Fuzzy Robust Multi-Objective Model for Sustainable and Resilient Supply Chain Network Design Under Disruption Risks and Demand Uncertainty

In today’s volatile global environment, designing sustainable and resilient supply chain networks is essential for balancing economic efficiency, environmental responsibility, and social equity. This study presents a multi-objective mathematical model for sustainable supply chain network design under facility disruption risks and demand uncertainty. A fuzzy robust optimization approach, incorporating triangular fuzzy numbers, is employed to handle uncertain demand while balancing model optimality and feasibility. The proposed network includes production centers, disruption-prone retailers, and customers, addressing both strategic retailer selection and tactical product allocation. The model optimizes three core sustainability objectives: minimizing total operational costs, reducing carbon emissions, and mitigating product shortages. Small-scale instances (five test problems) are validated using the exact ϵ-constraint method, while larger-scale problems are solved using three multi-objective metaheuristic algorithms: NSGA-II, MOPSO, and MOEA/D. A comparative analysis based on standard performance metrics and supported by Analysis of Variance (ANOVA) indicates that while MOEA/D offers superior computational speed, MOPSO and NSGA-II exhibit higher solution quality and diversity, with MOPSO demonstrating an overall well-balanced performance. Furthermore, comprehensive sensitivity analyses highlight the model’s responsiveness to disruption probabilities, warehouse capacities, product perishability rates, and demand fluctuations. The results demonstrate that the proposed approach effectively reduces costs and shortages while maintaining environmental targets, providing decision-makers with a practical and scalable framework for resilient supply chain design under real-world uncertainties.