Automated Guideway Transit is a form of public transportation tools where fully driverless vehicles operate in order to move passengers between specific locations. Automated Guideway Transit includes a large variety of systems including mass transit systems and limited people automated guideway transit systems. In this paper, we focus on a specific limited people mover system called personal rapid transit. We develop in this paper an optimization based software which could manage efficiently the empty vehicles movements within the personal rapid transit system. Within this context, a branch and bound algorithm is proposed and its efficiently is proved on a set of instances taken from the literature. Our algorithm is shown to get good quality results.