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. Note to Practitioners-This paper is motivated by the load balancing problem faced by BSS with finite-capacity docking stations and time-varying demand; stations become empty or full as their popularity as an origin or destination varies over the course of a day. The proposed RHC creates dynamic cooperative routes for a fleet of load balancing trucks to move bikes between stations by considering the current inventory, demand rates, and proximity of all stations and trucks. The strength of this controller is that it achieves optimality over a specified planning horizon and reacts quickly to random inventory changes which update the planning horizon on a rolling basis. Thus, the optimal routes found for a planning horizon are updated at the next decision point, i.e., an intersection. This event-driven RHC decreases the complexity of finding optimal routes so that it may be used in real time. Insights obtained from the application of this approach to the Boston BSS are that extending the length of the receding horizon provides marginal benefits beyond a certain value and that the controller is robust with respect to the stochastic behavior of the user demand and the truck travel time processes. The approach is amenable to extensions that can include incentivizing users so as to enhance load balancing beyond external truck-based interventions.