This paper deals with an inventory system composed of a warehouse supplied from a manufacturing plant. Customer orders arrive randomly with random order size and the production capacity is finite. The inventory at the warehouse is controlled by a base-stock policy. Transportation time from plant to warehouse is a constant. An analytical approach is proposed to evaluate the order-to-delivery lead-time of the warehouse, the total inventory on order and the inventory holding and backlogging cost. Numerical comparisons with simulation show that the analytical approach is very efficient.