Multi-period closed-loop supply chain network equilibrium with carbon emission constraints

One effective method to reduce industry's environmental footprint is the use of a closed-loop supply chain (CLSC). Based on the traditional forward supply chain, the CLSC incorporates collection and remanufacturing to reduce waste and satisfy environmental goals. In this study, we consider the CLSC network equilibrium, comprising manufacturers, retailers, demand markets and recyclers, in a multi-period planning horizon. In the scenario considered, all of the manufacturers make homogeneous products and have two types of mandatory carbon emission constraints during manufacturing/remanufacturing; one of which can be called a periodic carbon emission constraint, and the other, a global carbon emission constraint. Based on variational inequality and complement theory, the optimal behaviors and the equilibrium conditions of various players in the CLSC network are formulated, and the governing network equilibrium model is established. A modified projection and contraction algorithm is used to solve the model. The validity of the proposed model and the impact of the two types of carbon emission constraints on network equilibrium are demonstrated with numerical examples. The managerial insights obtained in this paper lead to areas of future research into CLSC networks.