Advances in Decision Sciences
Volume 2012 (2012), Article ID 679083, 19 pages
Research Article

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

1Department of Computer Science and Information Engineering, Hungkuang University, Shalu, Taichung 43302, Taiwan
2Department of Management, Zicklin School of Business, Baruch College, The City University of New York, One Bernard Baruch Way, P.O. Box B9-240, New York, NY 10010, USA

Received 15 April 2012; Revised 9 July 2012; Accepted 27 July 2012

Academic Editor: Henry Schellhorn

Copyright © 2012 Jia-Tzer Hsu and Lie-Fern Hsu. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


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.