Economic order quantity for imperfect quality items under inspection errors, batch replacement and multiple sales of returned items

Document Type : Article

Authors

1 Department of Industrial Engineering, Faculty of Engineering, University of Kashan, Kashan, P.O. Box 8731753153, Iran

2 Department of Management, Faculty of Humanities, University of Kashan, Kashan, Iran

Abstract

In classical inventory control problems, it is usually assumed that all of items are of perfect quality, and the inspection process works perfectly well. However, in practice, the order lots often contain imperfect quality items, and the inspection process, for recognition of these items, is not necessarily error-free. In this article, we extend the economic order quantity model under imperfect quality items where the inspection process involves type I and II errors. The type I error can lead to recognition of perfect quality items as defective, while the type II error can lead to delivery of imperfect quality items to customers even for several consecutive times. We present two cases depending on the length of special inspection process and determine optimal order sizes, analytically, for maximizing total profit per unit time for both cases. A numerical example is provided to compare two cases and a sensitivity analysis is discussed to assess the effect of main parameters on the total profit per unit time.

Keywords

References

REFERENCES
Aggarwal, K. K., & Aneja, S. (2016). An EOQ model with inspection error, rework and sales return. International Journal of Advanced Operations Management, 8(3), 185-199.
Al-Salamah, M. (2011). Economic order quantity with imperfect quality, destructive testing acceptance sampling, and inspection errors. Advances in Management and Applied Economics, 1(2), 59.
Chan, W. M., Ibrahim, R. N., & Lochert, P. B. (2003). A new EPQ model: integrating lower pricing, rework and reject situations. Production Planning & Control, 14(7), 588-595.
Chang, C. T., Cheng, M. C., & Soong, P. Y. (2016). Impacts of inspection errors and trade credits on the economic order quantity model for items with imperfect quality. International Journal of Systems Science: Operations & Logistics, 3(1), 34-48.
Chang, H. C., & Ho, C. H. (2010). Exact closed-form solutions for “optimal inventory model for items with imperfect quality and shortage backordering”. Omega, 38(3-4), 233-237.
Cheng, Y. L., Wang, W. T., Wei, C. C., & Lee, K. L. (2018). An integrated lot-sizing model for imperfect production with multiple disposals of defective items. Scientia Iranica, 25(2), 852-867.
Chiu, S. W., Gong, D. C., & Wee, H. M. (2004). Effects of random defective rate and imperfect rework process on economic production quantity model. Japan Journal of Industrial and Applied Mathematics, 21(3), 375.
Chung, K. J., Her, C. C., & Lin, S. D. (2009). A two-warehouse inventory model with imperfect quality production processes. Computers & Industrial Engineering, 56(1), 193-197.
Farhangi, M., Niaki, S. T. A., & Vishkaei, B. M. (2015). Closed-form equations for optimal lot sizing in deterministic EOQ models with exchangeable imperfect quality items. Scientia Iranica. Transaction E, Industrial Engineering, 22(6), 2621.
Hayek, P. A., & Salameh, M. K. (2001). Production lot sizing with the reworking of imperfect quality items produced. Production planning & control, 12(6), 584-590.
Hsu, J. T., & Hsu, L. F. (2012). A note on ‘‘optimal inventory model for items with imperfect quality and shortage backordering’’. International Journal of Industrial Engineering Computations, 3(5), 939-948.
Hsu, J. T., & Hsu, L. F. (2013). Two EPQ models with imperfect production processes, inspection errors, planned backorders, and sales returns. Computers & Industrial Engineering, 64(1), 389-402.
Hsu, L. F., & Hsu, J. T. (2016). Economic production quantity (EPQ) models under an imperfect production process with shortages backordered. International Journal of Systems Science, 47(4), 852-867.
Jaber, M. Y., Goyal, S. K., & Imran, M. (2008). Economic production quantity model for items with imperfect quality subject to learning effects. International Journal of Production Economics, 115(1), 143-150.
Jaber, M. Y., Zanoni, S., & Zavanella, L. E. (2014). Economic order quantity models for imperfect items with buy and repair options. International Journal of Production Economics, 155, 126-131.
Jaggi, C. K., Cárdenas-Barrón, L. E., Tiwari, S., & Shafi, A. A. (2017). Two-warehouse inventory model for deteriorating items with imperfect quality under the conditions of permissible delay in payments. Scientia Iranica. Transaction E, Industrial Engineering, 24(1), 390.
