We develop a model to determine an integrated vendor-buyer inventory policy for items with imperfect quality and planned back orders. The production process is imperfect and produces a certain number of defective items with a known probability density function. The vendor delivers the items to the buyer in small lots of equally sized shipments. Upon receipt of the items, the buyer will conduct a 100% inspection. Since each lot contains a variable number of defective items, shortages may occur at the buyer. We assume that shortages are permitted and are completely back ordered. The objective is to minimize the total joint annual costs incurred by the vendor and the buyer. The expected total annual integrated cost is derived and a solution procedure is provided to ﬁnd the optimal solution. Numerical examples show that the integrated model gives an impressive cost reduction in comparison to an independent decision by the buyer.
Hsu, Jia-Tzer and Hsu, Lie-Fern, "An Integrated Vendor-Buyer Cooperative Inventory Model for Items with Imperfect Quality and Shortage Backordering" (2012). CUNY Academic Works.