本研究主要探討在供應商提供一個全單位型數量折扣下，物品需求率與存貨水準有關之非即時退化性物品的存貨問題。存貨系統中允許缺貨發生且為部分欠撥，欠撥率為一隨機變數。目的在決定使得零售商的期望單位時間相關存貨總成本為最小之最適補貨策略。在文中我們發展一些定理來說明最適解唯一存在的必要且充分條件並建立一個簡單易懂的演算法來說明如何找出最適的訂購週期長度與訂購數量。更進一步，利用幾個數值範例來說明本模式之求解過程。最後，亦針對本模式的主要參數做敏感度分析以說明其對於最適解的影響。

This article deals with an inventory problem for non-instantaneous deteriorating items with stock-dependent demand when supplier offers an all-unit quantity discount. In the model, shortages are allowed and the backorder rate is a random variable. The purpose of this study is to determine an optimal ordering policy for minimizing the expected total relevant inventory cost for the retailer. We have developed some useful theorems to characterize the optimal solution and provide an easy and useful algorithm to find the optimal order quantity and replenishment time. Furthermore, several numerical examples are given to illustrate the solution procedure for the mathematical model developed. Finally, we also implement sensitivity analysis of the optimal solution with respect to major parameters.