Data-driven robust optimization of dual-channel closed-loop supply chain network design considering uncertain demand and carbon cap-and-trade policy

With the popularization of Internet applications and the development of e-commerce, the number of online consumers is constantly increasing. This study aims to provide a framework for a sustainable and environ-mentally friendly closed-loop supply chain network with dual-channel (online channel and offline channel). The goal is to assist managers in making economically and environmentally sustainable decisions. Accordingly, a multi-period mathematical model is designed to address the challenges of the appliance industry, which faces uncertain demand. The model considers the carbon cap-and-trade policy, the regional protection policy of the retailer, and multiple transport modes in the design of the supply chain network. To handle demand uncertainty, we propose a robust model that utilizes a data-driven polyhedral uncertainty set based on principal component analysis and kernel smoothing methods and transforms the robust model into a mixed-integer linear program-ming problem. Additionally, we present a two-stage adaptive genetic algorithm to effectively tackle the large-scale and complex nature of the supply chain network. Extensive computations are performed to verify the al-gorithm's effectiveness. Finally, sensitivity analysis is conducted on key parameters to gain valuable insights. The results demonstrate that an increase in online consumers can significantly reduce stockouts, while an increase in uncertain demand leads to a substantial increase in the total cost.