Integrating minimum cost flow and capacitated location in global supply chains under uncertainty

Modern supply chain networks face significant challenges in balancing operational efficiency and resilience under diverse real-world uncertainties such as demand fluctuations and disruptions. To address these complexities, this study proposes an Integrated Capacitated Facility Location and Minimum Cost Flow Problem under Multi-Uncertainty (ICLMF-MU). The integrated multi-objective optimization model simultaneously optimizes total cost, service utility, and total risk while accounting for unmet demands and disruptions in supply chain network design. To deal with the NP-hardness of the problem, we propose an enhanced hybrid non-dominated sorting genetic algorithm II (NSGA-II). A novel bi-level evaluation strategy couples an exact linear programming (LP) solver to maintain flow balance with a greedy heuristic as a fallback mechanism. Through a three-stage benchmarking process, the algorithm demonstrates strong convergence and consistent performance. A large-scale numerical study (100 nodes) evaluates performance under diverse global trade environments, contrasting cost-sensitive goods against strategic resources prone to export controls. Pareto frontier trade-off analysis identifies a distinct Criticality Premium, confirming that strategic sectors require a substantially greater investment to withstand sanctions compared to commercial scenarios. Furthermore, regret analysis exposes a Robustness Paradox: the min-risk strategy exhibits the highest operational regret and lowest real-world resilience by limiting network scope. In contrast, the max-utility and balanced strategies demonstrate superior robustness. Sensitivity analysis confirms this implicit redundancy provides the structural capacity needed to absorb large demand surges, with the medical strategy demonstrating superior overall resilience under extreme demand. These findings imply that for critical supplies, true robustness is an emergent property of sufficient capacity investment rather than the optimization of theoretical risk indicators alone, offering guidance for designing resilient networks in an unstable global trade landscape.