Rebalancing Bike Sharing Systems for Minimizing Depot Inventory and Traveling Costs

Smart shared mobility is an emerging transportation strategy that promotes sustainable and intelligent transportation. Bike sharing is one mode of smart shared mobility and is gaining popularity in recent years. To ensure a smooth operation of a bike sharing system (BSS), it is essential to redistribute the bicycles, which includes picking up returned bicycles and relocating them to best serve customers. A bike sharing rebalancing problem (BSRP) has thus emerged. This paper addresses a static BSRP which operates during the night when shared bikes are rarely utilized or when the BSS is closed. We studied a single-vehicle BSRP (sBSRP) and multi-vehicle BSRP (mBSRP) with the objective of minimizing the depot inventory cost as well as the traveling cost. For mBSRP, six formulations are presented i.e. five mixed integer programming models (mBSRP1-mBSRP5) and a mixed integer linear programming model (mBSRP6). In addition, an iterative procedure combined with the branch-and-cut algorithm in the CPLEX solver is developed to solve this problem. A real-world case study is employed to test the effectiveness of the formulations, and a set of benchmark instances are adopted to further compare the performances of mBSRP5 and mBSRP6. The experimental results show that mBSRP6 performs the best among the six models, offering the best solution quality and computational efficiency. Finally, mBSRP6 is applied to determine the depot inventory for the case study using random demand datasets.