We consider a production system with post-operation and early set-up. As soon as there are no more units(raw materials) to process and the machine becomes idle, it undergoes a post-operation. After the post operation, if the number of waiting units is greater than or equal to m, it begins a set-up. After the set-up, if the number of units is greater than or equal to N($geq$m), it begins to process the units. We first analyze the system by employing the decomposition property of the vacation queue. We, then, propose an algorithm that finds the optimal threshold values ($m^*$, $N^*$). Finally we present some numerical examples and interprete the system behavior.