In this article, using the equilibrium theory and method of variational inequality, the multi-commodity flow supply chain network with random demand is discussed, the behavior of the various decision-makers as well as the effect of their interaction in different tiers are analyzed, and then, the network equilibrium model with random demand is established. The equilibrium conditions of the system
... [Show full abstract] are obtained and the economic interpretations are given. Finally, a numerical example is given to show the rationality of our model.