future.