An economic production quantity model with random yield subject to process compressibility

This paper develops a new model for determining economic production quantity in an imperfect production system that generates defective items randomly. The production system utilizes an inspection subsystem to identify defective items (including reworkable and non-reworkable items) from non-defectives. Among defective items, reworkable items could be reworked once, and again an inspection is carried out. Furthermore, the inspection is error-prone that can result in returned items from customers. The proposed model considers realistic conditions in order to provide an optimal production plan. For example, rates of main and rework processes, batch size and back-order are considered as decision variables simultaneously such that rates of main and rework processes are not the same and take different values due to amount of the money that producer invests in each process (contributed as process compressibility). The objective function consists of different cost terms including shortage, regular production, setup of regular production, inventory holding, rework, inspection, disposal of scarped items and returned items from customer. The model is proved to be a convex nonlinear program. As it is difficult to obtain exact closed-form relations for the optimal solution, a problem-specific algorithm is designed. Under certain conditions, the algorithm can achieve the global optimum within a single iteration; otherwise it can be achieved in a polynomial time. Finally computational experiences are reported.