We address the optimal design of a multi-echelon supply chain and the associated inventory systems in the presence of uncertain customer demands. By using the guaranteed service approach to model the multi-echelon stochastic inventory system, we develop an optimization model for simultaneously optimizing the transportation, inventory and network structure of a multi-echelon supply chain. We formulate this problem as an MINLP with a nonconvex objective function including bilinear, trilinear and square root terms. By exploiting the properties of the basic model, we reformulate the problem as a separable concave minimization program. A spatial decomposition algorithm based on Lagrangean relaxation and piecewise linear approximation is proposed to obtain near global optimal solutions with reasonable computational expense. Examples for industrial gas supply chains with up to 5 plants, 50 potential distribution centers and 100 markets are presented.