Unearthing vulnerability of supply provision in logistics networks to the black swan events: Applications of entropy theory and network analysis

 Over the past two decades, the fragility of modern Logistics Networks (LNs) has been exposed by unexpected events with extreme impacts outside the realm of regular expectations, which are known as the black swan events. As a response to the growing dysfunctions of the global LNs due to the detrimental effects of the black swan events, this article develops a quantitative vulnerability assessment method by paying simultaneous attention to various structural properties of these networks. It adopts three prototypical examples of centrality indices known as betweenness, closeness, and eigenvector centrality. This work also develops a vulnerability index from the joint entropy of centrality values, which can be interpreted as a certain extent of risk to disruptions in supply provision in LNs. The proposed entropy-based vulnerability index enables a far more accurate analysis of vulnerability by measuring the degree of homogeneity and heterogeneity of centrality values. The suggested index is considered as an objective function that must be minimized to reduce the deleterious effects of the black swan events. To illustrate the proposed vulnerability assessment method, this paper analyzes a real-world global maritime network, concluding that the juxtaposition of centrality measures provides a richer insight into the vulnerability analysis of LNs. The results also favor the fact that increasing the homogeneity of a network through decentralization yields lower vulnerability and builds extra robustness into the networks.