Finding Sustainable Clusters in Supply Chains Dynamics via Graph Partitioning

This paper regards the clustering problem of supply chains. From a mathematical point of view, it is well-known that they may be modeled by connected graphs. Through this work, following the algorithm in [9], we address our attention on finding the smallest possible perturbation of the adjacency matrix of the graph associated to such supply chain, such that makes it disconnected. On a numerical analysis perspective, this problem consists in studying suitable approximations of a gradient system via spectral theory. Differently from standard methods like NMF or spectral clustering, the presented approach enables structured and interpretable perturbations, allowing for targeted policy analysis and scenario-based cluster exploration. Finally, selected numerical experiments on the special case of Japanese automotive industries will be reported.