A Multi-Objective Optimization Framework for Cross-Supply-Chain Integration: An Empirical Application to Tea and Ceramics

Cross-supply-chain integration involves complex interdependencies among industrial subsystems, constrained resource allocation, and conflicting performance objectives. This study develops a multi-objective optimization (MOO) decision-support framework that integrates relationship identification, synergy diagnosis, decision-variable transformation, multi-objective candidate generation and representative-path identification, and sensitivity and local robustness evaluation. The proposed framework maps relational information derived from Grey Relational Analysis (GRA) into a Cross-Supply-Chain Grey Relational Network (CS-GRN) to identify key coordination nodes. Furthermore, it incorporates a Coupling Coordination Degree Model (CCDM)-based metric as a decision-dependent synergistic performance function within the multi-objective optimization (MOO) formulation. Improvement magnitudes of selected critical nodes are formulated as continuous decision variables to balance synergistic performance, green sustainability, adjustment costs, and systemic balance. The tea and ceramics industries serve as an empirical case study based on time-series supply chain indicators from 2010 to 2025. The Non-dominated Sorting Genetic Algorithm II (NSGA-II) is employed to generate an internally non-dominated candidate archive, while representative improvement paths are identified through preference-based continuous numerical optimization and independently examined using a large-scale Sobol low-discrepancy benchmark. The empirical results identify critical cross-chain linkages and demonstrate clear trade-offs among the four objectives. Normalized adjustment-intensity scenario analysis further shows that decision priorities vary with allowable adjustment intensity, while weight-perturbation analysis characterizes the local sensitivity of the fixed baseline compromise path. Additional adjustment-cost coefficient sensitivity analysis indicates that the substantive interpretation of the representative improvement paths remains stable across the tested coefficient and proxy-specification ranges. The proposed framework provides an interpretable quantitative approach for linking cross-chain relationship identification with multi-objective decision-making in small-sample, multi-indicator industrial systems.