Optimizing a production system with rework and equal sized batch shipments

In several cases producing new or recovering defective products takes place on a common facility, with these activities are carried out in lots. Consequently, there is a necessity to coordinate the production and rework activities with respect to the timing of operations and also with regard to appropriate lot sizes for both processes while completely satisfying a given demand. Thereby, a decision has to be made on how to assign units completed at one stage to partial lots-called batches-for shipment to the next operation. In this paper we present a lot size model which addresses all of these aspects. Based on total relevant costs per unit time, an optimization method is developed to determine the economic production and rework quantity as well as the corresponding batch sizes for both activities. The algorithm is illustrated by a numerical example followed by a sensitivity analysis of the models behavior under different problem parameters.