This work presents the mathematical modeling of the cephalosporin C (CPC) adsorption process in a fixed-bed column. The application of Particle Swarm Optimization (PSO) algorithm for parameter estimation was first considered, which shows to be a useful tool for parameter estimation in adsorption processes. Modeling and simulation of CPC purification showed a good performance during both estimation and validation step. After this, a central composite rotational design (CCRD) was conceived taking into account both the superficial velocity of liquid and column length as process variables with the responses obtained from the application of the model, which works as a process simulator affording a process answer from a given input. It has been shown that the response surface methodology was an efficient optimization tool, since few simulations were required to find the optimum region for independent variables. (C) 2011 Elsevier Ltd. All rights reserved.