Robust optimization of uncertain E-commerce closed-loop supply chain networks under carbon policies.

With the rapid advancement of e-commerce, the increased transparency of product information and the proliferation of channel options have heightened demand uncertainty for businesses. Concurrently, policies such as seven-day no-reason returns and free return shipping have lowered the cost barrier for consumer returns, thereby exacerbating the unpredictability of return volumes. Additionally, unforeseen events like quality issues leading to reputation crises or geopolitical conflicts introduce further risks of supply chain disruptions for manufacturers. In light of global climate change and sustainability mandates, the government's restrictions on carbon emissions are increasingly stringent, however, most of the existing research focuses on traditional industries and lacks consideration of the cost and carbon policy synergies of e-commerce closed-loop supply chains under multiple uncertainties of demand-return-disruption, and there are difficulties in balancing the convergence efficiency with the quality of the solution set of the traditional multi-objective algorithms in the complex network optimization. Given these multifaceted challenges, this paper integrates uncertainties related to demand, returns, and disruption risks, innovatively proposes a dual-objective robust optimization framework, and constructs a dual-objective robust optimization model aimed at minimizing both total costs and carbon emissions within an e-commerce closed-loop supply chain network. The model uses the Box uncertainty set to characterize demand and return fluctuations, and a scenario-based approach to model the risk of facility disruptions in manufacturing centers for collaborative control of multiple sources of uncertainty. To address the limitations of the NSGA-II algorithm regarding convergence speed and population diversity, we incorporated the Prim algorithm into NSGA-II to enhance the initial population, and the Prim algorithm was used to improve the initial population and the Prim-NSGA II algorithm solution model was designed. Numerical experiments demonstrate that the proposed e-commerce closed-loop supply chain model exhibits strong robustness and validates its effectiveness. Compared to the traditional NSGA-II algorithm, the Prim-NSGAII algorithm improves the IGD index by 39.3% and the SM index by 69.1%, enhancing solution quality by 0.59% and 0.86%, respectively compared with that of the solution of the traditional NSGA-II algorithm, and the computation time is shorter. This study reveals the dynamic coupling relationship between carbon limitation policy and cost, which provides a basis for the government to formulate differentiated emission reduction strategies, and is significant for the optimization of e-commerce closed-loop supply chain networks under uncertain conditions.