A multi-product Inventory control model with Imperfect Production Process and Rework under Delayed Payment Policy

Document Type : Research Paper


1 School of Industrial Engineering, College of Engineering, University of Tehran, Iran

2 School of Industrial Engineering, College of Engineering, Islamic Azad University, South Tehran Branch, Iran


The traditional economic production quantity (EPQ) model assumes that during the production process no imperfect item is produced. But in the real production system, due to imperfect production process or other factors, imperfect quality items may be produced. Furthermore, it is well-known that the total production-inventory costs can be reduced by reworking the imperfect quality items produced with a smaller additional reworking and holding costs. In addition, the permissible delay in payments offered by the supplier is widely adopted in the businesses. In this study, we explore the effects of both reworking imperfect quality items and trade credit policy on the EPQ model with imperfect production processes and backlogging. A mathematical model considering reworking and shortage costs, interest earned and interest charged in addition to traditional inventory costs is developed. Besides an arithmetic-geometric mean inequality method is employed and an algorithm is developed to find the optimal production policy. Furthermore, some numerical examples and sensitivity analysis are provided to demonstrate the applicability of proposed model.


Main Subjects

1- Harris, F. (1915). “Operations and cost (factory management series)”, Chicago: A. W. Show Co.
2- Hadley, G. and Whiten, T. M. (1963). “Analysis of inventory systems”, Clifs, NJ: Prentice- Hall.
3- Darwish, M. A. (2008). “EPQ models with varying setup cost.” International Journal of Production Economics, Vol. 113, No. 1, PP. 297–306.
4- Porteus, E.L. (1986). “Optimal lot sizing, process quality improvement and setup cost reduction.” Operations Research, Vol. 34, No. 5, PP. 137–44.
5- Grubbstrom, R.W. and Wang, Z. (2003). “A stochastic model of multi-level/multi-stage capacity constrained production–inventory systems.” International Journal of Production Economics, Vol.81, No. 1, PP. 483–494.
6- Rosenblatt, M.J. and Lee, H.L. (1986). “Economic production cycles with imperfect production processes.” IIE Transactions, Vol. 18, No, 1, PP. 48–55.
7- Taleizadeh, A.A., Najafi, A.A. and Niaki, S.T.A. (2010a). “Economic production quantity model with scraped items and limited production capacity.” Scientia Iranica, Vol. 17, No. 1, PP. 58–69.
8- Chan, W.M., Ibrahim, R.N. and Lochert, P.B. (2003). “A new EPQ model: Integrating lower pricing, rework and reject situation.s” Production Planning and Control, Vol. 14, No. 7, PP. 588–595.
9- Salameh, M.K. and Jaber M.Y. (2000). “Economic order quantity model for items with imperfect quality.” International Journal of Production Economics, Vol. No. 1-3, PP. 59–64.
10- Taleizadeh, A.A., Cárdenas-Barrón, L.E. and Mohammadi, B., (2014). “A deterministic multi product single machine EPQ model with backordering, scraped products, rework and interruption in manufacturing process.” International Journal of Production Economics. Vol. 3, No. 2, PP. 9–27.
11- Sarkar, B., Cárdenas-Barrón., L.E, Sarkar., M. and Singgih., M.L. (2014). An economic production quantity model with random defective rate, rework process and backorders for a single stage production system. Journal of Manufacturing Systems, Vol. 33, No. 3, PP. 423-435.
12- Haley C.W. and Higgins, R.C. (1973). “Inventory policy and trade credit financing.” Management Science, Vol. 20, No. 4, PP. 464–471.
13- Chapman, C.B., Ward, S.C., Cooper, D.F., and Page, M. J. (1984). “Credit policy and inventory control.” Journal of the Operational Research Society, Vol. 35, No. 12, PP. 1055–1065.
14- Abada, P.L. and Jaggi, C.K. (2003). “A joint approach for setting unit price and the length of the credit period for a seller when end demand is price sensitive.” International Journal of Production Economics, Vol. 83, No. 2, PP. 115–122.
15- Chung K. and Huang, Y. (2003). “The optimal cycle time for EPQ inventory model under permissible delay in payments.” International Journal of Production Economics, Vol. 84, No. 3, PP. 307–318.
16- Chung K. and Huang, Y. (2006). “Retailer's optimal cycle times in the EOQ model with imperfect quality and a permissible credit period.” Quality and Quantity, Vol. 40, No. 1, PP. 59–77.
17- Khouja, M. and Mehrez, A. (1996). “Optimal inventory policy under different supplier credit policies.” Journal of Manufacturing Systems, Vol. 15, No. 5, PP. 334-339.