In this paper we develop two models for an inventory system in which the distributor manages the inventory at the retailers location. These type of systems correspond to the Vendor Managed Inventory (VMI) systems described ib the literature. These systems are very common in many different types of industries, such as retailing and manufacturing, although assuming different characteristics. The objective of our model is to minimize total inventory cost for the distributor in a multi-period multi-retailer setting. The inventory system includes holding and stock-out costs and we study the case where an additional fixed setup cost is charged per delivery. We construct a numerical experiment to analyze the model bahavior and observe the impact of the characteristics of the model on the solutions.