An Integrated Vendor-Buyer Cooperative Inventory Model for Items with Imperfect Quality and Shortage Backordering

We develop a model to determine an integrated vendor-buyer inventory policy for items with imperfect quality and planned backorders. 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 backordered. 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. 1. Introduction Supply chain management focuses on the material and information flows between facilities and their final customers and has been considered the most popular operations strategy for improving organizational competitiveness nowadays. Cao and Zhang [1] showed that firms have been attempting to achieve greater collaborative advantages with their supply chain partners in the past few decades, and that supply chain collaborative advantages have a bottom-line influence on firm performance. This means that the vendor and the buyer should work together in a cooperative manner towards maximizing their mutual benefits. Integrated inventory management has recently received a great deal of attention. Goyal [2] considered the joint optimization problem of a single vendor and a single buyer, in which he assumed that the vendor's production rate is infinite. Banerjee [3] assumed finite rate of production and developed a joint economic-lot-size (JELS) model for the product with a lot-for-lot shipment policy. He demonstrated the advantage of the JELS approach through an analysis of the cost trade-offs (in conjunction with an appropriate price adjustment) from the perspective of each party's optimal position. It was shown that a jointly optimal ordering policy, together with an appropriate price adjustment, could be beneficial economically for both the vendor and the buyer, or at the very least, did not place either at a disadvantage. Goyal and Szendrovits [4] considered a policy that combines a number of increasing shipment sizes which are then followed by a number of equally sized shipments. By relaxing the Banerjee [3] lot-for-lot