Based upon the general characteristics of the optimal feed rate profiles presented in an earlier article, efficient computational algorithms have been developed for fed-batch fermentation processes described by four or less mass balance equations. These algorithms make computations of optimal substrate feed rate profiles straight forward and simple for various fed-batch cultures for such products as antibiotics, amino acids, enzymes, alcohols, and cell mass. Numerical examples of penicillin fermentation and bacterial cell mass production are given in detail, illustrating the use of these algorithms.

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A unidirectional method is developed to solve optimal singular control problems with bounded state variables. The computational algorithm utilizes the necessary conditions of optimality and an unidirectional scheme to reduce the iterations required in two-point boundary value problems. The advantage of the method is that it satisfies all the necessary conditions of optimality and results in a considerable reduction in computational effort. Three numerical examples illustrate the use of these algorithms for solving several chemical reaction engineering problems.