With the advance of modern science and technology, and with the growing of economic, the competition between enterprises is more and more fierce. In addition, due to the tremendous changes of political, economic, and social environment, the randomicity of whole market demand has greatly increased. In these circumstances, the competition is not between enterprises, while it is between supply chains. Therefore, it is of great academic and realistic significance that we study the dynamic supply chain network equilibrium model and its coordination.The paper systematically and comprehensively generalizes current status quo study of supply chain modeling throughout the world, and then analyzes the basic characteristic and demerit of the traditional supply chain theory and application. Based on our analyses, we adopt the variational inequalities theory to develop a supply chain network equilibrium model, which contains stock, random demands and goodwill penalty cost. Afterward, we introduce the projected dynamical systems and its stability analysis, and based on which we establish the dynamical supply chain network equilibrium model. The model can be used to describe the dynamical process of supply chain network achieving equilibrium.In addition, it is pointed that the profit allocation between the manufacturers and retailers is unchangeable when supply chain network is equilibrium, and the equilibrium state is too ideal to be in the market economy. In order to be equilibrium, we introduce buy back contract and profit sharing contract into the supply chain network equilibrium model. We construct a specific numerical example, and compute the example by discrete time algorithm. It's proved by the numerical example that buy back contract and profit sharing contract can coordinate the profit allocation of supply chain network members, and can ensure the equilibrium of supply chain network.The study shows that the NASH noncooperative game among the supply chain network members can be simulated by means of variational inequality and projected dynamical system. Supply chain contracts can coordinate this kind of supply chain network, make that every supply chain member satisfies with their profit, and ensure that supply chain network achieving equilibrium. |