A data-driven robust optimization model for repositioning problem in bike-sharing systems

In this paper, we study a multi-period repositioning problem in a free-floating bike-sharing system by proposing a novel data-driven robust optimization model. We first analyze a stochastic optimization model based on an empirical distribution, which we reformulate as a dynamic programming model. However, we highlight the computational challenges associated with solving this stochastic model, particularly in large-scale settings. To overcome these challenges, we propose a sample-based robust optimization (SRO) approach. This method constructs multiple uncertainty sets for demand using historical data and optimizes the solution under the worst-case scenario, ensuring robustness against demand variability. The proposed SRO approach guarantees asymptotic optimality and, through a linear decision rule approximation, can be reformulated into a computationally tractable linear programming model. Numerical experiments demonstrate the superiority of the SRO model over the traditional mean value problem (MVP) approach, across various performance criteria. Specifically, the SRO model achieves an average total cost reduction ranging from 5.9% to 24.3%. Our findings show the effectiveness of the SRO framework in addressing the complexities of bike-sharing repositioning under uncertainty.