The present invention comprises the optimization of a four zone simulated moving bed system configured to separate a first component from a mixture containing the first component and a second component wherein the first component exhibits non-linear adsorption and non-negligible mass transfer resistances. In one example, the four zone simulated moving bed is optimized to separate Clarithromycin from a mixture containing Clarithromycin and 6,11-O-methyl erythromycin A. The present invention further comprises a four zone or a five zone apparatus having a first portion and a second portion and the optimization of the four zone or five zone apparatus to separate a first component from a mixture containing the first component and a second component and the method of using the same. In one example, the four zone and five zone simulated moving beds are optimized to separate Clarithromycin from a mixture containing Clarithromycin and 6,11-O-methyl erythromycin A. The present invention further comprises a batch elution system configured to separate Clarithromycin from a mixture containing Clarithromycin and 6,11-O-methyl erythromycin A.