A complementarity model for a supply chain network equilibrium problem with electronic commerce

In this paper, we develop a competitive supply chain network equilibrium model with multiple products, in which electronic commerce is considered. After analysing equilibrium conditions of the manufactures, retailers, and demand markets, and giving economic interpretations, equilibrium conditions of the supply chain network formulated as an equivalent complementarity model are established. In addition, a modified subgradient extragradient algorithm is proposed to find the solution of the complementarity problem, and the convergence of the proposed algorithm is proved. We also give some numerical examples to demonstrate the efficiency of the given model and algorithm.