Replenishment of imperfect items in an EOQ inventory model with partial backordering

This paper deals with an inventory model in which a percent of the items in the lot is imperfect. The supplier is far from the buyer. After the reception of the order, immediately the products are inspected and imperfect items are identified. Due to the fact that supplier is located at long distance and the demand is needed to cover, the imperfect items are replenished by perfect ones from a local supplier at higher cost. In addition, the imperfect items are withdrawn and sold at a salvaged price as second-degree items. The shortage is allowed and partially backordered. The following three cases are considered: Case I. The reordered items are received when inventory level is zero; Case II. The reordered items are received when the backordered quantity is equal to the imperfect items quantity; and Case III. The reordered items are received when shortage is still remained. These cases are studied and analyzed in detail. In each case, the aim is to obtain the optimal value of the length period and the percent of period duration in which the inventory level is positive. A numerical example is presented to show the applicability of proposed inventory model. The results show that Case I has the lowest holding and shortage cost, so the total benefit is higher than the other two cases