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Modelling and Simulation in Engineering
Volume 2013, Article ID 727685, 6 pages
Research Article

An EPQ Model with Unit Production Cost and Set-Up Cost as Functions of Production Rate

Faculty of Industrial and Mechanical Engineering, Islamic Azad University, Qazvin Branch, P.O. Box 34185-1416, Qazvin 34185-14161, Iran

Received 8 May 2013; Accepted 14 August 2013

Academic Editor: Hing Kai Chan

Copyright © 2013 Behrouz Afshar-Nadjafi. 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.


Extensive research has been devoted to economic production quantity (EPQ) problem. However, no attention has been paid to problems where unit production and set-up costs must be considered as functions of production rate. In this paper, we address the problem of determining the optimal production quantity and rate of production in which unit production and set-up costs are assumed to be continuous functions of production rate. Based on the traditional economic production quantity (EPQ) formula, the cost function associated with this model is proved to be nonconvex and a procedure is proposed to solve this problem. Finally, utility of the model is presented using some numerical examples and the results are analyzed.