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Mathematical Problems in Engineering
Volume 2016, Article ID 5382329, 10 pages
Research Article

Optimal Buyer’s Replenishment Policy in the Integrated Inventory Model for Imperfect Items

1Hechi University, Hechi 546300, China
2Guangxi University, Nanning 530004, China

Received 31 December 2015; Revised 14 June 2016; Accepted 9 August 2016

Academic Editor: Paolo Crippa

Copyright © 2016 Lu Yueli et al. 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.


In the classical economic order quantity (EOQ) models, a common unrealistic assumption is that all the items received are of good quality. However, in realistic environment, a received shipment usually contains a fraction of imperfect quality items. These imperfect items may be scrapped, reworked at a cost, or salvaged at a discounted price. While the percentage of imperfect items is random, the optimal ordering cycle is rarely considered in current literatures. This paper revisits the model (Maddah and Jaber, 2008) and extends it by assuming that the ordering cycle is determined by the demand rate, delivery quantity per shipment, and the mathematical expectation of the defective rate. The possibility of stockout or residue in the end of a cycle will be considered, and the loss of stockout and the salvage of the residue are counted into the cost. Besides, we consider consolidating the shipments of imperfect items over multiple deliveries. Thus, an integrated vendor-buyer inventory model for imperfect quality items with equal-size shipment policy is established to derive the optimal ordering cycle, ordering quantity, and number of deliveries. The computational method of the optimal delivery quantity per shipment and number of deliveries is given through theoretical results. Finally, sensitivity of main parameters is analyzed through simulation experiments and shown by some figures.