TY - JOUR T1 - A New EPQ Model for Imperfect Production, Screening, and Rework With Backorders Under Grey Uncertainty AU - Aydemir, Erdal AU - Eroğlu, Abdullah PY - 2024 DA - December Y2 - 2024 DO - 10.17093/alphanumeric.1507650 JF - Alphanumeric Journal JO - Alphanumeric PB - Muhlis ÖZDEMİR WT - DergiPark SN - 2148-2225 SP - 195 EP - 214 VL - 12 IS - 3 LA - en AB - The occurrence of imperfect products that are studied at a specific rate during production holds a significant and comprehensive position in the literature. The fundamental premises underlying the research on the EOQ and EPQ models are as follows: there exists a specific percentage of imperfect production; that the defective rate of production is in line with a certain probability distribution; and that defective products are in themselves defective, repairable (rework), and defective (selling at a low price) etc. The studies of EPQ models that consider the inspection rate and production rate hold significant significance in the literature. This work presents the development of a novel EPQ model to handle the issue of reduced production time to eliminate backorders. The model's functioning is described by including uncertainty modeling, specifically using grey values to represent production rate, costs and prices. KW - Economic production quantity model KW - rework KW - backorders KW - grey system theory CR - Aydemir, E., Bedir, F., & Ozdemir, G. (2015). Degree of Greyness Approach for an EPQ Model with Imperfect Items in Copper Wire Industry. Journal of Grey System, 27(2). CR - Aydemir, E., Bedir, F., Ozdemir, G., & Eroglu, A. (2014). An EPQ model with imperfect items using interval grey numbers. An International Journal of Optimization and Control: Theories & Applications (IJOCTA), 5(1), 21–32. https://doi.org/10.11121/ijocta.01.2015.00204 CR - Björk, K.-M. (2012). The Fuzzy Economic Order Quantity Problem with a Finite Production Rate and Backorders. Applied Computational Intelligence and Soft Computing, 2012, 1–8. https://doi.org/10.1155/2012/876230 CR - 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. https://doi.org/10.1080/09537280310001626179 CR - Chiu, Y.-S., Chiu, S., & Lin, H.-D. (2006). Solving an EPQ Model with Rework and Service Level Constraint. Mathematical and Computational Applications, 11(1), 75–84. https://doi.org/10.3390/mca11010075 CR - Chung, K.-J., & Hou, K.-L. (2003). An optimal production run time with imperfect production processes and allowable shortages. Computers & Operations Research, 30(4), 483–490. https://doi.org/10.1016/s0305-0548(01)00091-0 CR - De, S. K., & Bhattacharya, K. (2022). A Pollution Sensitive Marxian Production Inventory Model with Deterioration Under Fuzzy System. Journal of Optimization Theory and Applications, 192(2), 598–627. https://doi.org/10.1007/s10957-021-01979-9 CR - De Giovanni, P. (2019). An optimal control model with defective products and goodwill damages. Annals of Operations Research, 289(2), 419–430. https://doi.org/10.1007/s10479-019-03176-4 CR - Dharmesh, K., & Kunal, S. (2022). Sustainable Economic Production Quantity (SEPQ) Model for Inventory Having Green Technology Investments - Price Sensitive Demand with Expiration Dates. Economic Computation and Economic Cybernetics Studies and Research, 56(3/2022), 135–152. https://doi.org/10.24818/18423264/56.3.22.09 CR - Dobos, I., & Richter, K. (2003). A Production/Recycling Model With Stationary Demand And Return Rates. Central European Journal of Operations Research, 11, 35–46. CR - Dobos, I., & Richter, K. (2004). An extended production/recycling model with stationary demand and return rates. International Journal of Production Economics, 90(3), 311–323. https://doi.org/10.1016/j.ijpe.2003.09.007 CR - Eroglu, A., & Ozdemir, G. (2007). An economic order quantity model with defective items and shortages. International Journal of Production Economics, 106(2), 544–549. https://doi.org/10.1016/j.ijpe.2006.06.015 CR - Eroğlu, A., & Arslan, P. (2022). New Expansions In The Economic Production Quantity Model Containing Defective Products. International Journal of Engineering and Innovative Research, 4(2), 126–133. https://doi.org/10.47933/ijeir.1133085 