Optimal production lot with imperfect production process under permissible delay in payments and complete backlogging

The traditional economic production quantity (EPQ) model assumes that the production products are all perfect. It is not always true in the real production system, due to imperfect production process or other factors, imperfect quality items may be produced. Furthermore, it is well-known that the total production-inventory costs can be reduced by reworking the imperfect quality items produced with a relatively smaller additional reworking and holding costs. In addition, the permissible delay in payments offered by the supplier is widely adopted in the practical business market. In this study, we explore the effects of the reworking imperfect quality items and trade credit on the EPQ model with imperfect production processes and complete backlogging. A mathematical model which includes the reworking and shortage costs, interest earned and interest charged is presented. Besides, an arithmetic-geometric mean inequality approach is employed and an algorithm is developed to find the optimal production policy. Furthermore, some numerical examples and sensitivity analysis are provided to demonstrate the proposed model.