Green-blood supply chain network design: Robust optimization, bounded objective function & Lagrangian relaxation

The aim of this research is to consider the issue of sustainability in designing a blood supply chain network by presenting a multi objective mixed integer mathematical programming model that aims to simultaneously minimize the total cost of the supply chain network and the total environmental impacts of the activities of the supply chain network. As the nature of supplying the blood by the donors and also demand for the blood product are uncertain, a robust optimization approach is applied in the model to deal with this type of uncertainty. To convert the proposed multi objective model into a single objective one, the bounded objective function method is used. Then, as the presented mathematical model is a complicated mixed integer linear programming model, an algorithm based on the Lagrangian relaxation approach is proposed to solve the model. At the end, a computational study is done to present the competency of the proposed Lagrangian relaxation algorithm.