End-to-End deep learning for inventory management in capacitated bike-sharing systems with customer roaming behaviour

The inherent one-way travel characteristic of bike-sharing systems (BSS) frequently results in inventory imbalances across stations. To mitigate these imbalances, BSS operators typically set target inventory levels for each station independently and relocate bikes–often without accounting for user behaviour or inter-station relationships. This study addresses a network-level bike-sharing inventory management problem, focusing on optimising bike relocation and station inventory levels subject to station capacity constraints. We first propose a generalised customer roaming behaviour model that captures how customers select and roam to alternative stations when their initial requests cannot be fulfilled, or abandon the system, resulting in lost sales. Building upon the roaming behaviour model, we introduce an End-to-End (E2E) deep learning model to address the bike-sharing inventory management problem at the network level. A novel labelling procedure has also been developed to train the E2E deep learning model. Numerical experiments using real-world data from Citi Bike and Bluebikes reveal that the E2E deep learning model significantly outperforms network-level and station-level approaches, including variants of the predict-then-optimise framework. Results demonstrate that addressing the bike-sharing inventory management problem at the network level and employing the E2E deep learning model can substantially reduce user dissatisfaction. Results also suggest that BSS operators should offer compensation to customers who are unable to successfully return bikes and implement measures to increase the willingness of these unsatisfied users to travel longer distances, especially for bike returners, thereby mitigating overall user dissatisfaction and reducing operational costs.