Downstream bioprocessing and especially chromatographic steps, commonly used for the purification of multicomponent systems, are significant cost drivers in the production of therapeutic proteins. There has been an increased interest in the development of systematic methods for the design of such processes, and the appropriate selection of a series of chromatographic steps is still a major challenge to be addressed. Several models have been developed previously but have assumed that 100% recovery of the desired product is obtained at each chromatographic step. In this work, a mathematical framework is proposed, based on mixed integer optimisation techniques, that removes this assumption and allows full flexibility on the position of retention time cut-points, between which the desired product fraction is collected. The proposed model is demonstrated on three example protein mixtures, each containing up to 13 contaminants and selecting from a set of up to 21 candidate steps. The proposed model results in a reduction of one to three chromatographic steps over solutions that no losses are allowed. (C) 2011 American Institute of Chemical Engineers Biotechnol. Prog., 2011