a multi-product inventory control model with imperfect production process and rework under delayed payment policy

the traditional economic production quantity (epq) model assumes that during the production process no imperfect item is produced. but 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 smaller additional reworking and holding costs. in addition, the permissible delay in payments offered by the supplier is widely adopted in the businesses. in this study, we explore the effects of both reworking imperfect quality items and trade credit policy on the epq model with imperfect production processes and backlogging. a mathematical model considering reworking and shortage costs, interest earned and interest charged in addition to traditional inventory costs is developed. besides an arithmetic-geometric mean inequality method 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 applicability of proposed model.