We have investigated the direct esterification reaction between terephthalic acid (TPA) and ethylene glycol (EG) in semi-batch reactors, the first stage process for making polyethylene terephthalate (PET), to get optimum conditions for the minimum reaction time. An independent-variable-minimization problem, i.e., a free-end-time/fixed-end-point problem, has been formulated for the system, and then converted to a dependent-variable-minimization (fixed-end-time/free-end-point) problem by a coordinate transformation, for the latter problem readily yields to established solution methods. We have solved this reformulated problem to obtain the optimal temperature profiles in the reactor required for the minimum reaction time, by iteratively improving the temperature (manipulating variable) profile using the Pontryagin’s minimum principle. The results prove that the method employed here successfully finds an optimal solution for the PET esterification process. The reduction of the reaction time realized following this optimal temperature profile in the reactor was, however, found to be smaller than expected, due to the approximating assumptions of neglecting the solubility equation of TPA in the model. The results obtained using a more improved model of the system will be reported in the future.