Disruption risks exacerbate the complexity of low-carbon supply chain network design in an uncertain supply chain environment. Considering the low frequency and non-repeatability of these disruption events makes it impossible to collect data to obtain their probabilities. In this study, supply disruptions were regarded as uncertain events; supply chain uncertain disruption risk is defined and quantified based on the uncertainty theory, in which uncertain disruptions are characterized by the belief degree on account of expert estimation with duality, i.e., symmetry. Optimization models were constructed with the objective of minimizing expected carbon emissions and costs, which optimizes the selection of suppliers with uncertain disruptions, and the assignment of manufacturers and customers. The properties of the model were analyzed, and the models were solved separately using different methods according to different decision criteria. Finally, the validity of the proposed models and algorithm were verified using a real case study of a glass manufacturing company. The findings exhibit promising insights for designing a sustainable and resilient supply chain network in an uncertain environment.

Carbon asset management has become an important way to reduce carbon costs. There are three main carbon asset management modes, including carbon quota compliance, carbon asset autonomous management, and custody. A key challenge faced by capital-constrained enterprises is how to scientifically select a carbon asset management mode based on actual needs. This paper considers the impacts of setup costs of carbon asset management departments, carbon asset appreciation, custody costs, and revenue sharing, maximizes the enterprises’ profits, develops optimization models for three modes, and provides the optimal low-carbon production strategies. This paper provides evidence for enterprises to choose optimal modes under different capital levels and carbon emissions by comparing modes. The conclusions are as follows. When setup costs are low, the carbon asset autonomous management mode is suggested for the optimal profit. With higher setup costs, either carbon asset compliance or custody mode is recommended. Under abundant capital, the carbon asset custody mode is suggested. Given a certain amount of capital and low setup costs, high-emission enterprises are encouraged to adopt the carbon asset autonomous management mode for a win–win of profits and carbon emissions. The carbon asset custody and compliance modes are suggested for medium-emission and low-emission enterprises, respectively.