Optimal batch production with rework and non-zero setup cost for rework

This paper attempts to develop the optimal solution for an inventory problem consisting of a single machine which produces items some of which may be defective. We assume that no shortages are allowed and all defective items are to be reworked. Setup cost for rework and waiting time of defectives are considered. We consider two different policies where in the first policy in each cycle after the regular production the machine is setup for the rework of defectives of the same cycle. In the second policy several cycles constitute a period. All the defectives produced in the period are reworked in the last cycle of that period. At the end of the rework cycle the whole process starts all over again. One significant feature of this work is that we do not impose any restriction on the length of the period. We derive the total cost function which includes the setup cost for rework and regular production, waiting time cost of defectives for rework, rework and regular processing costs and holding cost. We then derive the optimal solution of the total cost function for the two different policies.