In this paper, we propose a logical control-based actor-critic algorithm as an efficient approach for the approximation of the capacitated fab scheduling problem. We apply the average reward temporal-difference learning method for estimating the relative value functions of system states, while avoiding deadlock situation by Banker's algorithm. We consider the Intel mini-fab re-entrant line for the evaluation of the suggested algorithm and perform a numerical experiment by generating some sample system configurations randomly. We show that the suggested method has a prominent performance compared to other well-known heuristics