Two-stage stochastic program for inventory rebalancing of bike-sharing systems

In recent years, bike sharing has become more prevalent in many major cities because of their convenience, environmental impact, and health benefits. As popularity and usage increase, there exists an urgent need for a decision-making model for the efficient operations of bike-sharing systems. This study addresses inventory rebalancing, which is one of the critical operational decisions of bike-sharing systems. Due to demand uncertainty and fluctuation, the usability of bike-sharing systems can be limited, e.g., stations become full or empty and users cannot check-in/out bikes. Hence, inventory rebalancing should be done properly to maximize the availability of service. Given this, this study intends to develop a decision-making model designed to determine an optimal daily inventory rebalancing plan based on real-world practice. In particular, this study proposes a two-stage stochastic program that can be formulated to determine initial inventory levels for each one-day operations while minimizing operational cost for bike relocation and expected penalty cost for unmet demand caused by uncertainty. The sampling-based approach is used to solve the proposed two-stage stochastic program based on scenario data composed from the historical data obtained from the Houston BCycle. To evaluate the proposed model, numerical experiments are conducted under various settings, and the results show that the proposed inventory rebalancing model can be successfully applied to improve usability of bike-sharing systems.