Economic production quantity concerning learning and the reworking of imperfect items

The classical economic production quantity (EPQ) model assumes that items produced are of perfect quality and the production rate is constant. However, production quality depends on the condition of the process. Due to process deterioration or other factors, the production process may shift and produce imperfect quality items. These imperfect quality items sometimes can be reworked and repaired; hence, overall production-inventory costs can be reduced significantly. In addition, it can be found in practice that the time or cost required to repetitively produce a unit of a product decreases when the number of units produced by a worker or a group of workers increases. Under this circumstance, the unit production cost cannot be regarded as constant and, therefore, cannot be ignored when taking account of the total cost. This paper incorporates the effects of learning and the reworking of defective items on the EPQ model since they were not considered in existing models. An optimal operation policy that minimizes the expected total cost per unit time is derived. A numerical example is provided to illustrate the proposed model. In addition, sensitivity analysis is performed and discussed.