A mathematical framework for developing efficient methods to calculate the cyclic steady state (CSS) of the simulated moving-bed (8MB) process is established based on single-column models. The formulation and methods presented are equally applicable to recently developed 8MB enhancements that vary some of the operating parameters during a switching interval. These include, among others, Varicol, PowerFeed, ModiCon, and modulation of solvent strength during process operation. The solution methods can be classified into two major classes: dynamic methods which integrate in time, either truly or artificially, the governing equations over a large number of cycles until CSS is reached, and methods which rely on the direct prediction of the CSS by simultaneously discretizing the spatial and temporal coordinates. The performance of each solution method is measured in terms of CPU time, number of cycles to attain CSS, and CPU time per cycle. The various methods are compared for the separation of two binary mixtures that are sufficiently different, in isotherm models and selected operating parameters, for their overall analysis to provide conclusions of general applicability.