Abstract
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.
Similar content being viewed by others
References
Zheng, J.F., Gao, Z.Y., Zhao, X.M.: Modeling cascading failures in congested complex networks. Physica A 385(2), 700–706 (2007)
Qian, Y., Wang, B., Xue, Y., Zeng, J., Wang, N.: A simulation of the cascading failure of a complex network model by considering the characteristics of road traffic conditions. Nonlinear Dyn. 80(1–2), 413–420 (2015)
Wang, J., Liu, Y.H., Zhu, J.Q., Jiao, Y.: Model for cascading failures in congested Internet. J. Zhejiang. Univ. SC. A 9(10), 1331–1335 (2008)
Ren, H.P., Song, J., Yang, R., Baptista, M.S., Grebogi, C.: Cascade failure analysis of power grid using new load distribution law and node removal rule. Physica A 442, 239–251 (2016)
Seo, J., Mishra, S., Li, X., Thai, M.T.: Catastrophic cascading failures in power networks. Theor. Comput. Sci. 607, 306–319 (2015)
Yin, R.R., Liu, B., Liu, H.R., Li, Y.Q.: The critical load of scale-free fault-tolerant topology in wireless sensor networks for cascading failures. Physica A 409, 8–16 (2014)
Liu, H.R., Dong, M.R., Yin, R.R., Han, L.: Cascading failure in the wireless sensor scale-free networks. Chinese Phys. B 24(5), 050506 (2015)
Shuang, Q., Zhang, M., Yuan, Y.: Node vulnerability of water distribution networks under cascading failures. Reliab. Eng. Syst. Safe. 124, 132–141 (2014)
Wu, J.J., Sun, H.J., Gao, Z.Y.: Cascading failures on weighted urban traffic equilibrium networks. Physica A 386(1), 407–413 (2007)
Guimera, R., Arenas, A., Díaz-Guilera, A., Giralt, F.: Dynamical properties of model communication networks. Phys. Rev. E 66(2), 026704 (2002)
Sachtjen, M.L., Carreras, B.A., Lynch, V.E.: Disturbances in a power transmission system. Phys. Rev. E 61(5), 4877 (2000)
Motter, A.E., Lai, Y.C.: Cascade-based attacks on complex networks. Phys. Rev. E 66, 065102 (2002)
Crucitti, P., Latora, V., Marchiori, M.: Model for cascading failures in complex networks. Phys. Rev. E 69, 045104 (2004)
Wang, J., Zhang, C., Huang, Y., Xin, C.: Attack robustness of cascading model with node weight. Nonlinear Dyn. 78(1), 37–48 (2014)
Li, S., Li, L., Yang, Y., Luo, Q.: Revealing the process of edge-based-attack cascading failures. Nonlinear Dyn. 69(3), 837–845 (2012)
Wang, J.: Mitigation of cascading failures on complex networks. Nonlinear Dyn. 70(3), 1959–1967 (2012)
Jun, L., Xiong, Q.Y., Shi, X., Wang, K., Shi, W.R.: Load-redistribution strategy based on time-varying load against cascading failure of complex network. Chinese Phys. B 24(7), 076401 (2015)
Ash, J., Newth, D.: Optimizing complex networks for resilience against cascading failure. Physica A 380, 673–683 (2007)
Kim, D.H., Motter, A.E.: Fluctuation-driven capacity distribution in complex networks. New J. Phys. 10(5), 053022 (2008)
Arqub, O.A., Abo-Hammour, Z.: Numerical solution of systems of second-order boundary value problems using continuous genetic algorithm. Inform. Sci. 279, 396–415 (2014)
Ivanov, D.: An adaptive framework for aligning (re) planning decisions on supply chain strategy, design, tactics, and operations. Int. J. Prod. Res. 48(13), 3999–4017 (2010)
Christopher, M., Peck, H.: Building the resilient supply chain. Int. J. Logist. Manag. 15(2), 1–14 (2004)
Blackhurst, J., Wu, T., O’grady, P.: A network-based decision tool to model uncertainty in supply chain operations. Prod. Plan Control 18(6), 526–535 (2007)
Bellamy, M., Basole, R.: Network analysis of supply chain systems: a systematic review and future research. Syst. Eng. 16(2), 235–249 (2013)
Rice, J.B., Caniato, F.: Building a secure and resilient supply network. Supply Chain Manag. Rev. 7(5), 22–30 (2003)
Jüttner, U., Maklan, S.: Supply chain resilience in the global financial crisis: an empirical study. Supply Chain Manag. 16(4), 246–259 (2011)
