Research Of Return Supply Chain Supernetwork Model Based On Variational Inequalities

With increasingly fierce competitions among enterprises and the enhancement of awareness of self-protection of consumers, a series problems triggered by returning have caused more and more attention of companies and consumers. As a branch of reverse logistics, it has also drawn the concern of the theoretical circle. Most models exist can be solved by integer programming now. They are good descriptions for the logistic networks of linear, homogeneous or various products. But it is difficult for describing networks of nonlinear, more periods, more products and more modes. Although that also can be solved by optimization algorithms, it is easily fallen into local optimization solutions. The supernetwork can deal with this situation. And it is good mathematic description for reverse supply chain especially.In this paper, we present a return supply chain supernetwork model, which consists of m manufacturers, n distributors and o markets. It is assumed that manufacturers produce homogeneous products; the distributors can return products to manufacturers freely according to each manufacturer's return price when the products have disfigurement or they dissatisfy with them and the consumers may purchase the products from the distributors according to their economic status. Based on this, the optimality conditions for the manufacturers, distributors and the consumers are established respectively using the variational inequalities. The optimization situation for the supply chain supernetwork model is described and the stationary points for this situation are gotten. The properties of relevant variational inequalities, which are solved by modified projection method are analyzed and approved. In addition, the Nagurney and Qiang (simply, N-Q measure) network efficiency measure, which can also assess the importance of network components and their rankings, is applied into return supply chain. At last, examples are illustrated to validate the utility of the supply chain supernetwork model.