Determining the optimal lot size for the finite production model with random defective rate, the rework process, and backlogging

This paper considers the effects of the reworking of defective items on the economic production quantity (EPQ) model with backlogging allowed. The classic EPQ model assumes that manufacturing facility functions perfectly during a production run. However, due to process deterioration or other factors, the production process may shift and produce imperfect quality items. In this study, a random defective rate is considered and when regular production ends, the reworking of defective items starts immediately. Not all of the defective items are reworked, a portion of them are scrap and are discarded. Repairing and holding cost per reworked item and disposal cost per scrap item are included in the proposed mathematical modelling and analysis. The renewal reward theorem is utilized to deal with the variable cycle length, and the optimal lot size that minimizes the overall costs for the imperfect quality EPQ model is derived where backorders are permitted.