A Feasible Solution for Rebalancing Large-Scale Bike Sharing Systems

City bikes and bike-sharing systems (BSSs) are one solution to the last mile problem. BSSs guarantee equity by presenting affordable alternative transportation means for low-income households. These systems feature a multitude of bike stations scattered around a city. Numerous stations mean users can borrow a bike from one location and return it there or to a different location. However, this may create an unbalanced system, where some stations have excess bikes and others have limited bikes. In this paper, we propose a solution to balance BSS stations to satisfy the expected demand. Moreover, this paper represents a direct extension of the deferred acceptance algorithm-based heuristic previously proposed by the authors. We develop an algorithm that provides a delivery truck with a near-optimal route (i.e., finding the shortest Hamiltonian cycle) as an NP-hard problem. Results provide good solution quality and computational time performance, making the algorithm a viable candidate for real-time use by BSS operators. Our suggested approach is best suited for low-Q problems. Moreover, the mean running times for the largest instance are 143.6, 130.32, and 51.85 s for Q = 30, 20, and 10, respectively, which makes the proposed algorithm a real-time rebalancing algorithm.