An inherent characteristic of fermentation processes is that a batch phase is required at the beginning when the initial condition of the inhibitory product is very small, i.e. far from its peak which is optimal for the growth of biomass. Furthermore, since the volumetric flow rates are set to zero during the batch period, all the other continuous decision variables have no impact on the process either. On the other hand, the initial concentrations of the substrates and the switching time point from the batch to the continuous phase are crucial decision parameters for the objective function and the constraints in the optimization problem. Thus, the original optimization problem is decomposed into two sub-problems. The first one minimizes the batch time subject to end conditions concerning concentrations bounds, which are supplied by the optimizer of the continuous phase where initial concentrations are used as decision parameters as well. This interaction procedure is finished when the end concentrations of the batch period are equal to the corresponding optimized values of the continuous period. For the fermentation process considered, however, the reformulation of the sub-problems is physically equivalent to the original problem formulation.

The aim of the optimization is the maximization of the product total amount per time while minimizing the start-up period. To keep the production costs at a convenient level, different constraints are included in the optimization problem such as a glucose waste limit, a lower bound for the outlet product concentration and also technical constraints which involve upper bounds for the biomass concentration in the reactor. Previous to the numerical optimization and based on experimental results, several model parameters were adjusted using robust dynamic simulation (discretization by five orthogonal collocation points) in combination with parameter estimation methods. For the simulation and computation of the sensitivities, we propose a new multiple-time-scaling-approach to solving the resulting optimization problem which possesses strong nonlinear properties.