Abstract: The aforementioned closed-loop supply chain network design models consider only competition among the member enterprises in the network. The remanufacturing closed-loop supply chain network design model is developed extends the aforementioned models to consider competition among closed-loop supply chains. The design model is not limited to linear costs, but, rather, which can handle nonlinear costs. Moreover, continuous variables are used first in the model formulations. The network considering remanufacturing closed-loop supply chain competition based on crucial functional activities is presented. The operational and recovery cost functions, design cost functions is developed based on functional activity arc sections. The competitive behaviors among remanufacturing closed-loop supply chains are analyzed by using the equilibrium theory. The remanufacturing closed-loop supply chain network design model with continuous variables is formulated by using the variational inequality theory. Numerical examples are solved by using the proposed models to design the remanufacturing closed-loop supply chain network, and analyze what impact the rate for remanufacturing will have on sales, operational and recovery costs, design costs and profits for every remanufacturing closed-loop supply chain, and the demands, the amount of return, prices for every demand market.

Key words: closed-loop supply chain, network design, remanufacturing, supply chain competition, variational inequality