A dual channel equilibrium model of a competitive closed-loop supply chain network with random demands is developed, with both physical and electronic transactions. The competitive dual channel closed-loop supply chain network is comprised by noncooperative manufacture/remanufacturing firms with production capacity constraints, distribution/recycling centers, retailers/recovery points with random market demand as well a binding price ceiling
of the goods. With the help of variational inequality theory, the network structure of the closed-loop supply chain is identified and the dual channel equilibrium conditions are derived. An algorithm for solving the equilibrium pattern is designed by logarithmic-quadratic proximal prediction-correction method. Numerical examples were given to show the impact of produc- tion capacity constrains and price ceiling on the network equilibrium pattern. The results show
that a shortage of the good arises when the government imposes a binding price ceiling on competitive markets, which is more serious in the existence of production capacity constraints. The profit of manufacture/remanufacturing firms, retailers/recovery points and supply chain is increased by adding a direct channel. However, the profit of distribution/recycling centers is decreased.