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.Scope and purposeFor manufacturing purposes most often quite sophisticated equipment is used. Nevertheless, some defective units occur even in production systems comprised of high quality facilities. In many cases defective items incorporate substantial values and hence there is an economic incentive to rework those products into an ‘as new’ condition. As a result, there is a necessity for companies to integrate the recovery of non-conforming units into their regular production activities. Although joint determination of production and rework lot sizes has attracted many researchers, the simultaneous analysis of lot-sizing and scheduling problems has yet to be covered adequately in traditional models in this area of investigation. Moreover, most of these approaches restrict the number of shipments between stages to either the transportation of whole lots or to the conveyance of individual units immediately after their completion. It seems more realistic to also allow transports of partial lots larger than one and smaller than the entire lot. Therefore, in this paper we will present a lot size model that addresses all of these features and enables us to gain insights and a better understanding of such specific planning situations.