By using the methods of equilibrium theory and variational inequality, a multi-tiers competitive closed-loop supply
chain network equilibrium model with random demands is proposed. Based on this model, a mathematical program with
equilibrium constraints for the location model of facility competition is developed. The equilibrium model is used to capture
the change of equilibrium state for the network resulting from the entering facilities, and incorporate the effect of changes
directly into the location decision model. According to the characteristic of the model, a solution method of integrating the
genetic algorithm and the modified projection method is built to solve the problem. Finally, numerical examples are solved
and analyzed by using the proposed model and algorithm, the station of competitive developing trends for the network, and
the location decision for the entering facilites and the manufacturing and operation decision are obtained.