A tri-level programming model based on Conditional Value-at-Risk for three-stage supply chain management

•We introduce a tri-level programming model for a three-stage supply chain.•The proposed model can be transferred into a bilevel programming model.•The retailer maximizes his CVaR about profit to control potential risk.

For the problem of supply chain management, the existing literature mainly focuses on the research of the single-stage supply chain or the two-stage supply chain that consists of a manufacturer and a retailer. To our best knowledge, little attention has been paid to the study of a more extensive supply chain that consists of a material supplier, a manufacturer and a retailer, which is a more practical and interesting case. Therefore, based on the Conditional Value-at-Risk (CVaR) measure of risk management, this paper proposes a tri-level programming model for the three-stage supply chain management. In this model, the material supplier and the manufacturer maximize their own profit while the retailer maximize his/her CVaR of expected profit. Further, we show that the proposed tri-level programming model can be transferred into a bilevel programming model, which can be solved by the existing methods. Numerical results show that the proposed model is efficient for improving the risk management of the three-stage supply chain.