Simulated moving bed (SMB) chromatography is attracting more and more attention since it is a powerful technique for complex separation tasks. Nowadays, more than 60% of preparative SMB units are installed in the pharmaceutical and in the food industry [SDI, Preparative and Process Liquid Chromatography: The Future of Process Separations, International Strategic Directions, Los Angeles, USA, 2002. http://www.strategicdirections.com]. Chromatographyis the method of choice in these fields, because often pharmaceuticals and fine-chemicals have physico-chemical properties which differ little from those of the by-products, and they may be thermally instable [J. Kinkel, M. Schulte, R. Nicoud, F. Charton, Simulated moving bed (SMB) chromatography: an efficient method for performing large-scale separation of optical isomers, Chiral Eur. 95 (1995) 121-132; J. Strube, A. Jupke, A. Epping, H. Schmidt-Traub, M. Schulte, R. Devant, Design, optimization and operation of chromatographic processes in the production of enantiomerically pure pharmaceuticals, Chirality 11 (1999) 440-450]. In these cases, standard separation techniques as distillation and extraction are not applicable [S. Imamoglu, Simulated moving bed chromatography (SMB) for applications in bioseparation, Adv. Biochem. Eng. Biotechnol. 76 (2002) 211-231]. The use of the SMB technology leads to more efficient operations in terms of dilution and adsorbent utilization than the classical batch separation. Optimization of SMB processes is still a challenging task, particularly when a rigorous first-principles process model is used. SMB processes exhibit strong non-linear behavior and they are of periodic nature. Additionally, their hybrid, non-steady and non-ideal characteristics have to be taken into account. Model-based optimization strategies are therefore of great importance for research and practice. In this article, we report new efficient numerical approaches for the solution of the dynamic optimization problem arising from SMB processes [A. Toumi, Optimaler Betrieb und Regelung von Simulated Moving Bed Prozessen, Dissertation, Fachbereich Bio und Chemieingemeurwesen, University of Dortmund, 2004]. They have been developed in the software package MUSCOD-II [D. Leineweber, Efficient reduced SQP methods for the optimization of chemical processes described by large sparse DAE models, Dissertation, vol. 613, VDI Reihe 3, Verfahrenstechnik, VDI Verlag, 1999], a recent implementation of the direct multiple shooting method where the optimal state trajectory and the corresponding operating parameters are determined simultaneously [H. Bock, K. Plitt, A multiple shooting algorithm for direct solution of optimal control problems, in: Proceedings of the 9th IFAC World Congress Budapest, Pergamon Press, 1984, pp. 243-247; H. Bock, Randwertproblemmethoden zur Parameteridentifizierung in Systemen nichtlinearer Differentialgleichungen, Dissertation, Bonner Mathematische Schriften, 1987, p. 183]. Numerical results show excellent performance for a benchmark enantiomer separation. Finally, the ability to solve the non-linear programs quickly also enables us to consider more challenging operating regimes like VARICOL [P. Adam, R. Nicoud, M. Bailly, O. Ludemann-Hombourger, Process and device for separation with variable-length chromatographic columns, US Patent 6,413,419 (2002)] and PowerFeed [Z. Zhang, M. Mazzotti, M. Morbidelli, PowerFeed operation of simulated moving bed units: changing flow-rates during the switching interval, J. Chromatogr. A 1006 (2003) 87-99]. (c) 2007 Published by Elsevier B.V.