A solution procedure based on Lagrangian relaxation for supply chain planning problem with CSR investment

In this paper, we consider a supply chain planning problem for a single manufacturer with corporate social responsibility (CSR) investment decision under uncertain demand. The activity of CSR is modeled as the investment to customers. In the mathematical model, we assume that the average demand increases if the investment of CSR is increased. The objective function is the total profit including the piecewise linear investment costs. The supply chain planning problem is formulated as a mixed integer nonlinear programming problem. An efficient solution procedure based on Lagrangian relaxation is developed. The effectiveness of the proposed method is confirmed from computational experiments.