Optimal Lot Size in a Manufacturing System with Imperfect Raw Materials and Defective Finished Products

Document Type : Article

Author

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

Abstract

In real-world manufacturing systems, encountering with imperfect raw materials and generation of defective finished products are inevitable. In order to cope with these practical problems, this paper studies a manufacturer which orders raw materials from external source (supplier), and then produces a finished product. The raw materials contain imperfect quality items and, in addition, the production process is defective. The imperfect raw materials are sold after screening process, while the defective finished products go under a further rework process. It is also assumed that defective rate of machine is a random variable, resulting three possible cases regarding occurrence of backordering shortage. The aim is to determine economic order/production lot sizes for each case in such a way that the total cost of system is minimized. The optimal closed form solution is derived for each case separately. Moreover the applicability of the proposed manufacturing model is illustrated via a numerical example.

Keywords

Main Subjects


1.Porteus, E. Optimal lot sizing, process quality improvement and setup cost reduction", Oper. Res., 34(1), pp. 137-144 (1986). 2. Rosenblatt, M.J. and Lee, H.L. Economic production cycles with imperfect production processes", IIE Trans., 18(1), pp. 48-55 (1986). 3. Salameh, M.K. and Jaber, M.Y. Economic production quantity model for items with imperfect quality", Int. J. Prod. Econ., 64(1-3), pp. 59-64 (2000). 4. C_ardenas-Barr_on, L. Observation on: economic production quantity model for items with imperfect quality", Int. J. Prod. Econ., 67(2), p. 201 (2000). 5. Maddah, B. and Jaber, M.Y. Economic order quantity for items with imperfect quality: revisited", Int. J. Prod. Econ., 112(2), pp. 808-815 (2008). 6. Rezaei, J. Economic order quantity model with backorder for imperfect items", In Proceedings of IEEE international Engineering Management Conference,, 11-13 September. St. John's, Newfoundland, Canada, pp. 466-470 (2005). 7. Yu, J.C.P., Wee, H.M., and Chen, J.M. Optimal ordering policy for a deteriorating item with imperfect quality and partial backordering", J. Chin. Inst. Ind. Eng., 22(6), pp. 509-520 (2005). 8. Wee, H.M., Yu, J.C.P., andWang, K.J. An integrated production-inventory model for deteriorating items with imperfect quality and shortage backordering considerations", Lect. Notes Comput. Sci. LNCS 3982, pp. 885-897 (2006). 9. Papachristos, S. and Konstantaras, I. Economic ordering quantity models for items with imperfect quality", Int. J. Prod. Econ., 100(1), pp. 148-154 (2006). 10. Wee, H.M., Yu, J., and Chen, M.C. Optimal inventory model for items with imperfect quality and shortage backordering", Omega, 35(1), pp. 7-11 (2007). 11. Khan, M., Jaber, M.Y., Gui_rida, A.L., and Zolfaghari, S. A review of the extensions of a modi_ed EOQ model for imperfect quality items", Int. J. Prod. Econ., 132(1), pp. 1-12 (2011). 12. Wahab, M.I.M., Mamun, S.M.H., and Ongkunaruk, P. EOQ models for a coordinated two-level international supply chain", Int. J. Prod. Econ., 134(1), pp. 151-158 (2011). 13. Konstantaras, I., Skouri, K., and Jaber, M.Y. Inventory models for imperfect quality items with shortages and learning in inspection", Appl. Math. Model., 36(11), pp. 5334-5343 (2012). 14. Liu, J. and Zheng, H. Fuzzy economic order quantity model with imperfect items, shortages and inspection errors", Syst. Eng. Procedia, 4(1), pp. 282-289 (2012). 15. Hsu, J.T. and Hsu, L.F. An EOQ model with imperfect quality items, inspection errors, shortage backordering, and sales returns", Int. J. Prod. Econ., 143(1), pp. 162-170 (2013). 16. Rad, M.A., Khoshalhan, F., and Glock, C.H. Optimizing inventory and sales decisions in a two-stage supply chain with imperfect", Comput. Ind. Eng., 74(1), pp. 219-227 (2014). 