Effects of random defective rate and imperfect rework process on economic production quantity model

This paper considers the economic production quantity (EPQ) model with a random defective rate and an imperfect rework process. The assumption of perfect quality production condition of the classical EPQ model is unrealistic. Due to process deterioration or other factors, production of defective items is inevitable. This study assumes that the defective rate is a random variable and all items produced are inspected. The imperfect quality items fall into two groups, the repairable and the scrap. The reworking of the repairable defective items starts when the regular production process finishes in each cycle. The rework process is also assumed to be imperfect, with a random scrap rate. Since the scrap items are produced during a production run, it follows that the production cycle length is not a constant. The renewal reward theorem is utilized to cope with the variable cycle length. A mathematical model is developed to minimize the overall costs and to derive the optimal lot size for the imperfect quality EPQ model where shortages are not permitted. A numerical example is provided to demonstrate its practical usage.