Stochastic Multi-Objective Sustainable Supply Chain Network Design with Solar Energy and Water Footprint Integration: A Hybrid NSGA-II Approach

This study addresses the sustainable supply chain network design (SSCND) problem by integrating economic and environmental dimensions through a multi-objective, multi-echelon stochastic mathematical model. The proposed model focuses on simultaneously optimizing total cost, carbon emissions, water footprint, and renewable energy utilization. Strategic solar energy investment alongside facility location and sizing decisions are considered under uncertain conditions. Initially, a multi-product stochastic model is developed and solved utilizing the augmented epsilon constraint (AUGMECON2) method to obtain Pareto-optimal solutions for small-scale instances. For validation purposes, the exact solutions obtained using AUGMECON2 were used as the benchmark for the small-scale instance, while the proposed hybrid NSGA-II algorithm generated near-optimal solutions with deviations of 0.30%, 1.53%, 0.03%, and 0.0006% for total cost, carbon emissions, renewable energy use, and water footprint, respectively. Compared with the cost-oriented solution, the renewable energy-focused solution increased total cost by 76.33% while reducing the water footprint by 6.36% and carbon emissions by 3.57%. For medium- and large-scale instances, where exact solutions became computationally impractical, the hybrid NSGA-II algorithm remained applicable and generated feasible Pareto solutions within 59.05 s and 309.62 s, respectively. Overall, the presented framework provides a scalable decision-support tool for sustainable supply chain planning under uncertainty.