由於及時(Just in time, JIT)的生產系統的經驗，我們可以知道許多有關於降低前置時間及設置成本的利益，因此本研究主要是探討需求量服從羅吉斯分配的前提下，考慮可控制的前置時間內，允許缺貨且缺貨發生時考慮部分欠撥、部分銷售損失混合的存貨系統。提出一個以訂購數量Q、請購點r、設置成本A與前置時間L為決策變數的存貨模型，我們稱之為(Q, r, A, L)模型，最後以計量的方法求出使得全年期望總成本能達最小化的最適解。

Due to the experience of the Just in time (JIT), we can know the benefit of shortening the lead time and reducing the setup cost. This paper mainly focuses on the inventory model for the logistic demand. In the controllable lead time, the shortages are allowed and the total mixture of backorders and lost sales. We propose amount of stockout during the stockout period is considered to be a of the order quantity Q, reorder point r, setup cost A and lead time L, denoted by (Q, r, A, L) model. Finally we utilize the numerical examples to express the optimal solutions of the minimum total costs.