This article presents an algebraic approach for solving realistic production lot-size problem with backlogging and random defects. Traditional methods for determining optimal lot size are by using the differential calculus on production-inventory cost function with the need to prove optimality first. Recent articles have proposed algebraic approaches to the solution of economic order quantity (EOQ) and economic production quantity (EPQ) models without reference to the use of derivatives. With the intention of assisting students or practitioners who has little knowledge of calculus, this article extends their works and proposes an alternative way for learning the realistic inventory model that takes the backlogging and random scrap rate into consideration. We demonstrate that optimal lot size for the aforementioned model can be derived algebraically and overall production costs can be obtained immediately as well.
WSEAS Transactions on Mathematics 6(6), pp.736-740