Optimizing the Crowdsourcing-based Bike Station Rebalancing Scheme

User dynamics in both spatial and temporal domains bring uncertainty to bike-sharing systems (BSSs) and usually lead to bike imbalance. This may generate out-of-service events due to bike underflow or overflow, at a bike station. In this paper, we recruit workers through crowdsourcing to rebalance loads among bike stations. We assume that workers have their individual sources and destinations, and assign them to move bikes from overflow stations to underflow stations. We partition the complex spatial and temporal problem into a sequence of slices with a fixed duration in the temporal domain. In each slice, we focus on the spatial domain and allocate a pair of overflow/underflow stations to a worker such that the summation of detour cost among workers is minimized. The hardness of finding the min-cost allocation is shown by a reduction from a 3-dimensional matching problem (i.e., matching among workers, overflow stations, and underflow stations). We propose a 3-approximation algorithm for the problem when the detour cost is proportional to the detour distances. Then, the configuration dynamic in the sequence of slices is captured by carefully determining the rebalancing frequency and target for each rebalancing operation. We investigate heuristic approaches to decide rebalancing frequencies and targets over a sequence of slices in order to minimize the total number of bike movements (i.e., the total number of workers), and hence to derive the average total detours per slice. We simulate our algorithms on both real-world and synthetic datasets based on different time-slice granularities. The experiment results show that our approaches can reduce the average total detour per slice.