CR - Eroğlu, A., Sütçü, A., & Sulak, H. (2008). Rassal Olarak Kusurlu Uretim Yapan Uretim Surec\cleri Iċ\cin Ekonomik Uretim Miktarı Modeli. Gazi Üniversitesi Mühendislik Mimarlık Fakültesi Dergisi, 23(4), 923–929. CR - Eroğlu, R., & Aydemir, E. (2020). Tamir sürecini içeren geri dönüşüm süreci için yeni bir envanter modeli geliştirilmesi. Mühendislik Bilimleri Ve Tasarım Dergisi, 8(4), 1086–1098. https://doi.org/10.21923/jesd.776390 CR - Eroğlu, R., & Aydemir, E. (2021). Geri dönüşüm sürecinde kusurlu yeniden üretim durumu için yeni bir envanter modeli. DEU Muhendislik Fakultesi Fen Ve Muhendislik, 23(68), 381–397. https://doi.org/10.21205/deufmd.2021236804 CR - Gharaei, A., Hoseini Shekarabi, S. A., & Karimi, M. (2021). Optimal lot-sizing of an integrated EPQ model with partial backorders and re-workable products: an outer approximation. International Journal of Systems Science: Operations & Logistics, 10(1). https://doi.org/10.1080/23302674.2021.2015007 CR - Glock, C. H., & Jaber, M. Y. (2013). An economic production quantity (EPQ) model for a customer-dominated supply chain with defective items, reworking and scrap. International Journal of Services and Operations Management, 14(2), 236. https://doi.org/10.1504/ijsom.2013.051831 CR - 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. https://doi.org/10.1080/095372801750397707 CR - Hyun Kim, C., & Hong, Y. (1999). An optimal production run length in deteriorating production processes. International Journal of Production Economics, 58(2), 183–189. https://doi.org/10.1016/s0925-5273(98)00119-4 CR - Karagül, N., & Eroğlu, A. (2022). Production lot sizing with quality screening, rework and shortages backordered. Pamukkale University Journal of Engineering Sciences, 28(4), 604–612. https://doi.org/10.5505/pajes.2021.16689 CR - Karbassi Yazdi, A., Kaviani, M. A., Sarfaraz, A. H., Cárdenas-Barrón, L. E., Wee, H.-M., & Tiwari, S. (2019). A comparative study on economic production quantity (EPQ) model under space constraint with different kinds of data. Grey Systems: Theory and Application, 9(1), 86–100. https://doi.org/10.1108/gs-08-2018-0035 CR - Khalilpourazari, S., Mirzazadeh, A., Weber, G.-W., & Pasandideh, S. H. R. (2019). A robust fuzzy approach for constrained multi-product economic production quantity with imperfect items and rework process. Optimization, 69(1), 63–90. https://doi.org/10.1080/02331934.2019.1630625 CR - Khara, B., Dey, J. K., & Mondal, S. K. (2020). Sustainable recycling in an imperfect production system with acceptance quality level dependent development cost and demand. Computers & Industrial Engineering, 142, 106300. https://doi.org/10.1016/j.cie.2020.106300 CR - Kozlovskaya, N., Pakhomova, N., & Richter, K. (2016). The Optimal Disposal Rate for the Extended EOQ Repair and Waste Disposal Model with Switching Costs. In Nachhaltiges Entscheiden (pp. 549–568). Springer Fachmedien Wiesbaden. https://doi.org/10.1007/978-3-658-12506-6\_29 CR - Liu, S., & Forrest, J. Y.-L. (2010). Grey Systems: Theory and Applications. Springer Verlag. CR - Liu, S., Yang, Y., & Forrest, J. (2017). Grey Data Analysis. Springer Singapore. https://doi.org/10.1007/978-981-10-1841-1 CR - Mezei, J., & Björk, K.-M. (2015). An economic production quantity problem with backorders and fuzzy cycle times. Journal of Intelligent & Fuzzy Systems, 28(4), 1861–1868. https://doi.org/10.3233/ifs-141472 CR - Nahmiasj, S., & Rivera, H. (1979). A deterministic model for a repairable item inventory system with a finite repair rate†. International Journal of Production Research, 17(3), 215–221. https://doi.org/10.1080/00207547908919609 CR - Rezaei, J. (2016). Economic order quantity and sampling inspection plans for imperfect items. Computers & Industrial Engineering, 96, 1–7. https://doi.org/10.1016/j.cie.2016.03.015 CR - Richter, K. (1997). Pure and mixed strategies for the EOQ repair and waste disposal problem. OR Spektrum, 19(2), 123–129. https://doi.org/10.1007/bf01545511 CR - Rosenblatt, M. J., & Lee, H. L. (1986). Economic Production Cycles with Imperfect Production Processes. IIE Transactions, 18(1), 48–55. https://doi.org/10.1080/07408178608975329 