A graph theory-based methodology for vulnerability assessment of supply chains using the life cycle inventory database

Owing to the growing number of risk factors that can be triggered by natural and manmade disasters, management of disruption risks in supply chains has become increasingly significant. Since the market concentration of raw material suppliers is a determinant of the supply disruption risk, identification of raw materials vital in a supply chain and concurrently whose markets are highly concentrated will help supply chain risk management. In this study, we develop a graph theory-based methodology for assessing supply chain vulnerability to disruption risks by using the life cycle inventory (LCI) database as a data source for nationwide supply chains. A supply chain structure, i.e., raw material-to-product links and overall chain, is modeled by a directed graph and its adjacency matrix, adapted from physical input–output data in the LCI database. The reachability components in the supply chain are identified by Boolean matrix calculations. Vulnerability indicators for each reachability component are determined on the basis of market concentration as measured by the Herfindahl–Hirschman Index in terms of domestic production regions and import partners as a proxy for the extent of supply disruption risks. The methodology developed is demonstrated using the national-level LCI database of Japan, and vulnerability factors are presented for 23 types of Japanese synthetic resins.