Optimal manufacturing batch size with rework in a single-stage production system – A simple derivation Leopoldo Eduardo Ca ´rdenas-Barro ´n * Department of Industrial and Systems Engineering, Instituto Tecnolo ´ gico y de Estudios Superiores de Monterrey, Campus Monterrey, Me ´xico, E.Garza Sada 2501 Sur, C.P. 64 849, Monterrey, Mexico Received 17 March 2005; accepted 11 July 2007 Available online 29 February 2008 Abstract This paper presents a simple derivation of the two inventory policies proposed by [Jamal, A. A. M., Sarker, B. R., & Mondal, S. (2004). Optimal manufacturing batch size with rework process at single-stage production system. Computers and Industrial Engineering, 47(1), 77–89.]. In order to find the optimal solutions for both policies they used differential cal- culus. Our simple derivation is based on an algebraic derivation. The final results that we obtained are equivalent to the results that [Jamal, A. A. M., Sarker, B. R., & Mondal, S. (2004). Optimal manufacturing batch size with rework process at single-stage production system. Computers and Industrial Engineering, 47(1), 77–89.] found. But, our results are more sim- ple and easy to compute manually. We also established the range of real values of proportion of defectives products for which there is an optimal solution, the closed-form for the total inventory cost for both policies, the mathematical expres- sions for determining the cost penalty and the additional total cost for working with a non-optimal solution. Ó 2008 Elsevier Ltd. All rights reserved. Keywords: Rework process; Defectives products; EPQ inventory model and algebraic development 1. Introduction Jamal, Sarker, and Mondal (2004) presented an inventory model, which dealt with the optimum batch quantity in a single-stage system in which rework is done by addressing two different operational policies to minimize the total system cost. The first policy deals with rework of defective products being completed within the same cycle. The second policy deals with the rework of defective products being done after N cycles. Related to this work is the paper by Ca ´rdenas-Barro ´n (2007a) where an error appearing on Jamal et al. (2004)’s paper is corrected. Such error appears in the solutions of the two numerical examples. However, the main idea and contribution of the paper are not affected. Recently, Sarker, Jamal, and Mondal (2008) extended the previous work to the case of a multi-stage manufacturing systems environment under the same two operational policies. Where in the first policy the 0360-8352/$ - see front matter Ó 2008 Elsevier Ltd. All rights reserved. doi:10.1016/j.cie.2007.07.017 * Tel.: +52 81 83 28 42 35; fax: +52 81 83 28 41 53. E-mail address: lecarden@itesm.mx Available online at www.sciencedirect.com Computers & Industrial Engineering 55 (2008) 758–765 www.elsevier.com/locate/caie