CR - Rosmiati, R., Bahari, S., & Laka, A. (2022, ). Production Economic Management Model in Product Design. Proceedings of the International Conference on Applied Science and Technology on Social Science 2021 (Icast-SS 2021). https://doi.org/10.2991/assehr.k.220301.061 CR - Salameh, M., & Jaber, M. (2000). Economic production quantity model for items with imperfect quality. International Journal of Production Economics, 64(1–3), 59–64. https://doi.org/10.1016/s0925-5273(99)00044-4 CR - Sana, S. S. (2010). An economic production lot size model in an imperfect production system. European Journal of Operational Research, 201(1), 158–170. https://doi.org/10.1016/j.ejor.2009.02.027 CR - Sanjai, M., & Periyasamy, S. (2019). An inventory model for imperfect production system with rework and shortages. International Journal of Operational Research, 34(1), 66. https://doi.org/10.1504/ijor.2019.096939 CR - Schrady, D. A. (1967). A deterministic inventory model for reparable items. Naval Research Logistics Quarterly, 14(3), 391–398. https://doi.org/10.1002/nav.3800140310 CR - Shah, N. H., Patel, D. G., & Shah, D. B. (2016). EPQ model for returned/reworked inventories during imperfect production process under price-sensitive stock-dependent demand. Operational Research, 18(2), 343–359. https://doi.org/10.1007/s12351-016-0267-4 CR - Soleymanfar, V. R., Makui, A., Taleizadeh, A. A., & Tavakkoli-Moghaddam, R. (2021). Sustainable EOQ and EPQ models for a two-echelon multi-product supply chain with return policy. Environment, Development and Sustainability, 24(4), 5317–5343. https://doi.org/10.1007/s10668-021-01660-1 CR - Soni, H., & Shah, N. H. (2011). Optimal policy for fuzzy expected value production inventory model with imprecise production preparation-time. International Journal of Machine Learning and Cybernetics, 2(4), 219–224. https://doi.org/10.1007/s13042-011-0020-5 CR - Taleizadeh, A. A., Cárdenas-Barrón, L. E., & 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, 150, 9–27. https://doi.org/10.1016/j.ijpe.2013.11.023 CR - Taleizadeh, A. A., Naghavi-Alhoseiny, M.-S., Cárdenas-Barrón, L. E., & Amjadian, A. (2024). Optimization of price, lot size and backordered level in an EPQ inventory model with rework process. RAIRO - Operations Research, 58(1), 803–819. https://doi.org/10.1051/ro/2023073 CR - Wang, X., & Tang, W. (2009). Fuzzy EPQ inventory models with backorder. Journal of Systems Science and Complexity, 22(2), 313–323. https://doi.org/10.1007/s11424-009-9166-6 CR - Wee, H.-M., Wang, W.-T., & Yang, P.-C. (2013). A production quantity model for imperfect quality items with shortage and screening constraint. International Journal of Production Research, 51(6), 1869–1884. https://doi.org/10.1080/00207543.2012.718453 CR - Widyadana, G. A., & Wee, H. M. (2009). Economic Production Quantity (EPQ) deteriorating inventory model with machine breakdown and stochastic repair time. 2009 IEEE International Conference on Industrial Engineering and Engineering Management, 548–552. https://doi.org/10.1109/ieem.2009.5373279 CR - Wu, M.-f., Chiu, Y.-s. p., & Sung, P.-c. (2014). Optimization of a multi-product EPQ model with scrap and an improved multi-delivery policy. Journal of Engineering Research, 2(4). https://doi.org/10.7603/s40632-014-0027-7 CR - Xie, N.-m., & Liu, S.-f. (2011). A novel grey relational model based on grey number sequences. Grey Systems: Theory and Application, 1(2), 117–128. https://doi.org/10.1108/20439371111163747 CR - Xie, N. (2017). Explanations about grey information and framework of grey system modeling. Grey Systems: Theory and Application, 7(2), 179–193. https://doi.org/10.1108/gs-05-2017-0012 CR - Yang, Y., & Liu, S.-f. (2011). Reliability of operations of grey numbers using kernels. Grey Systems: Theory and Application, 1(1), 57–71. https://doi.org/10.1108/20439371111106731 CR - Çelik Eroğlu, Ş., & Şahin, Y. (2023). Geri Dönüşüm Süreci İçin Yeni Bir Bulanık Envanter Modeli. DEU Muhendislik Fakultesi Fen Ve Muhendislik, 25(73), 21–36. https://doi.org/10.21205/deufmd.2023257303 UR - https://doi.org/10.17093/alphanumeric.1507650 L1 - https://dergipark.org.tr/en/download/article-file/4033505 ER -