Receding Horizon Control for Station Inventory Management in a Bike-Sharing System

A docking bike-sharing system (BSS) is modeled as a network representing the underlying transportation network. Mobile agents (replenishment trucks) traverse the network making routing decisions and deciding how and when to replenish station inventories so as to prevent imbalances due to users' one-way rides as well as time-varying demand. This load balancing process entails selecting both optimal routes for the agents and the number of bikes to load/unload at a station with an objective of minimizing a user dissatisfaction metric. First, we establish a time-dependent replenishment fill-to level policy for each station based on the demand rates and station capacities. Next, we focus on developing a receding horizon controller (RHC) to find optimal routes. The controller proceeds in an event-driven manner to determine after each event the optimal routes for a fleet of agents over a finite planning horizon, with the control applied over a shorter action horizon. The proposed controller is applied to a simulated BSS with station and demand parameters taken from the public data sets of Bluebikes, the BSS in Boston, MA, USA, and a cost-benefit analysis is performed on agent shift hours. In order to demonstrate the robustness of the RHC, sensitivity analysis is also performed on the arc travel times and the demand processes.