17. Skouri, K., Konstantaras, I., Lagodimos, A.G., and Papachristos, S. An EOQ model with backorders and rejection of defective supply batches", Int. J. Prod. Econ., 155(1), pp. 148-154 (2014). 18. Paul, S., Wahab, M.I.M., and Ongkunaruk, P. Joint replenishment with imperfect items and price discount", Comput. Ind. Eng., 74(1), pp. 179-185 (2014). 19. Hlioui, A., Gharbi, A., and Hajji, A. Replenishment, production and quality control strategies in three-stage supply chain", Int. J. Prod. Econ., 166(1), pp. 90-102 (2015). 20. Shari_, E., Sobhanallahi, M.A., and Mirzazadeh, A. An EOQ model for imperfect quality items with partial backordering under screening errors", Cogent Eng., 2(1), Article: 994258 (2015). 2578 H. Mokhtari/Scientia Iranica, Transactions E: Industrial Engineering 26 (2019) 2561{2578 21. Alamri, A.A., Harris, I., and Syntetos, A.A. E_cient inventory control for imperfect quality items", Eur. J. Oper. Res., 254(1), pp. 92-104 (2016). 22. Chang, C.T., Cheng, M.C., and Soong, P.Y. Impacts of inspection errors and trade credits on the economic order quantity model for items with imperfect quality", Int. J. Syst. Sci.: Oper. Logist., 3(1), pp. 34-48 2016. 23. Rezaei, J. Economic order quantity and sampling inspection plans for imperfect items", Comput. Ind. Eng., 96(1), pp. 1-7 (2016). 24. Yu, H.F., and Hsu, W.K. An integrated inventory model with immediate return for defective items under unequal-sized shipments", J. Ind. Prod. Eng., 34(1) pp. 70-77 (2017). 25. Sarkar, B. and Saren, S. Product inspection policy for an imperfect production system with inspection errors and warranty cost", Eur. J. Oper. Res., 248(1), pp. 263-271 (2016). 26. Ongkunaruk, P., Wahab, M.I.M., and Chenc, Y. A genetic algorithm for a joint replenishment problem with resource and shipment constraints and defective items", Int. J. Prod. Econ.m 175(1), pp. 142-152 (2016). 27. Taleizadeh, A., Lashgari, M., Akram, R., and Heydari, J. Imperfect economic production quantity model with upstream trade credit periods linked to raw material order quantity and downstream trade credit periods", Appl. Math. Model., 40(19-20), pp. 8777- 8793 (2016). 28. Cheikhrouhou, N., Sarkar, B., Ganguly, B., Malik, A.I., Batista, R., and Lee, Y.H. Optimization of sample size and order size in an inventory model with quality inspection and return of defective items", Annals of Operations Research, pp. 1-23 (2017) (In Press). 29. Taleizadeh, A.A., and Zamani Dehkordi, N. Economic order quantity with partial backordering and sampling inspection", J. of Ind. Eng. Inter., 13(3), pp. 331-345 (2017). 30. Mokhtari, H. and Rezvan, M.T. A single-supplier, multi-buyer, multi-product VMI production-inventory system under partial backordering", Operational Research, pp. 1-21 (2017) (In Press). 31. Jaber, M.Y., Zanoni, S., and Zavanella, L.E. Economic order quantity models for imperfect items with buy and repair options", Int. J. Prod. Econ., 155(1), pp. 126-131 (2014). 32. Chiu, S.W., Chou, C.L., and Wu, W.K. Optimizing replenishment policy in an EPQ based inventory model with nonconforming items and breakdown", Econ. Model., 35(1), pp. 330-337 (2013). 33. Bouslah, B., Gharbi, A., and Pellerin, R. Joint optimal lot sizing and production control policy in an unreliable and imperfect manufacturing system", Int. J. Prod. Econ., 144(1), pp. 143-156 (2013). 34. Mokhtari, H., Naimi-Sadigh, A., and Salmasnia, A. A computational approach to economic production quantity model for perishable products with backordering shortage and stock-dependent demand", Scientia Iranica, 24(4), pp. 2138-2151 (2017). 35. Tayyab, M., and Sarkar, B. Optimal batch quantity in a cleaner multi-stage lean production system with random defective rate", J. of Cleaner Prod., 139(1), pp. 922-934 (2016). 36. Mokhtari, H. 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), pp. 1039-1058 (2018).