A multi commodity pickup and delivery open tour m-TSP formulation for bike sharing rebalancing problem

Bike sharing systems (BSSs) offer a mobility service whereby public bikes, located at different stations across an urban area, are available for shared use. An important point is that the distribution of rides between stations is not uniformly distributed and certain stations fill up or empty over time. These empty and full stations lead to demand for bikes and return boxes that cannot be fulfilled leading to unsatisfied and possibly even lost customers. To avoid this situation, bikes in the systems are redistributed by the provider. In this paper, a mathematical model is proposed to rebalance the stations employing non-identical trucks based on travelling salesman problem (TSP) formulation. This model is categorized as static repositioning where the demands of stations in one period are considered. In the mentioned model, several types of bikes have been considered in BSSs and it is assumed that there are two depots, and the trucks start from one and return to another one. Finally, a numerical example confirms the applicability of the proposed model. The results show that the model would simultaneously obtain the minimum paths, the minimum implementing truck’s costs and the minimum ofloading/unloading bikesprogram.