Battery Swapping Tour Optimization Problem in Dockless Electric Bike Sharing Service Systems With Distance-Aware User Incentives

Dockless electric bike (E-bike) sharing has emerged as a modern and eco-friendly mode of urban transportation, providing convenient services for users. Typically, the service provider deploys a truck from a central depot to visit multiple parking locations, replacing low-energy batteries in E-bikes and returning to the depot. However, the cost of visiting numerous locations can be substantial. One effective strategy is to aggregate low-energy E-bikes together, prompting the adoption of incentive mechanism to encourage users to relocate their bikes to the proper parking locations, albeit at an additional incentive cost. The challenge lies in balancing the tour cost of the truck and the incentive cost for E-bike users. To address this issue, this paper formulates an online battery swapping optimization problem, which is NP-hard and cannot be approximated within a competitive factor of 2. For the offline and online problems, the paper proposes a $\frac{20}{3}$-approximation algorithm and an $O(\epsilon ^{-1})$-competitive algorithm. The simulation results using the real-world data demonstrate that the proposed algorithms outperform existing baselines by identifying suitable battery swapping locations to minimize both tour and incentive costs for service providers.