Determining the optimal production policy for a system with imperfect production and shortage

Abstract The classic EPQ model assumes that items are produced of perfect quality and no shortage is permitted. In the real world situation, however, due to process deterioration or other factors, the occurrence of imperfect quality items is inevitable. This paper develops an extended economic production quantity (EPQ) model with imperfect production, shortage, and imperfect rework. We assume that the quality scan is conducted during the production. The scanned imperfect items are classified as the repairable and scrap. We consider that not all of the repairable items can be restored to meet the specified quality standard. Only some portion of defective items can be restored as normal items, the other results in defective, due to repair failure, can be sold at a discounted price to a secondary market. The renewal reward theorem is utilized to deal with the variable cycle length. The production quantity and the shortage level are determined in an optimal manner so as to minimize the average system cost. A numerical example is used to demonstrate its practical usage. (© 2008 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)