This work focuses on the optimal control of two typical processes in the context of industrial crystal growth. First, the annealing of bulk GaAs crystals is considered and an optimal control problem is solved in order to find optimised heating profiles for the furnace. A reduced order model for the annealing furnace has been developed in order to speed up the optimisation algorithm. As a second application, our control algorithm is used to optimise a VGF-process for growing GaAs crystals: the growth rate of the GaAs crystal is maximised under side conditions for the resulting thermal stress.