The coordination between manufacturers on social responsibility in a supply chain network: Model and algorithm

This paper considers a three-tier supply chain network with multiple manufacturers, multiple distributors, and multiple retailers. The problem of the supply chain network with decentralized decision-makers is formulated as a variational inequality model and the problem of the supply chain network with centralized decision-makers, i.e., a system optimal problem, is also formulated as a nonlinear optimization problem. Since the solution of a system optimal problem is usually not achievable or stable when each member tries to maximize its own profits, a strategy of taking social responsibility as well as the corresponding variational inequality model are then proposed, which ensure the equilibrium of the supply chain network and the maximization of total profits simultaneously. We found that the coordination between manufacturers on social responsibility can achieve the goal of system optimum. An algorithm of a diagonalization method with a super-network representation is proposed and tested with a numerical example.