An Optimization Model for Bike Repositioning in Bike-sharing Systems Considering Both Demands for Borrowing or Returning Bikes and Costs of Repositioning Operations

Traditional bike-rebalancing models in bike-sharing systems required that the number of bikes allocated at each bike station be known and that they meet the exact demand values, which may increase costs sharply for repositioning small numbers of bikes. (The number of bikes at some stations after repositioning considering both demand and operation costs may be just a few less than the exact demand, with little impact on the number of satisfied demands for borrowing or returning bikes, whereas the route length or time expense of truck scheduling may increase significantly if scheduled to meet the exact demand values). Therefore, this paper proposes a new bike-rebalancing model, which does not require a strict allocation in advance for a given number of bikes to all stations. The proposed model comprehensively considered both demands for borrowing and returning bikes and costs of repositioning operations. It also analyzed the constraints and dynamic evolution of bike-borrowing-and-returning in time and space. The model facilitated the optimization of the scheduled routes of trucks, and the determination of both the number of bikes allocated at each bike station and the number of satisfied demands. Genetic algorithms were developed for solving the proposed models, and the code and genetic operator were created to solve the models. A numerical example showed that, through the adjustment of weights amongst multiple goals in the proposed model, a truck routing scheme can be determined that can not only finely satisfy the demand for borrowing and returning bikes, but also save costs for repositioning operations. Results indicate that, in comparison with the traditional bike-repositioning model, the proposed model leads to a 30% reduction in scheduling time with an approximately 2% reduction in the satisfied demand for borrowing or returning bikes. The repositioning time will obviously increase if the number of bikes allocated to each bike station are required to meet demands strictly. This research provides a foundation for bike repositioning in bike-sharing systems. © 2019, Editorial Department of China Journal of Highway and Transport. All right reserved.