Simulated moving bed (SMB) chromatography is an established separation technology, where chromatographic columns are interconnected to a ring. The feeding and drains are switched over cyclically, such that a continuous separation becomes possible. For a faultless operation, the volumetric flow rates and switching time must be carefully adjusted. Therefore, it is desirable to calculate these values in dependence of the model parameters exactly. In this contribution, a new method is introduced to compute operating points for dispersion-free SMB plants and to predict the associated time trajectories of the concentrations at the drains in cyclic steady state for user-specified purities and degree of robustness. Simulation results are presented to show the potential of this new method.