Study on the bi-level programming model for closed loop supply chain under competitive environment

A bi-level programming model is proposed by using the methods of equilibrium theory and variational inequality. The upper level model accounts for that the environmental protection agency can promote environmental benefit at possibly lower incentive and supervision costs. The lower level model describes the competitive behavior of the decision-makers under different incentive and supervision strategies, and a closed loop supply chain network equilibrium model in competitive environments is formulated. Finally, a numerical example tested on the proposed algorithm illustrates the validity of the model along with the discussion. The result provides a theoretic support for the environmental protection agency to make effective policies.