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.