The optimization of the closed-loop supply chain network

This paper develops a model of a general closed-loop supply chain network, which includes raw material suppliers, manufacturers, retailers, consumers and recovery centers. The objective of this paper is to formulate and optimize the equilibrium state of the network by using the theory of variational inequalities. Several examples and figures are used to describe the effects of parameters (the return ratio, the transformation rate of raw materials, and the transformation rate of recyclable products) on the equilibrium shipments and net revenues.