A note on optimal replenishment policy for imperfect quality EMQ model with rework and backlogging

A recent article on optimal replenishment policy of imperfect EMQ model by Chiu [S.W. Chiu, Optimal replenishment policy for imperfect quality EMQ model with rework and backlogging, Applied Stochastic Models in Business and Industry 23 (2007) 165–178], used mathematical modeling and differential calculus to derive the optimal ordering policy that minimizes overall costs. This paper presents a straightforward algebraic approach to replace the use of calculus on the cost function for determining the optimal replenishment solutions as well as the long-run average production-inventory costs for such an imperfect EMQ model. The algebraic method presented in this paper may enable students or practitioners with little or no knowledge of calculus to learn or to manage with ease the real-life manufacturing systems.