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Mathematical Problems in Engineering
Volume 2006, Article ID 98502, 13 pages

The effect of service level constraint on EPQ model with random defective rate

Department of Industrial Engineering and Management, Chaoyang University of Technology, 168 Gi-Feng East Road, Wu-Feng, Taichung 413, Taiwan

Received 16 September 2004; Revised 20 February 2005; Accepted 3 April 2005

Copyright © 2006 Yuan-Shyi Peter Chiu. 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 study the effect of service level constraint on the economic production quantity (EPQ) model with random defective rate. We first prove that the expected overall cost for imperfect quality EPQ model with backlogging permitted is less than or equal to that of the same model without backlogging. Secondly, the relationship between “imputed backorder cost” and maximal shortage level is derived for decision-making on whether the required service level is achievable. Then an equation is proposed for calculating the intangible backorder cost for the situation when the required service level is not attainable. By including this intangible backorder cost in the mathematical analysis, one can derive a new optimal lot-size policy that minimizes expected total costs as well as satisfies the service level constraint. Numerical example is provided to demonstrate its practical usage.