Economic production quantity (EPQ) model for three type imperfect items with rework and learning in setup
Imperfect quality items are unavoidable in an inventory system due to imperfect production process, natural disasters, damages, or many other reasons. The setup cost and production cycle time can be related in terms of process deterioration and learning and forgetting effects. Learning reduces production run length and setup cost, whereas deterioration and forgetting increases both. Keeping these facts in mind, this paper investigates an Economic Production Quantity (EPQ) model with imperfect quality items with varying set-up costs. Mathematical model and solution procedures are developed with major insight to its characteristics. Numerical example and sensitivity analysis are provided to illustrate and analyze the model performance. It can be observed that our model has a significant impacts on the optimal lot size and optimal profit of the model.
[1] Rosenblatt, M.J. and Lee, H.L., Economic production cycles with imperfect production processes. IIE Transactions, 18(1), 48–55, (1986).
[2] Schwaller, R.L., EOQ under inspection costs. Production and Inventory Management Journal, 29, 22–24, (1988).
[3] Zhang, X. and Gerchak, Y., Joint lot sizing and inspection policy in an EOQ model with random yield. IIE Transactions, 22(1), 398– 401, (1990).
[4] Salameh, M.K. and Jaber, M.Y., Economic production quantity model for items with imperfect quality. International Journal of Production Economics, 64(1), 59–64, (2000).
[5] Goyal, S.K. and Cardenas-Barron, L.E., Note on: economic production quantity model for items with imperfect quality a practical approach. International Journal of Production Economics, 77(1), 85–87, (2002).
[6] Ouyang, L-Y., Chen, C-K. and Chang, H-C., Quality improvement, setup cost and leadtime reductions in lot size reorder point models with an imperfect production process. Computers and Operations Research, 29(12), 1701–1717, (2002).
[7] Papachristos, S. and Konstantaras, I., Economic ordering quantity models for items with imperfect quality. International Journal of Production Economics, 100, 148–54, (2006).
[8] Jaber, M.Y., Lot sizing for imperfect production process with quality corrective interruptions and improvements, and reduction in setups. Computers and Industrial Engineering, 51(4), 781–790, (2006).
[9] Wee, H.M., Yu, J. and Chen, M.C., Optimal inventory model for items with imperfect quality and shortage backordering. Omega, 35, 7–11, ( 2007).
[10] Maddaha, B. and Jaber, M.Y., Economic order quantity for items with imperfect quality: Revisited. International Journal of Production Economics, 112 , 808–815, (2008).
[11] Chung, K.J., Her, C.C. and Lin, S.D., A twowarehouse inventory model with imperfect quality production processes. Computers and Industrial Engineering, 56, 193–197, (2009).
[12] Darwish, M.A., EPQ models with varying setup cost. International Journal of Production Economics, 113, 297–306, (2008).
[13] Khan, M., Jaber, M.Y., Guiffrida, A.L., Zolfaghari, S., A review of the extensions of a modified EOQ model for imperfect quality items. International Journal of Production Economics, 132, 1–12, (2011).
[14] Al-Salmah, M. and Alsawafy, O., Economic order quantity for items with Two types of imperfect quality. International Journal of Optimization and Control: Theories & Applications, 2(1), 73–82, (2012)
[15] Tsou, J.C, Hejazi, S.R. and Barzoki, M.R., Economic production quantity model for items with continuous quality characteristic, rework and reject. International Journal of Systems Science. 43(12), 2261–2267, (2012).
[16] Mukhopadhyay, A. and Goswami, A., An EOQ model with imperfect items with shortages under declining demand and deterioration. Review Bulletin of Calcutta Mathematical Society, 20(1), 11–28, (2012).
[17] Wee, H-M., Wang, W-T., and Yang, P-C., A production quantity model for imperfect quality items with shortage and screening constraint. International Journal of Production Research, 51(6), 1869–1884, (2013).
[18] Mukhopadhyay, A. and Goswami, A., Application of uncertain programming to an inventory model for imperfect quantity under time varying demand. Advanced Modeling and Optimization, 15(3), 565–582, (2013).