Economic Production Quantity in Reworkable Production Systems with Inspection Errors, Scraps and Backlogging

Document Type : Research Paper


1 Young researchers club, Islamic Azad University, Tehran, Iran

2 Department of Industrial Engineering, Sharif University of Technology, Tehran, Iran

3 RambarzinBorj Construction Company, Tehran, Iran


The classical economic production quantity (EPQ) model is a well-known and commonly used inventory control technique. Common assumptions in this model are that all units produced are of perfect quality and shortage is not allowed, since in practice shortage, non-conforming product or scrap items are possible, these assumptions will underestimate the actual required quantity. The objective of this paper is to provide a framework to integrate production of imperfect quality items, inspection errors, rework, scrap items and backlogging into a single EPQ model. To achieve this objective a suitable mathematical model is developed and the optimal production lot size which minimizes the total cost is derived. The sensitivity analysis results indicate the model is very sensitive to shortage cost per unit shortage and type-I error of inspection. While findings of this study show that the model is very sensitive to parameters type-I error of inspection, proportion of defectives in production process and shortage cost per unit short, it is much less sensitive to parameters like proportion of scraps in rework process and Type-II error of inspection. If the existence of such error and shortages are ignored, then the obtained results may differ considerably from the optimal outcome. This will impose additional costs to the system.


Main Subjects

[1] Bedworth D.D., Bailey J.E. (1987), Integrated Production Control Systems; 2nd Ed. John Wiley &
Sons; New York.
[2] Goyal S.K., Cardenas-Barron L.E. (2002), Note on: economic production quantity model for items
with imperfect quality – a practical approach; International Journal of Production Economics 77; 85–
[3] Haji A., Shadrokh S.S., Shamsi R. (2010), The effect of inspection errors on the optimal batch size in
reworkable production systems with scraps; Int. J. Product Development 10(1/2/3); 201–216.
[4] Jamal A.M.M., Sarker B.R., Mondel S. (2004), Optimal manufacturing batch size with network
process at a single-stage production system; Computers and Industrial Engineering 47; 77-89.
[5] Markland R.E., Vickery S.K., Davis R.A. (1998), Operation Management; 2nd Ed., Ohio; Southwestern.
[6] Nahmias S. (2001); Production and operations analysis; 4th Ed., McGraw-Hill Irwin Inc.
[7] Rardin R.L. (1997), Optimization in Operations Research; Prentice-Hall Inc.
[8] Rosenblatt M.J., Lee H.L. (1986), Economic production cycles with imperfect production processes;
IIE Transactions 18; 48–55.
[9] Salameh M.K., Jaber M.Y. (2000), Economic production quantity model for items with imperfect
quality; International Journal of Production Economics 64; 59–64.
[10] Zipkin P. H. (2000), Foundations of inventory management; McGraw-Hill Inc.
[11] Zhang X., Gerchak Y. (1990), Joint lot sizing and inspection policy in and EOQ model with random
yield; IIE Transactions 22; 41-47.
Volume 3, Issue 3 - Serial Number 3
November 2009
Pages 170-188
  • Receive Date: 05 May 2008
  • Revise Date: 13 September 2008
  • Accept Date: 19 February 2009
  • First Publish Date: 01 November 2009