Supply chain management (SCM) is concerned with a complex business relations network that contains interrelationships between various entities, such as suppliers, manufacturers, distribution centers and customers. SCM integrates these entities and manages their interrelationships through the use of information technology to meet customer expectations (i.e., higher product variety and quality, lower costs and faster responses) effectively along the entire value chain. Thus, one of the vital issues in supply chain management is the design of the value chain network. In this paper, a fuzzy linear programming model for the optimization of the multi-stage supply chain model with triangular and trapezoidal membership functions is presented. The model determines the fuzzy capacities of the facilities (plants or distribution centers (DCs)) and the design of the network configuration with a minimum total cost. The total cost involves the shipping cost from suppliers; transportation costs between plants and DCs; distribution costs between DCs and customer zones; and opportunity costs from not having the material at the right time. The developed model is solved by a professional software package (LINDO), and the computational results are discussed. © 2011 The Franklin Institute. Published by Elsevier Ltd. All rights reserved.