In this paper we examine a deterministic inventory model with a linear demand rate. We suppose that in each time T j-1 , the inventory level is zero and immediately, it is replaced its level with an asked of size S j , for j=1, 2, …, (m-1), allowing to satisfy the demand to the next reposition time. The main result is to find the optimal reposition time T j-1, that will minimize the total cost in a planning horizon.