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Journal of Optimization
Volume 2014, Article ID 767943, 14 pages
Research Article

Ordering Cost Reduction in Inventory Model with Defective Items and Backorder Price Discount

1Department of Mathematics, Government Arts College, Udumalpet, Tamil Nadu 642 126, India
2Department of Mathematics, Gandhigram Rural University, Gandhigram, Tamil Nadu 624302, India

Received 31 May 2014; Accepted 21 October 2014; Published 12 November 2014

Academic Editor: Eric S. Fraga

Copyright © 2014 Karuppuchamy Annadurai and Ramasamy Uthayakumar. 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 real market, as unsatisfied demands occur, the longer the length of lead time is, the smaller the proportion of backorder would be. In order to make up for the inconvenience and even the losses of royal and patient customers, the supplier may offer a backorder price discount to secure orders during the shortage period. Also, ordering policies determined by conventional inventory models may be inappropriate for the situation in which an arrival lot contains some defective items. To compensate for the inconvenience of backordering and to secure orders, the supplier may offer a price discount on the stockout item. The purpose of this study is to explore a coordinated inventory model including defective arrivals by allowing the backorder price discount and ordering cost as decision variables. There are two inventory models proposed in this paper, one with normally distributed demand and another with distribution free demand. A computer code using the software Matlab 7.0 is developed to find the optimal solution and present numerical examples to illustrate the models. The results in the numerical examples indicate that the savings of the total cost are realized through ordering cost reduction and backorder price discount.