عنوان مقاله [English]
The economic order quantity (EOQ) problem is one of the most common used models for the production planning and inventory control problems. A common and unrealistic assumption in these problems is considering prefect quality for all units. In this study, a multi-product EOQ model with imperfect items is proposed. In this system, all received products are not perfect, and imperfect items are scraped. Moreover, in this model the warehouse construction cost is considered as a part of inventory system costs. The objective of this study is to determine the optimal order quantity and reorder point of each product such that the total inventory cost is minimized. The proposed model is a development of a convex nonlinear programming problem therefore an exact algorithm is developed to solve this problem. Finally, to demonstrate the applicability of proposed procedure, a numerical problem is represented.
 Harris., F.W. (1913). “How many parts to make at once factory”. The Mag Manage, Vol. 10, pp. 135–136 and 152.
 Erlenkotter, D. (1990). “Ford Whitman Harris and the economic order quantity model”. Operations Research, Vol. 38, pp. 937-946.
 Taft, E.W. (1918). “The most economical production lot”, Iron Age, Vol. 101, pp. 1410–1412.
 Hadley, G., & Whitin, T.M. (1963). “Analysis of Inventory Systems”. Prentice-Hall, Englewood Cliffs, NJ.
 Abboud, N.E., & Sfairy, R.G. (1997). “Time-limited free back-orders EOQ model”. Applied Mathematical Modelling, Vol. 21, pp. 21-25.
 Mehdizadeh, E., Valizadeh, S., & Pasandideh, H.R. (2013). “A multi-product inventory model with capacity warehouse constraints, budget and minimum service level in partial backlogging shortage”. Sharif Journal of Industrial Engineering & Management, Vol. 29, pp. 101-111.
 Whitin, T.M. (1953). “The theory of inventory management”. Princeton University Press, Princeton, NJ, USA.
 Weiss, H.J. (1982). “Economic order quantity models with nonlinear holding costs”. European Journal of Operational Research, Vol. 9, pp. 56-60.
 Zhang, X., & Gerchak, Y. (1990). “Joint lot sizing and inspection policy in an EOQ model with random yield”. IIE transactions, Vol. 22, pp. 41-47.
 Salameh, M. K., & Jaber, M. Y. (2000). “Economic production quantity model for items with imperfect quality”. International journal of production economics, Vol.64, pp. 59-64.
 Tsou, J.-C. (2007). “Economic order quantity model and Taguchi’s cost of poor quality”. Applied Mathematical Modelling, Vol. 31, pp. 283-291.
 Goyal, S.K., & Giri, B.C. (2001). “Recent trends in modeling of deteriorating inventory”. European Journal of operational research, Vol. 134, pp. 1-16.
 Bakker, M., Riezebos, J., & Teunter, R.H. (2012). “Review of inventory systems with deterioration since 2001”. European Journal of Operational Research, Vol. 221, pp. 275-284.
 Fatemi ghomi, S.M.T. (2010). “An EOQ model for deteriorating items: genetic algorithm approach. Sharif Journal of Industrial Engineering & Management, Vol. 26, 83-90.
 Konstantaras, I., Skouri, K., & Jaber, M.Y. (2012). “Inventory models for imperfect quality items with shortages and learning in inspection”. Applied Mathematical Modelling, Vol. 36, pp. 5334-5343.
 Pasandideh, S. H. R., Niaki, S. T. A., Nobil, A. H., & Cárdenas-Barrón, L. E. (2015). “A multiproduct single machine economic production quantity model for an imperfect production system under warehouse construction cost”. International Journal of Production Economics, Vol. 169, pp. 203-214.
 Sana, S. S. (2013). “An EOQ model for stochastic demand for limited capacity of own warehouse”. Annals of Operations Research, pp. 1-17.
 Hsu, J. T., & Hsu, L. F. (2013). “An EOQ model with imperfect quality items, inspection errors, shortage backordering, and sales returns”. International Journal of Production Economics, Vol. 143, pp. 162-170.
 Rezaei, J., & Salimi, N. (2012). “Economic order quantity and purchasing price for items with imperfect quality when inspection shifts from buyer to supplier”. International Journal of Production Economics, Vol. 137, pp. 11-18.
 Taleizadeh, A. A., Pentico, D. W., Jabalameli, M. S., & Aryanezhad, M. (2013). “An EOQ model with partial delayed payment and partial backordering”. Omega, Vol. 41, pp. 354-368.
 Taleizadeh, A. A. (2014). “An EOQ model with partial backordering and advance payments for an evaporating item”. International Journal of Production Economics, Vol. 155, pp. 185-193.
 Glock, C. H., Grosse, E. H., & Ries, J. M. (2014). “The lot sizing problem: A tertiary study”. International Journal of Production Economics, Vol. 155, pp. 39-51.
 Andriolo, A., Battini, D., Grubbström, R. W., Persona, A., & Sgarbossa, F. (2014). “A century of evolution from Harris׳ s basic lot size model: Survey and research agenda”. International Journal of Production Economics, Vol. 155, pp. 16-38.
 Cárdenas-Barrón, L. E., Chung, K. J., & Treviño-Garza, G. (2014). “Celebrating a century of the economic order quantity model in honor of Ford Whitman Harris”. International Journal of Production Economics, Vol. 155, pp. 1-7.