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Mathematical and Computational Applications is published by MDPI from Volume 21 Issue 1 (2016). Articles in this Issue were published by another publisher in Open Access under a CC-BY (or CC-BY-NC-ND) licence. Articles are hosted by MDPI on as a courtesy and upon agreement with the previous journal publisher.
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Math. Comput. Appl. 2010, 15(3), 364-370;

An Algebraic Approach for Determining the Optimal Lot Size for EPQ Model with Rework Process

Department of Business Administration, Chaoyang University of Technology, Taichung 413, Taiwan
Department of Information Management, Tamkang University, 151, Ying Chuan Road, Tamsui, Taipei Hsien 251, Taiwan
College of Business, Ph.D. Program & Department of Industrial Engineering and Systems Management, Feng Chia University, Taichung 407, Taiwan
Author to whom correspondence should be addressed.
Published: 1 December 2010
PDF [152 KB, uploaded 4 April 2016]


This paper presents a simple algebraic approach for deriving the optimal lot size for economic production quantity (EPQ) model with rework process. Conventional methods for solving lot size problems are by using differential calculus on the long-run average production-inventory cost function with the need to prove optimality first. A few recent articles proposed the algebraic approach to the solution of classic economic order quantity (EOQ) and EPQ model without reference to the use of derivatives. This paper extends it to an EPQ model with reworking of defective items. We demonstrate that optimal lot size and optimal production-inventory cost for such an imperfect EPQ model can be derived without derivatives. As a result, it may enable the practitioners or students who with little knowledge of calculus to understand or handle with ease the realistic production systems.
Keywords: Operations management; Inventory control; Manufacturing; Lot sizing; EPQ Operations management; Inventory control; Manufacturing; Lot sizing; EPQ
This is an open access article distributed under the Creative Commons Attribution License (CC BY 3.0).

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Chiu, S.W.; Cheng, C.-B.; Wu, M.-F.; Yang, J.-C. An Algebraic Approach for Determining the Optimal Lot Size for EPQ Model with Rework Process. Math. Comput. Appl. 2010, 15, 364-370.

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