Research Of The Closed-loop Supply Chain Supernetwork Based On The Variational Inequalities

The variational inequality is an important branch of mathematics and makes a lot of important application in theoretical and applied science, such as, applied mathematics, physics, linear and nolinear programming problem, economics and transport fields. With the lead of Professor Anna Nagurney, the supernetwork research center investingates network's equilibrium situation using variational inequality, and gets notable progenies through using the traffic supernetwork's prinpiles to investigate supply chain supernetworks, financial supernetworks and knowledge supernetworks.Based on the previous researches and practices, we develop a framework for the modeling analysis, and computation of solutions to a closed-loop supply chain supernetwork consist of raw material suppliers, manufacturers, retailers, demand markets and recyclers. Whereas the aims of the principal parts in the closed-loop supernetwork system are conflict. Based on Anna Nagurney's method, we model the optimizing behavior of the various decision-makers, derive the equilibrium conditions, and establish the finite-dimensional variational inequality formulation. We provide qualitative properties of the equilibrium pattern in terms of esistence and uniqueness results and also establish conditions under which the proposed computational procedure is guaranteed to converge. Finally, we illustrate the model through several numerical examples for which the equilibrium prices and product shipments are computed. It is necessary to lucubrate the closed-loop supply chain deeply for it can reflect real economy very well.