Harris’s classic square root economic order quantity (EOQ) model forms the basis for many other models that relax one or more of its assumptions. A key assumption of the basic EOQ model is that stockouts are not permitted. Due to the excess demands, stock-out situations may arise occasionally. Sometimes, shortages are permitted and they are backordered and satisfied in the very next replenishment. Therefore the objective of this paper is to develop a partial backlogging inventory model, and proposes a new algorithm to minimize the total cost, at the same time also propose the prediction method and algorithm of ordering period. Finally, a practical example of the numerical analysis is given.