Optimal batch production with minimum rework cycles and constraint on accumulated defective units

This paper deals with the issue of economic batch quantity (EBQ) in a single machine system in which defective items are produced in each cycle of production. The accumulated defective items produced in a period, consisting of several equal cycles, are all reworked in the last cycle of this period called the rework cycle. At the end of each period the whole process will start all over again. We assume that there is a limitation on the total defective items. We also do not adopt the restriction that the rework process rate be equal to the normal production rate. In addition we assume that there is a set up time for rework process. Further we assume that the number of rework cycles be as small as possible, which is mainly due to changeover costs needed for going from normal production to rework as well as special attention required for rework to satisfy the zero defect criterion. Finally, for the ease of production and resource planning, the rework cycle has to have the same length as the other cycles. For this system, assuming no shortages are permitted we obtain the economic batch quantity which minimizes the total cost of the system.