Risk-averse two-stage stochastic programming for the inventory rebalancing of bike-sharing systems

As the popularity and usage of bike-sharing systems increase, a better decision-making model tailored for the successful operations of bike-sharing systems is needed. This study is motivated to address operator-based inventory rebalancing of bike-sharing systems, and the main objective is to develop a mathematical optimization model designed to derive an optimal daily inventory rebalancing plan. Specifically, this study proposes a risk-averse two-stage stochastic programming to determine optimal initial inventory levels for each station to minimize operational costs for relocating bikes and expected penalty costs due to unmet requests. This study adopts the conditional value at risk to properly measure the risk associated with unmet requests to implement risk-averse stochastic programming. Numerical experiments are conducted based on scenario data generated by empirical distributions fitted to trip data from the Houston BCycle to validate and evaluate the proposed model. The results show that the proposed model can be successfully applied to inventory rebalancing to improve the usability of bike-sharing systems.