A robust stochastic optimization approach for closed-loop supply chain design under uncertainty within the circular economy framework

Growing environmental volatility, increasing societal expectations, and resource scarcity have prompted organizations to redesign supply chains in line with circular economy (CE) principles. Closed-loop supply chains (CLSCs) enable product recovery and material recirculation but operate under significant uncertainty in demand, return flows, costs, and environmental factors. Despite extensive research, limited studies systematically compare alternative uncertainty-management paradigms within a unified CE-based CLSC framework. This study develops a multi-period bi-objective mathematical model for CLSC network design that minimizes total cost and carbon emissions under uncertainty. A scenario-based framework captures variability in demand, return rates, transportation costs, emission parameters, and secondary market conditions. From a business analytics perspective, the proposed framework functions as an advanced decision-support tool that enables data-driven evaluation of alternative uncertainty-management strategies for resilient and sustainable circular supply chains. The study contributes to frontier technology-enabled supply chain planning by integrating robust and stochastic optimization techniques for strategic network design under uncertainty. Four uncertainty-handling approaches Risk Neutral, Worst Case (Risk Averse), Hybrid, and Mulvey Robust Optimization (MRO) are comparatively evaluated. The Augmented Epsilon Constraint (AEC) method generates Pareto-optimal solutions, and the Relative Ideal Distance (RID) index identifies the preferred trade-off. Computational results show that MRO provides more stable performance and lower cost variability than alternative approaches, while maintaining favorable environmental outcomes. Sensitivity analysis highlights the dominant influence of recovery efficiency and return rates on system performance. The findings offer decision-support insights for designing cost-efficient, robust, and environmentally sustainable CLSC networks under uncertainty.