Economic production quantity (EPQ) models under an imperfect production process with shortages backordered

Abstract

In this paper, we develop economic production quantity (EPQ) models to determine the optimal production lot size and backorder quantity for a manufacturer under an imperfect production process. The imperfect production process is characterised by the fraction of defective items at the time of production γ. The paper considers different cases of the EPQ model depending on (1) whether γ is known with certainty or is a random variable, and (2) whether imperfect items are drawn from inventory (a) as they are detected, (b) at the end of each production period or (c) at the end of each production cycle. Straightforward convexity results are shown and closed-form solutions are provided for the optimal order and backorder quantities for each of the cases we considered. We provide two numerical examples: one in which the defective probability follows a uniform distribution and the second which we assume follows a beta distribution, to illustrate the effects of yield variability and timing of the withdrawal of defectives on the optimal solutions. We obtain similar results for both numerical examples, which show that both the yield variability and the withdrawal timing are not critical factors.

Keywords:

• EPQ
• imperfect quality
• inventory backorder

Acknowledgements

The authors would like to thank an associate editor and the anonymous reviewers for their valuable suggestions to the earlier versions of this manuscript.

Additional information

Notes on contributors

Lie-Fern Hsu

Lie-Fern Hsu is an associate professor in the Department of Management, Zicklin School of Business, Baruch College, The City University of New York. She received a BS in management science from National Chiao-Tung University (Taiwan), an MBA from Washington State University and a PhD in operations research from Case Western Reserve University. She has had publications in Computers & Industrial Engineering, Computers and Operations Research, European Journal of Operational Research, IEEE Transactions on Reliability, International Journal of Advanced Manufacturing Technology, International Journal of Industrial Engineering Computations, International Journal of Production Economics, International Journal of Production Research, Journal of Information and Optimization Sciences, Naval Research Logistics, Production Planning and Control, Quality and Reliability Engineering International, Queueing Systems: Theory and Applications, RAIRO - Operations Research, Reliability Engineering and System Safety and The International Journal of Flexible Manufacturing Systems.

Jia-Tzer Hsu

Jia-Tzer Hsu is an associate professor in the Department of Computer Science and Information Engineering, Hungkuang University, Taichung, Taiwan. He received a BS in electrical engineering from National Cheng-Kung University (Taiwan) and an MS in electrical engineering, an MS in engineering mechanics, and a PhD in computer and electrical engineering from the University of Florida. He has had publications in Computers & Industrial Engineering, IEEE Transactions on Circuits and Systems, IEEE Transactions on Power Electronics, IEEE Transactions on Aerospace and Electronic Systems, International Journal of Advanced Manufacturing Technology, International Journal of Industrial Engineering Computations, International Journal of Kansei Information and International Journal of Production Economics. His current research interests are in the field of operations research, numerical analysis and finite-element modelling for magnetic devices.