Economic order quantity models for imperfect items with buy and repair options

One of the celebrated extensions of the economic order/production quantity (EOQ/EPQ) model is one that assumes a received shipment contains a fraction of imperfect (non-conforming) quality items, where these items, detected by 100% screening, are sold as a single batch at a discounted price. This paper revisits this model (Salameh and Jaber, 2000, Int. J. Prod. Econ. 64 (1), 59-64) and extends it by assuming that a shipment is coming from a distant supplier and, therefore, it is not feasible to replace the imperfect items with an additional order to the same supplier. To address this restriction, two models are presented. The first assumes that imperfect items are sent to a repair shop who charges a cost plus a markup margin, while the second model assumes that imperfect items are replaced by good ones from a local supplier at a higher cost. The inventory environment assumed in this paper is relevant in todays globalised supply chains, thus practical implications of the problem faced are discussed. Numerical results are also presented and discussed. The results show that there exists a threshold value of the unit purchase cost of an emergency-ordered item and a fraction of defectives to which it is decided to either buy or repair.