Notes on the mathematical modeling approach used to determine the replenishment policy for the EMQ model with rework and multiple shipments

A recent article (Chiu et al. (2011) [22]) used mathematical modeling along with differential calculus to derive the optimal replenishment lot size for an economic manufacturing quantity (EMQ) model with rework and multiple shipments. Unlike the conventional method that uses differential calculus with the system cost function to solve the economic lot size problem, this paper proposes a straightforward algebraic approach. It is demonstrated that both the optimal replenishment lot size Q ∗ and a simplified form for the long-run average cost E[TCU( Q ∗ )] for such a specific lot size problem can be derived without using differential calculus. This approach enables practitioners or students who may not have sufficient knowledge of differential calculus to better understand such a practical vendor–buyer integrated system.