Optimization model for low-carbon supply chain considering multi-level backup strategy under hybrid uncertainty

When constructing a supply chain, the profit, environmental impact, and hybrid uncertainties the supply chain faces should be considered. This research investigates the problem of low-carbon supply chain design under hybrid uncertainty, where demand is regarded as a stochastic variable, supply and transportation disruptions are regarded as uncertain events, and the coefficient of emission reduction capacity of suppliers is regarded as an uncertain variable. Based on the probability theory and uncertainty theory, a mixed-integer optimization model is constructed to handle the disruption risk by utilizing a multi-level backup strategy and to reduce carbon emissions by investing in suppliers. This model guarantees that manufacturers' demand is satisfied to a given confidence level, manufacturers prefer to construct a supply chain within the acceptable supply chain risk, the emission reduction investment scheme and the supply decision to manufacturers are determined to maximize the profit of the supply chain. To facilitate the solution, we perform deterministic equivalent transformation of stochastic and uncertainty constraints, linearize the nonlinear constraints, and analyze the mathematical properties of the model. Finally, the validity of the proposed model is verified by case studies. The results show that although the larger the supply levels, that is, the more priority levels of suppliers, the more beneficial it is to improve the reliability, too large supply levels will reduce profits. The reasonable setting of the supply levels can optimize the emission reduction investment scheme. In addition, the confidence level of carbon emission should be set within a certain range to avoid the disparity between profit growth and emission reduction. Finally, the greater the belief degree of disruption or the lower the emission reduction capacity of suppliers, the more significant the effect of a multi-level backup strategy.