Slowing for Sustainability: A Hybrid Optimization and Sensitivity Analysis Framework for Taiwan’s Cross-Border E-Commerce

Cross-border e-commerce logistics has long prioritized delivery speed; however, the trade-offs between cost-effectiveness, carbon emissions, risk, and financial performance have received relatively little attention. To address this deficiency, this study constructs a fuzzy nonlinear multi-objective optimization framework that integrates the particle swarm optimization (PSO) algorithm and the Sobol sensitivity analysis to capture the uncertainty and nonlinear dynamics of logistics systems. Using operational data from a Taiwanese cross-border e-commerce exporter from 2023 to 2024, empirical results show that extending the standard 25-day delivery time to an acceptable maximum of 32–37 days (i.e., an extension of 7–12 days) can reduce logistics costs per order by 22–38%, carbon emissions by 18–31%, and increase financial returns. Sobol sensitivity analysis further demonstrates that extended delivery time (T) is a significant controllable factor ( S 1 = 0.62 , S T 1 = 0.75 ). This study empirically verifies the profitability and sustainability of moderately T, challenges the current “speed-first” model, and provides a transparent, replicable, and scalable decision-making framework for promoting low-carbon, economically viable cross-border e-commerce supply chains.