Abstract: A network diagram is used to represent the basic structure of a supply chain network such that the network design of a supply chain is simplified to determine the capacity and flow for each node. Based on the equilibrium conditions of the supply chain network and the simplified stochastic factors, the issue of optimal decisionmaking for both the manufacturing center and distribution center with stochastic demands is discussed. The optimality conditions are described by using variational inequalities. Then, a comprehensive supply chain network design model with stochastic demands is built. Analysis through numerical examples is used to illustrate the effectiveness of the model.

Key words: supply chain with stochastic demands, network diagram, variational inequalities, optimization