A free-floating bike repositioning problem with faulty bikes

The Free-Floating Bike-sharing System (FFBS) assists the commuters to pick up and drop off a rented bike without going to a docking station before and after the ride. However, the convenience of FFBS can also be a problem for users because the randomly scattered and faulty bikes can bring about bike unavailability and maintenance difficulties. This not only results in a negative impact on the company’s service quality but also causes safety concerns. In this study, a framework for bike repositioning with faulty bikes is presented comprising two steps: 1) shifting faulty bikes to the nearest node using optimal path by service vehicles, 2) repositioning operation: to obtain optimal inventory at all nodes and faulty bikes collection to depots. This framework is realized by minimizing the total routing cost based on various time and capacity constraints. The model is validated through a numerical study using CPLEX solver.