Robust bi-level optimization for green opportunistic supply chain network design problem against uncertainty and environmental risk

- We formulate a robust GrOSCN by the bi-level programming.
- We are the first to introduce the CVaR for GrOSCD.
- We achieve an exact solution by using KKT conditions.
- We integrate risk parameters and cost to design a GrSCN.
- The resulted robust model is better-managed in the case of operational risks.

The main objective of this research is to introduce the concept of Green Opportunistic Supply Chain (GrOSC) and to design it in a lean and agile manufacturing setting under uncertain and risky environment. The model considers the uncertainties of the market-related information, i.e. the demand and transportation and shortage costs, under Vendor Managed Inventory (VMI) strategy. Addressing the retailer's risk aversion level through Conditional Value at Risk (CVaR) to deal with these uncertainties leads to a bi-level programming problem. The Karush-Kuhn-Tucker (KKT) conditions are adopted to transform the model into a single-level mixed integer linear programming problem. Since, the realization of the uncertain parameters is the only information available, a data-driven approach is employed to avoid distributional assumptions. The effectiveness of the model is finally demonstrated through a numerical example.