Optimal manufacturing batch size with rework in a single-stage production system – A simple derivation

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 calculus. 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 simple 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 expressions for determining the cost penalty and the additional total cost for working with a non-optimal solution.