Perhaps, Hadley and Whitin , and Johnson and Montgomery were the first researchers to models with two backorder costs. a linear and a fixed cost per unit. Their solution procedure is treat the EOQ/EPQ inventory based on calculus and solved the system equations resulting from the first-order conditions. Recently. Sphicas indicates that Johnson and Montgomery 's arguments to locate the optimal solutions are not complete. Therefore, Sphicas adopts an algebraic approach to demonstrate how a relatively complex model can be fully analyzed without derivatives and obtained the explicit identification of the models. EOQ/EPQ inventory models.