經濟生產批量模型已經被研究很長一段時間了，而其中一項假設則為在生產過程中生產率為常數。但是，現實中有一種情形為藉由不斷重複生產，生產率會因此增加。這種情況學者稱為學習效果。因此，我們想要知道這種情況是如何運作及如何改善生產率。這些議題變成為了這篇文章中最重要的議題。在這篇文章 中我們探討的重點為傳統的經濟生產批量模型加入了生產的學習曲線。
這篇文章的背景為我們生產自家的產品而且希望能夠讓利潤更有效。而本篇文章的目標為最低成本的情況下找出最佳生產批量。而在本篇中我們總共探討兩種情況。第一種情況為基本的經濟生產模型，而第二種情況則為我們在生產的階段加上學習的效果，最後，我們會藉由我們的模型來觀察模型中參數對於結果的影響。

The economic production quantity (EPQ) model has been developed for a long time. One of the assumptions is that there has a constant production rate. But in real situations, there occurs a situation is that the production rate would increase by repetitive manufactures. This phenomenon called effect of learning. Hence, we want to know how this effect working and how to improve the productivity in this model. These issues become the most important thing here. In this paper we discuss the traditional EPQ model with production learning.
This research’s background is that we manufacture our own products, and we want to make the efficiency profit. The objective of this research is that we want to minimize the total system cost to find the optimal production quantity. Totally we build two environments to discuss them. The first case is that the traditional EPQ model. And the second case we illustrate is that we add the learning curve with the production. Finally, we could observe the relationship between the parameters and our objectives.

Reference
1. Argote, L. and Epple, D., Learning Curves in Manufacturing, Science, vol. 247, No.4945, 1990.
2. Bedworth, D. D. and Bailey, J. E., 1987, Integrated Production Control Systems. 2nd Ed. New York, NY: John Wiley & Sons
3. Cheng, T. C. E., 1989, an economic production quantity model with flexibility and reliability considerations. European Journal of Operational Research, 39, 174–179.
4. Gupta, T., & Chakraborty, S. (1984). Looping in a multistage production system. International Journal of Production Research, 22(2), 299–311.
5. Harris, F. W., 1913, how many parts to make at once. The Magazine of Management, 10(2), 135-136.
6. Hayek, P. A., & Salameh, M. K. (2001). Production lot sizing with the reworking of imperfect quality item produced. Production Planning and Control, 12(6), 584–590.
7. Jamal, A. M. M., Sarker, B. R. and Mondal, S., 2004.Optimal manufacturing batch size with rework process at a single-stage production system. Computers & Industrial Engineering, 47, 77-89.
8. Krishan Rana, Ephrem Eyob, 2006.Incorporation of learning curves in economic order quantity(EOQ) and economic production quantity (EPQ) models. Scientific Journal of administrative development.
9. Lee, H. L., & Rosenblatt, M. J. (1986). Economic production cycles with imperfect production processes. IIE Transactions, 18(1), 48–55.
10. Mohamad Y. Jaber and Maurice Bonney.1996.Optimal lot sizing under learning considerations: The bounded learning case. Appl. Math. Modeling.,
11. Mohamad Y. Jaber,, Maurice Bonney.1999. The economic manufacture/order quantity (EMQ/EOQ) and the learning curve: Past, present, and future. Int. J. Production Economics 59 (1999) 93D102
12. Moueen K. Salameh, Mohamed-Asem U. Abdul-Malak, and Mohamad Y. Jaber. Mathematical modeling of the effect of human learning in the finite production inventory model. Appl. Math. Modelling, 1993, Vol. 17, November
13. Porteus, E. L., 1986, Optimal lot-sizing process quality improvement and setup cost reduction. Operations Research, 34(1), 137-144
14. S. R. Hejazi, J. C. Tsou , M. Rasti Barzoki 2008, Optimal lot size of EPQ model considering imperfect and defective products, Journal of Industrial Engineering International.
15. Waters, C. D. J., 1994, Inventory Control and Management. (Chichester:Wiley).
16. Wright, T.P., "Factors Affecting the Cost of Airplanes", Journal of Aeronautical Sciences, 3(4) (1936): 122–128
17. Yelle, L. E., “The Learning Curve: Historical Review and Comprehensive
Survey,” Decision Science, 10, 19