Nonlinear Dynamics

, Volume 92, Issue 3, pp 1403–1417 | Cite as

Modeling and analysis of under-load-based cascading failures in supply chain networks

  • Yingcong Wang
  • Fengpeng Zhang
Original Paper


The phenomena of cascading failures often happen in complex networks. In most infrastructure networks, the subsequent failures of nodes are caused by overload and many overload cascading failure models are developed. Recently, some of these models are adopted to investigate the cascading failure phenomenon in supply chain networks, which cannot capture the real case very well. The subsequent failures of upriver/downriver firms in supply chain networks are triggered by the decreased product demand/material supply, i.e., under-load cascading failures take place. Based on the under-load failures, this paper proposed a more realistic cascading failure model for supply chain networks. In this model, the node firms are characterized by capacities with upper bound parameter \(\alpha \) and lower bound parameter \(\beta \). Results showed that \(\alpha \) has a negative relationship with cascading size, while \(\beta \) has a positive relationship with cascading size. In addition, cascading size is mainly determined by \(\beta \), and \(\alpha \) helps mitigate the cascading propagation. In reality, \(\alpha \) is correlated with the spare production capacity of firms, the holding cost of which is high under stable operation of the market. \(\beta \) is related to the core competence of firms, which is hard to improve in the short term. Our work may be helpful for developing the cascade control and defense strategies in supply chain networks.


Cascading failure Supply chain network Under-load Load capacity 



We gratefully acknowledge helpful suggestions from the anonymous reviewers. This work is supported by the National Natural Science Foundation of China (Grant No. 61702463) and the Doctoral Scientific Research Foundation of Zhengzhou University of Light Industry.

Compliance with ethical standards

Conflict of interest

No conflict of interest exists in the submission of this manuscript.


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Authors and Affiliations

  1. 1.School of Electrical and Information EngineeringZhengzhou University of Light IndustryZhengzhouChina
  2. 2.Otis Electric Elevator Co., LtdHangzhouChina

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