Efficient multi-objective modeling of sustainable supply chains

Purpose-This study tackles the challenge of designing sustainable supply chain networks under uncertainty and system complexity. Existing approaches largely depend on fixed stochastic techniques that struggle to capture the dynamic nature of real-world operations. As supply chains evolve to handle multiple products, periods and decision levels, traditional optimization models become computationally intensive and less adaptable. The aim is to introduce a scalable decision-support framework that simultaneously optimizes economic, environmental and reliability objectives while effectively modeling demand and facility uncertainties. Design/methodology/approach-We propose fuzzy enhanced multi-objective optimization with surrogates for sustainable supply chains (FEMOS-SC), a hybrid framework integrating fuzzy logic, the e-constraint method and machine-learning-based surrogate modeling. Fuzzy sets are applied to model uncertainty in demand and reliability, while the e-constraint method enables flexible Pareto trade-off generation among sustainability goals. To improve computational efficiency, surrogate models are trained for complex objective functions, reducing overall solution time. The framework is validated using a publicly available dataset enhanced with synthetic fuzzy inputs and temporal dimensions, and benchmarked against existing optimization models. Findings-FEMOS-SC maintains Pareto quality across all objectives and achieves balanced outcomes at a minimum cost of 4.00-5.20 M USD, low emissions of 2.00-3.30 kt CO2 and reliability ranging from 0.77 to 0.94. Increasing reliability thresholds leads to moderate rises in cost and emissions, revealing realistic and interpretable trade-offs. The surrogate-assisted structure notably reduces computational effort compared with conventional approaches, confirming the framework's efficiency in uncertain environments. Originality/value-This study contributes a novel integration of fuzzy uncertainty modeling, e-constraint multi-objective optimization and surrogate learning within a unified framework. Unlike existing approaches that address these aspects in isolation, FEMOS-SC jointly ensures scalability, adaptability and computational efficiency for complex supply chains. It offers both theoretical and practical value by enabling planners to efficiently analyze cost, emission and reliability trade-offs, making it a suitable decision-support tool for realtime sustainable logistics planning.