The rate of biomass production is optimised for a predeÿned feed exhaustion using the residue ratio as a degree of freedom. Three modes of operation are considered: continuous, repeated batch, and repeated fed-batch operation. By means of the Production Curve, the transition points of the optimal modes of operation are derived. The analytical expressions of these transitions for variable bioreaction kinetic parameters are determined. The key measures "degree of di culty of conversion" and "degree of exhaustion" are introduced to deÿne the optimal modes in more general terms. The "degree of di culty" describes the e ect of the kinetic parameters and the feed substrate concentration on the conversion; the "degree of exhaustion" describes the desired ÿnal condition. In fed-batch operation, the proposed constant feed policy approximates the optimal feed policy closely. ?