Integrated multi‐echelon supply chain design with inventories under uncertainty: MINLP models,computational strategies

We address in this article a problem that is of significance to the chemical industry, namely, 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 to simultaneously determine the transportation, inventory, and network structure of a multi‐echelon supply chain. The model is an MINLP with a nonconvex objective function including bilinear, trilinear, and square root terms. By exploiting the properties of the basic model, we reformulate this problem as a separable concave minimization program. A spatial decomposition algorithm based on the integration of Lagrangean relaxation and piecewise linear approximation is proposed to obtain near global optimal solutions with reasonable computational expense. Examples for specialty chemicals and industrial gas supply chains with up to 15 plants, 100 potential distribution centers, and 200 markets are presented. © 2009 American Institute of Chemical Engineers AIChE J, 2010