A fairness-aware coordinated two-echelon static rebalancing approach for large-scale bike-sharing systems

Effectively solving large-scale static bike-sharing rebalancing problems (SBRPs) remains a significant challenge, particularly when aiming to simultaneously minimize computational complexity, ensure operational efficiency, and promote task fairness. Dividing and conquering, enabling concurrent execution of tasks, and balancing task durations are critical to achieving the above objectives. Existing studies have significantly reduced computational complexity through divide-and-conquer approaches such as cluster-first, route-second, but have overlooked that enabling concurrent execution of tasks is essential for operational efficiency and that balancing task durations is crucial for task fairness. To address these gaps, we propose a clustering-free divide-and-conquer strategy and a coordinated two-echelon rebalancing framework for large-scale SBRPs. Specifically: (i) Municipal districts containing stations are defined as fixed zones, a central depot with no inventory is located at the centroid of all stations, and a zonal depot with an initial inventory is established at the centroid of the stations in each zone; (ii) First- and second-echelon rebalancing models are formulated to optimize inter- and intra-zonal routes to rebalance bike distribution at the zone and station levels, respectively; (iii) The first-echelon subproblem is solved to optimality using Gurobi, while the second-echelon subproblem is addressed by HABEF, a hybrid algorithm developed in this paper to jointly balance operational efficiency and task fairness; (iv) A two-echelon coordination strategy is designed to increase task concurrency and minimize makespan. Experiments show that our approach is highly effective, yielding high-quality solutions within acceptable computation time. The resulting solutions exhibit more balanced task durations, higher task concurrency, and a shorter makespan. Notably, regardless of variations in the number of tasks, our approach consistently outperforms existing methods in achieving a superior balance between operational efficiency and task fairness.