It has been shown in the literature that the use of Pontryagin＇s maximum principle to the optimization of feeding policy for fed-batch fermentation processes leads to a singular control strategy. This paper applies a numerical approach to find the optimal piecewise-constant feed profile for a repeated fed-batch fermentation process for the maximum cell productivity. It is shown that for a process with substrate-inhibited growth kinetics, the singular control strategy is not true optimal if there! is no singular are in the control. For a growth kinetics with constant yield coefficient, the degenerate case of having no singular are occurs when the initial cell concentration x(0) is lower than the concentration x(c) at which the cell has a maximum growth rate. The computed piecewise-constant suboptimal feeding profile for the degenerate case motivates us to search an alternative type of singular control strategy that gives the true optimal solution.