No Access

An EPQ Model for Deteriorating Items With Imperfect Production, Two Types of Inspection Errors and Rework Under Complete Backordering

Chayanika Rout

Department of Mathematics, Indian Institute of Technology Kharagpur, Kharagpur, India

E-mail Address: fantu.rout@gmail.com

Corresponding author.

Search for more papers by this author

Debjani Chakraborty

Department of Mathematics, Indian Institute of Technology Kharagpur, Kharagpur, India

E-mail Address: debjani@maths.iitkgp.ernet.in

Search for more papers by this author

, and

Adrijit Goswami

Department of Mathematics, Indian Institute of Technology Kharagpur, Kharagpur, India

E-mail Address: goswami@maths.iitkgp.ernet.in

Search for more papers by this author

https://doi.org/10.1142/S0219198920400113Cited by:11 (Source: Crossref)

This article is part of the issue:

Special Issue on Operations Research and Game Theory: Modeling and Computation
Guest Editors: S. K. Neogy, R. B. Bapat, D. Dubey and T. Parthasarathy

Abstract

This paper presents an EPQ model which illustrates imperfect production and imperfect inspection processes for items that are subject to a constant rate of deterioration. The model considers two types of inspection errors, namely, Type I error of falsely screening out a proportion of nondefects, thereby passing them on for rework and Type II error of falsely not screening out a proportion of defects, thus selling those to customers which results in defect sales returns. The screened and returned items are then reworked and the proportion that could not be reworked successfully is scrapped. Shortages are allowed and are completely backlogged. Finally, we calculate the optimal production lot size and the optimal backordering quantity in order to minimize the total inventory cost per unit time. A numerical example is also considered to exemplify the obtained theoretical results which is followed by the complete sensitivity analysis of the involved parameters for even better managerial insights.

Keywords:

References

Al-Salamah, M. [2016] Economic production quantity in batch manufacturing with imperfect quality, imperfect inspection, and destructive and non-destructive acceptance sampling in a two-tier market, Comput. Ind. Eng. 93, 275–285. Web of Science, Google Scholar
Chiu, Y.-P. [2003] Determining the optimal lot size for the finite production model with random defective rate, the rework process, and backlogging, Eng. Opt. 35(4), 427–437. Web of Science, Google Scholar
Chung, K.-J., Her, C.-C. and Lin, S.-D. [2009] A two-warehouse inventory model with imperfect quality production processes, Comput. Ind. Eng. 56(1), 193–197. Web of Science, Google Scholar
Cárdenas-Barrón, L.-E. [2009] Economic production quantity with rework process at a single-stage manufacturing system with planned backorders, Comput. Ind. Eng. 57(3), 1105–1113. Web of Science, Google Scholar
Flapper, S.-D.-P. and Teunter, R.-H. [2004] Logistic planning of rework with deteriorating work-in-process, Int. J. Prod. Econ. 88(1), 51–59. Web of Science, Google Scholar
Ghare, P.-M. and Schrader, G.-F. [1963] A model for exponentially decaying inventory, J. Ind. Eng. 14(5), 238–243. Google Scholar
Ghosh, S.-K., Khanra, S. and Chaudhuri, K.-S. [2011] Optimal price and lot size determination for a perishable product under conditions of finite production, partial backordering and lost sale, Appl. Math. Comput. 217(12), 6047–6053. Web of Science, Google Scholar
Glock, C.-H. and Jaber, M.-Y. [2013] A multi-stage production-inventory model with learning and forgetting effects, rework and scrap, Comput. Ind. Eng. 64(2), 708–720. Web of Science, Google Scholar
Hayek, P.-A. and Salameh, M.-K. [2001] Production lot sizing with the reworking of imperfect quality items produced, Prod. Plan. Control 12(6), 584–590. Web of Science, Google Scholar
Hsu, J.-T. and Hsu, L.-F. [2013] Two EPQ models with imperfect production processes, inspection errors, planned backorders, and sales returns, Comput. Ind. Eng. 64(1), 389–402. Web of Science, Google Scholar
Jamal, A.-M.-M., Sarker, B.-R. and Mondal, S. [2004] Optimal manufacturing batch size with rework process at a single-stage production system, Comput. Ind. Eng. 47(1), 77–89. Web of Science, Google Scholar
Krishnamoorthi, C. and Panayappan, S. [2012] An EPQ model with imperfect production systems with rework of regular production and sales return, Am. J. Oper. Res. 2(2), 225. Google Scholar
Krishnamoorthi, C. and Panayappan, S. [2013] An EPQ model for an imperfect production system with rework and shortages, Int. J. Oper. Res. 17(1), 104–124. Google Scholar
Lee, H.-L. and Rosenblatt, M.-J. [1989] A production and maintenance planning model with restoration cost dependent on detection delay, IIE Trans. 21(4), 368–375. Web of Science, Google Scholar
Manna, A.-K., Dey, J.-K. and Mondal, S.-K. [2017] Imperfect production inventory model with production rate dependent defective rate and advertisement dependent demand, Comput. Ind. Eng. 104, 9–22. Web of Science, Google Scholar
Pal, S. and Mahapatra, G.-S. [2017] A manufacturing-oriented supply chain model for imperfect quality with inspection errors, stochastic demand under rework and shortages, Comput. Ind. Eng. 106, 299–314. Web of Science, Google Scholar
Porteus, E.-L. [1986] Optimal lot sizing, process quality improvement and setup cost reduction, Oper. Res. 34(1), 137–144. Web of Science, Google Scholar
Taft, E.-W. [1918] The most economical production lot, Iron Age 101(18), 1410–1412. Google Scholar
Tai, A.-H. [2013] Economic production quantity models for deteriorating/imperfect products and service with rework, Comput. Ind. Eng. 66(4), 879–888. Web of Science, Google Scholar
Wee, H.-M. [1993] Economic production lot size model for deteriorating items with partial back-ordering, Comput. Ind. Eng. 24(3), 449–458. Web of Science, Google Scholar
Widyadana, G.-A. and Wee, H.-M. [2012] An economic production quantity model for deteriorating items with multiple production setups and rework, Int. J. Prod. Econ. 138(1), 62–67. Web of Science, Google Scholar
Yoo, S.-H., Kim, D.-S. and Park, M.-S. [2009] Economic production quantity model with imperfect-quality items, two-way imperfect inspection and sales return, Int. J. Prod. Econ. 121(1), 255–265. Web of Science, Google Scholar