An enterprise network is analyzed from the viewpoint of an end-product manufacturer who receives customer orders and organises his production and supply policy so as to minimize the sum of his average holding cost and average stock-out cost. For each main component to be ordered, the producer has several possible suppliers. The arrivals of customers’ orders are random and delivery times from suppliers are also supposed random. This supply system is represented as a queuing network where the producer uses a base-stock inventory control policy that keeps constant the inventory position level (current inventory level+pending replenishment orders). The decision variables are the reference inventory position level and the percentages of orders sent to the different suppliers. In the queuing network model, the percentages of orders are implemented as Bernoulli branching parameters. A close-form expression of the expected cost criterion is obtained as a complex non-linear function of decision variables. A decomposed approach is proposed for solving the optimization problem in an approximate manner. The quality of the approximate solution is evaluated by comparison to the exact solution, which can be computed numerically in some simple cases, in particular in the two-supplier case. Numerical applications show the important economic advantage for the producer of sending orders to several suppliers rather than to a single one.