Rebalancing in bike sharing systems: Application to the Lisbon case study

This work presents a mathematical programming formulation for the static Bike Rebalancing Problem to meet the practical constraints faced by the operators of Bike Sharing Systems. Adaptating a Mixed Integer Linear Programming formulation, it now includes different types of vehicles and bicycles, the autonomy of each vehicle, the duration of its route and the stations that require inspection actions. An intermediate station is introduced to temporarily store bicycles, relaxing the restrictions imposed by the vehicles' capacity. After incorporating different acceleration procedures, a Branch-and-Cut scheme is run for 30 min to find optimized routes for the reposition vehicle on five real instances of the Lisbon Bike Sharing System. The computed routes resulted in a 30% to 75% decrease in total length, when compared to the real routes. This decrease is mainly attributed to the integration of all the mentioned factors in one global model, encouraging its future implementation.