Semi-preemptive routing on a linear and circular track

The problem of routing a robot (or vehicle) between nn stations in the plane in order to transport objects is well studied, even if the stations are specially arranged, e.g. on a linear track or circle. The robot may use either all or none   of the stations for reloading. We will generalize these concepts of preemptiveness/nonpreemptiveness and allow the robot to choose k≤nk≤n reload-stations. We will show that the problem on the linear and circular track remains polynomially solvable.