A Study on the Inventory Model with Partial Backorders under the Lead Time Uncertainty

조달기간(調達期間)이 불확실(不確實)한 상황하에서의 부분부(部分負) 재고모형(在庫模型)에 관한 연구(硏究)

This paper presents a single-echelon, single item, stochastic lead time and static demand inventory model for situations in which, during the stockout period, a fraction ${\beta}$ of the demand is backordered and the remaining fraction $(1-{\beta})$ is lost. In this situations, an objective function representing the average annual cost of inventory system is obtained by defining a time-proportional backorder cost and a fixed penalty cost per unit lost. The optimal operating policy variables minimizing the average annual cost are calculated iteratively. At the extremet ${\beta}=1$, the model presented reduces to the usual backorder case. A numerical example is solved to illustrate the algorithm developed.