Design of Fuzzy Economic Order Quantity (EOQ) Model in the Presence of Inspection Errors in Single Sampling Plans

  • Julia T. Thomas Department of Mathematics, National Institute of Technology, Calicut, India
  • Mahesh Kumar Department of Mathematics, National Institute of Technology, Calicut, India
Keywords: EOQ, imperfect quality, acceptance sampling plan, inspection errors, backorders

Abstract

Inventory management is the core of the supply chain management system, in which the economic order quantity (EOQ) model is a fundamental inventory model. This paper develops a fuzzy EOQ model in the presence of inspection errors in single sampling plans. The model assumes probability of mis-classifications. An inventory system is hypothesized where the orders undergo acceptance sampling, back-orders are eliminated, and defectives are set aside from the inventory. Due to the presence of vagueness in real time data, the rate at which an order turn to be scrap, the costs of holding, and the back-orders are characterized by fuzzy random variables. Since total profit involved is a random variable, maximum total expected profit is obtained. Some numerical examples are presented, and a sensitivity analysis study is carried out to check the validity of the model developed.

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Author Biographies

Julia T. Thomas, Department of Mathematics, National Institute of Technology, Calicut, India

Julia T. Thomas is a Research Scholar in the Department of Mathematics at National Institute of Technology, Calicut, Kerala. Her research deals with Reliability Theory, Acceptance Sampling Plans and Supply Chain Management.

Mahesh Kumar, Department of Mathematics, National Institute of Technology, Calicut, India

Mahesh Kumar received his Ph.D. degree in applied statistics from Indian Institute of Technology (IIT) Bombay in the year 2006. His current research includes stress-strength reliability, statistical reliability, applied probability, acceptance sampling plans, and fuzzy reliability estimation, stochastic programming, and estimation problems in epidemic models. He is presently a faculty in the Department of Mathematics, NIT Calicut, India.

References

M. Al-Salamah. Economic order quantity with imperfect quality, destructive testing acceptance sampling, and inspection errors. Advances in Management and Applied Economics, 1(2):59, 2011.

H. M. Beheshti. A decision support system for improving performance of inventory management in a supply chain network. International Journal of Productivity and Performance Management, 2010.

S.K. Bhuiya and D. Chakraborty. A fuzzy random EPQ model with fuzzy defective rates and fuzzy inspection errors. Journal of Intelligent & Fuzzy Systems, 30(6):3527–3541, 2016.

D. Bose and A. Guha. Economic production lot sizing under imperfect quality, on-line inspection, and inspection errors: Full vs. sampling inspection. Computers & Industrial Engineering, 160:107565, 2021.

B. Bouslah, A. Gharbi. Integrated production, sampling quality control and maintenance of deteriorating production systems with AOQL constraint. Omega, 61:110–126, 2016.

H. Chang. An application of fuzzy sets theory to the EOQ model with imperfect quality items. Computers & Operations Research, 31(12):2079–2092, 2004.

Chaube, Shshank and Singh, SB and Pant, Sangeeta and Kumar, Anuj. Time-dependent conflicting bifuzzy set and its applications in reliability evaluation. Advanced Mathematical Techniques in Engineering Sciences, 111–128, 2018.

DJordjević, Lena and Antić, Slobodan and Čangalović, Mirjana and Lisec, Andrej. A metaheuristic approach to solving a multiproduct EOQ-based inventory problem with storage space constraints. Optimization Letters, 11(6):1137–1154, 2017.

A. Eroglu, G. Ozdemir. An economic order quantity model with defective items and shortages. International Journal of Production Economics, 106(2):544–549, 2007.

K.V Geetha and M. Prabha. Effective inventory management using postponement strategy with fuzzy cost. Journal of Management Analytics pages 1–29, 2021.

M. D. Hanna and J. M. Jobe. Including quality costs in the lot-sizing decision. International Journal of Quality & Reliability Management.

C. M. Hwang, and M. S. Yang. On fuzzy renewal processes for fuzzy random variables and extended theorems. International Journal of Intelligent Systems, 26(2):115–128, 2011.

M. Khan, M.Y. Jaber and M. Bonney An economic order quantity (EOQ) for items with imperfect quality and inspection errors. International Journal of Production Economics 133(1):113–118, 2011.

M. Khouja and A. Mehrez. Economic production lot size model with variable production rate and imperfect quality. Journal of the Operational Research Society, 1994.

D. P. Koumanakos. The effect of inventory management on firm performance. International Journal of Productivity and Performance Management, 2008.

Kumar, Anuj and Pant, Sangeeta and Ram, Mangey and Yadav, Om. 2022. Meta-heuristic Optimization Techniques: Applications in Engineering. Walter de Gruyter GmbH & Co KG.

Kumar, Amit and Ram, Mangey and Pant, Sangeeta and Kumar, Anuj. 2018 Industrial system performance under multistate failures with standby mode. In Modeling and Simulation in Industrial Engineering, pp. 85–100.

G. Liao. Optimal economic production quantity policy for randomly failing process with minimal repair, backorder and preventive maintenance. International Journal of Systems Science, 44(9): 1602–1612, 2013.

B. Liu, Y. Liu. Expected value of fuzzy variable and fuzzy expected value models. IEEE Transactions on Fuzzy Systems, 10(4): 445–450, 2002.

Pant, Sangeeta and Kumar, Anuj and Ram, Mangey. Solution of nonlinear systems of equations via metaheuristics. International Journal of Mathematical, Engineering and Management Sciences, 4(5): 1108–1126, 2019.

R Core Team (2021). R: A language and environment for statistical computing. R Foundation for Statistical Computing, Vienna, Austria. URL https://www.R-project.org/.

M. J. Rosenblatt and H.L. Lee. Economic production cycles with imperfect production processes. IIE Transactions, 10(4):445–450, 2002.

M. K. Salameh and M. Y. Jaber. Economic production quantity model for items with imperfect quality. International Journal of Production Economics, 64(1-3):59–64, 2000.

X. Wang, W. Tang, Y. Sai and K. Zhang. Fuzzy random EOQ model with defective items and shortages. 2008 IEEE International Conference on Networking, Sensing and Control, 107–110, IEEE, 2008.

M. Yavuz. Fuzzy inventory management. Production Engineering and Management under Fuzziness, pages 25–38, Springer, 2010.

Published
2022-04-16
Section
Articles