Scheduling Accumulated Rework in a Normal Cycle: Optimal Batch Production with Minimum Rework Cycles

In this paper we consider a single machine system that produces items part of which are defective. The defective items produced in a time period, consisting of several equal cycles, are accumulated and are all reworked in the last cycle of this period called the rework cycle. At the end of the rework cycle the whole process will start all over again. The first significant objective of this study is that, for the ease of production and resource planning, the rework cycle has to have the same length as the other cycles. The other objective is that the number of rework cycles be as small as possible, because of changeover costs needed for going from normal production to rework as well as special attention required for rework to satisfy the zero defect criterion. For this system, assuming no shortages are permitted we drive the total system cost per unit time and obtain the economic batch quantity which minimizes this total cost.