Dynamic Resource Redistribution and Demand Estimation: An Application to Bike Sharing Systems

Shortage of bikes and docks is a common issue in bike sharing systems. To tackle this problem, operators use a fleet of vehicles to redistribute bikes across the network. We propose a model that captures successful user trips in the system, and a new mixed integer programming formulation that solves the dynamic redistribution problem by producing routes and pick-up/drop-off decisions for the vehicles. In order to scale to large instances, we develop a decomposition method based on proper station grouping, accompanied by an optimization with partial information approach, where relevant information for each group (routing and redistribution options) is modeled using piecewise linear concave functions and explicitly included in the model. We test our methods on both synthetic and real-world data, and show that our algorithms can scale to large real-world systems, with short running times that allow for real-time information to be taken into account. Furthermore, since accurate estimation of user demand is essential for efficient redistribution, we also develop data-driven and optimization-based approaches to consider lost and shifted demand. Our methods are general and not tied to the specific application domain; for instance, the optimization with partial information can be applied to any pick-up and delivery vehicle routing problem.