Economic production quantity model with imperfect quality during a process adjustment period

We consider a manufacturing process that generates non-conforming items until proper adjustment of the process is reached. Items produced after machine adjustment are assume perfect. The demand rate is assumed constant. The process stops when the production of conforming items is sufficient to cover the demand, then the cycle is repeated perpetually. Mathematical models for deterministic and random machine adjusting period are proposed. We find the optimal production quantity that results in minimum expected total cost. Two examples are presented. We also show that the optimal production size increases as the adjustment period increases, then at some value, it becomes constant.