This Master dissertation report contemplates the development of a mathematical model for a supply chain optimization. The main objective is to schedule inbound and outbound deliveries in two-echelon distribution system and quantify the vehicle fleet size at the minimum overall cost. The problem studies the periodic replenishment of a given set of routes from a distribution centre, which acts as a cross-dock warehouse. The model is defined linear and deterministic and the costs considered are the fixed fleet vehicle cost, the fixed cost of incoming shipments, the cost of making the routes and the inventory holding costs. First, a model for periodic replenishment is presented. The frequency of outgoing deliveries is set at the optimal cycle time of each individual route. Also, a second model is defined for non-periodic replenishments. In this case, outgoing deliveries are scheduled in order to minimize the total cost of the multi-echelon distribution system. Then, both models are tested in a set of experiments in which some factors vary in order to see how do the models work. An analysis of the results of this datasets prove that some costs affect more than others to the solution of the model.