Alternative approach for solving replenishment lot size problem with discontinuous issuing policy and rework

Conventional approach for solving the replenishment lot size problem is by using differential calculus on the long-run average production cost function with the need to prove optimality first. Recent studies proposed an algebraic approach to the solution of classic economic order quantity (EOQ) and the economic production quantity (EPQ) models without reference to the use of derivatives. This paper extends it to the solution of a specific EPQ model as was examined by Chiu et al. [Chiu, S. W, Chen, K. -K, Lin, H. -D. Numerical method for determination of the optimal lot size for amanufacturing system with discontinuous issuing policy and rework. International Journal forNumerical Methods in Biomedical Engineering. doi: 10.1002/cnm.1369. (in Press; Published online March-10-2010).]. As a result, optimal replenishment lot size and a simplified optimal production-inventory cost formula for such a particular EPQ model can be derived without derivatives. This alternative approach may enable practitioners who with little knowledge of calculus to understand the realistic production systems with ease.