Jauhari, W. A., Sofiana, A., Kurdhi, N. A., & Laksono, P. W. (2016). An integrated inventory model for supplier-manufacturer-retailer system with imperfect quality and inspection errors. International Journal of Logistics Systems and Management, 24(3), 383-407.
Khan, M., Jaber, M. Y., & Bonney, M. (2011). An economic order quantity (EOQ) for items with imperfect quality and inspection errors. International Journal of Production Economics, 133(1), 113-118.
Khan, M., Jaber, M. Y., Guiffrida, A. L., & Zolfaghari, S. (2011). A review of the extensions of a modified EOQ model for imperfect quality items. International Journal of Production Economics, 132(1), 1-12.
Khanna, A., Kishore, A., & Jaggi, C. K. (2017). Inventory Modeling for Imperfect Production Process with Inspection Errors, Sales Return, and Imperfect Rework Process. International Journal of Mathematical, Engineering and Management Sciences, 2(42), 242-258.
Lin, T. Y., & Chen, M. T. (2011). An economic order quantity model with screening errors, returned cost, and shortages under quantity discounts. African Journal of Business Management, 5(4), 1129-1135.
Mokhtari, H. (2018). A joint internal production and external supplier order lot size optimization under defective manufacturing and rework. The International Journal of Advanced Manufacturing Technology, 95(1-4), 1039-1058.
Mokhtari, H. (2018). Optimal Lot Size in a Manufacturing System with Imperfect Raw Materials and Defective Finished Products. Scientia Iranica, In Press.
Nobil, A. H., Afshar Sedigh, A. H., Tiwari, S., & Wee, H. M. (2018). An imperfect multi-item single machine production system with shortage, rework, and scrapped considering inspection, dissimilar deficiency levels, and non-zero setup times. Scientia Iranica, In Press.
Nobil, A. H., Sedigh, A. H. A., & Cárdenas-Barrón, L. E. (2017). Multi-machine economic production quantity for items with scrapped and rework with shortages and allocation decisions. Scientia Iranica, In Press..
Pal, S., & Mahapatra, G. S. (2017). A manufacturing-oriented supply chain model for imperfect quality with inspection errors, stochastic demand under rework and shortages. Computers & Industrial Engineering, 106, 299-314.
Rezaei, J. (2005). Economic order quantity model with backorder for imperfect quality items. In Engineering Management Conference, 2005. Proceedings. 2005 IEEE International (Vol. 2, pp. 466-470). IEEE.
Rezaei, J., & Davoodi, M. (2008). A deterministic, multi-item inventory model with supplier selection and imperfect quality. Applied Mathematical Modelling, 32(10), 2106-2116.
Salameh, M. K., & Jaber, M. Y. (2000). Economic production quantity model for items with imperfect quality. International journal of production economics, 64(1-3), 59-64.
Sharifi, E., Sobhanallahi, M. A., Mirzazadeh, A., & Shabani, S. (2015). An EOQ model for imperfect quality items with partial backordering under screening errors. Cogent Engineering, 2(1), 994258.
Sofiana, A., & Rosyidi, C. N. (2017, December). Integrated vendor-buyer inventory model considering imperfect quality and inspection errors with controllable lead time. In Industrial Engineering and Engineering Management (IEEM), 2017 IEEE International Conference on (pp. 1321-1325). IEEE.
Taleizadeh, A. A., Sari-Khanbaglo, M. P., & Cárdenas-Barrón, L. E. (2017). Outsourcing rework of imperfect items in the economic production quantity (EPQ) inventory model with backordered demand. IEEE Transactions on Systems, Man, and Cybernetics: Systems, (99), 1-12.
Tsou, J. C., Hejazi, S. R., & Barzoki, M. R. (2012). Economic production quantity model for items with continuous quality characteristic, rework and reject. International Journal of Systems Science, 43(12), 2261-2267.
Vishkaei, B. M., Niaki, S. T. A., Farhangi, M., & Rashti, M. E. M. (2014). Optimal lot sizing in screening processes with returnable defective items. Journal of Industrial Engineering International, 10(3), 70.
Wee, H. M., Yu, J., & Chen, M. C. (2007). Optimal inventory model for items with imperfect quality and shortage backordering. Omega, 35(1), 7-11.
Yassine, A., Maddah, B., & Salameh, M. (2012). Disaggregation and consolidation of imperfect quality shipments in an extended EPQ model. International Journal of Production Economics, 135(1), 345-352.
Yoo, S. H., Kim, D., & Park, M. S. (2009). Economic production quantity model with imperfect-quality items, two-way imperfect inspection and sales return. International Journal of Production Economics, 121(1), 255-265.
Zhou, Y. W., Chen, J., Wu, Y., & Zhou, W. (2015). EPQ models for items with imperfect quality and one-time-only discount. Applied Mathematical Modelling, 39(3-4), 1000-1018.
Scientia Iranica
Volume 28, Issue 5
Transactions on Industrial Engineering (E)
September and October 2021
Pages 2890-2909

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