Hearnshaw, E., Wilson, M.: A complex network approach to supply chain network theory. Int. J. Oper. Prod. Man. 33(4), 442–469 (2013)
Tang, L., Jing, K., He, J., Stanley, H.E.: Robustness of assembly supply chain networks by considering risk propagation and cascading failure. Physica A 459, 129–139 (2016)
Yan, Y., Liu, X., Zhuang, X.T.: Cascading failure model and method of supply chain based on complex network. J. Shanghai Jiaotong Univ. 44(3), 322–325 (2010)
Zeng, Y., Xiao, R.B.: Modelling of cluster supply network with cascading failure spread and its vulnerability analysis. Int. J. Prod. Res. 52(23), 6938–6953 (2014)
Geng, L., Xiao, R.B., Xie, S.S.: Research on self-organization in resilient recovery of cluster supply chains. Discrete Dyn. Nat. Soc. 2013, 1–11 (2013)
Tang, L., Jing, K., He, J., Stanley, H.E.: Complex interdependent supply chain networks: cascading failure and robustness. Physica A 443, 58–69 (2016)
Wang, Y.C., Xiao, R.B.: An ant colony based resilience approach to cascading failures in cluster supply network. Physica A 462, 150–166 (2016)
Sheffi, Y.: Supply chain management under the threat of international terrorism. Int. J. Logist. Manag. 12(2), 1–11 (2001)
Norrman, A., Jansson, U.: Ericsson’s proactive supply chain risk management approach after a serious sub-supplier accident. Int. J. Phys. Distrib. Logist. Manag. 34(5), 434–456 (2004)
Pettit, T.J., Fiksel, J., Croxton, K.L.: Ensuring supply chain resilience: development of a conceptual framework. J. Bus. Logist. 31(1), 1–21 (2010)
Barrat, A., Barthelemy, M., Pastor-Satorras, R., Vespignani, A.: The architecture of complex weighted networks. Proc. Natl. Acad. Sci. USA 101(11), 3747–3752 (2004)
Macdonald, P.J., Almaas, E., Barabási, A.L.: Minimum spanning trees of weighted scale-free networks. EPL Europhys. Lett. 72(2), 308 (2005)
Boccaletti, S., Latora, V., Moreno, Y., Chavez, M., Hwang, D.: Complex networks: structure and dynamics. Physica A 424, 175–308 (2006)
Motter, A.E.: Cascade control and defense in complex networks. Phys. Rev. Lett. 93(9), 098701 (2004)
Duan, D.L., Ling, X.D., Wu, X.Y., OuYang, D.H., Zhong, B.: Critical thresholds for scale-free networks against cascading failures. Physica A 416, 252–258 (2014)
Duan, D.L., Wu, X.Y.: Cascading failure of scale-free networks based on a tunable load redistribution model. Acta Phys. Sin. 63(3), 030501 (2014)
Wang, J.W., Rong, L.L.: A model for cascading failures in scale-free networks with a breakdown probability. Physica A 388, 1289–1298 (2009)
Liu, J., Xiong, Q., Shi, X., Wang, K., Shi, W.: Robustness of complex networks with an improved breakdown probability against cascading failures. Physica A 456, 302–309 (2016)
Chopra, S., Sodhi, M.: Managing risk to avoid supply-chain breakdown. MIT Sloan Manag. Rev. 46(1), 53–61 (2004)
Kinney, R., Crucitti, P., Albert, R., Latora, V.: Modeling cascading failures in the North American power grid. Eur. Phys. J. B 46(1), 101–107 (2005)
Crucitti, P., Latora, V., Marchiori, M.: A topological analysis of the Italian electric power grid. Physica A 338(1), 92–97 (2004)
Latora, V., Marchiori, M.: Efficient behavior of small-world networks. Phys. Rev. Lett. 87(19), 198701 (2001)
Choi, T.Y., Hong, Y.: Unveiling the structure of supply networks: case studies in Honda, Acura, and DaimlerChrysler. J. Oper. Manag. 20(5), 469–493 (2002)
Hur, D., Hartley, J.K., Hahn, C.K.: An exploration of supply chain structure in Korean companies. Int. J. Logist. Res. App. 7(2), 151–164 (2004)
Sun, H., Wu, J.: Scale-free characteristics of supply chain distribution networks. Mod. Phys. Lett. B 19(17), 841–850 (2005)
Barabási, A.L., Albert, R.: Emergence of scaling in random networks. Science 286(5439), 509–512 (1999)
Klemm, K., