Hybrid multi-criteria decision-making and quantum-inspired metaheuristics for large-scale supply chain network optimisation

Abstract Large-scale supply chain network (SCN) optimization faces significant challenges due to multi-objective trade-offs, dynamic demand patterns, and computational scalability issues. This paper proposes a hybrid optimisation framework that integrates quantum particle swarm optimisation (QPSO) with the fuzzy analytical hierarchy process (FAHP) to handle conflicting objectives, including cost minimisation, sustainability enhancement, and network resilience improvement. The framework incorporates a post-hoc explainability module based on Shapley value analysis, applied after QPSO convergence, providing interpretable insights into facility locations, product flows, and inventory decisions to support transparent stakeholder communication. The framework is evaluated on fifteen benchmark instances spanning 50 to 500 nodes, together with one anonymised industrial case study. Across the benchmark suite, the framework achieved an average cost reduction of 12.4%, an average sustainability improvement of 18.3%, and an average social-impact improvement of 14.6% relative to a tuned standard PSO baseline. In the industrial case study, the optimized configuration reduced operating cost by 12.4%, lowered carbon emissions by 15.7%, and increased employment by 12.4%; the recurrence of the value 12.4% across the benchmark cost reduction, the case-study cost reduction, and the case-study employment increase is coincidental and not a transcription or copy-paste error: each figure is computed independently from a different quantity (a benchmark average over fifteen instances, an absolute cost change of $18.5M to $16.2M, and a headcount change of 1,247 to 1,402 jobs, respectively), as detailed in the Discussion. All industrial case study improvements are statistically significant (cost and carbon emissions reductions: p < 0.001; employment creation and service-level improvement: p < 0.05; Wilcoxon signed-rank test), as detailed in Table 12. The benchmark instances span regional, multi-regional, large-scale, and extreme-scale network configurations (50 to 500 nodes), with detailed generation parameters and dataset specifications provided in the experimental setup. The proposed QPSO reduced the number of iterations required for convergence by 75.8% compared to standard PSO and achieved up to 3.12× faster runtime for networks with over 500 nodes while maintaining solution quality comparable to or better than the specific tuned metaheuristic baselines evaluated in this study; because no exact (MILP) solver baseline was computed, these solution-quality results are reported relative to those baselines rather than against a certified optimality bound. All benchmark improvements are statistically significant (p < 0.001, Wilcoxon signed-rank test); the bootstrapped 95% confidence interval for the cost-reduction result is [11.4%, 14.0%] (Cohen′s d = 2.84). Real-world validation using data from a global electronics manufacturer indicates practical applicability, with estimated annual cost savings of $2.3M, a 15.7% reduction in carbon emissions, and a 19.4% improvement in network resilience; one-time implementation costs are estimated at $1.83M--$2.43M with a payback period of 9.5--12.7 months. Solution quality on the full 50–500-node suite is reported relative to those tuned metaheuristic baselines; exact-solver verification using the CBC MILP solver on representative small instances (up to 10 nodes; Table 4, Section 5.1.4) confirmed that the model is well-posed and that QPSO solutions fall within 3% of certified optima on those instances. This exact-solver scope is acknowledged as a limitation: verification on instances beyond 10 nodes is computationally intractable with the available hardware, and solution quality for the full benchmark suite is therefore reported relative to identically tuned metaheuristic baselines rather than against certified optima.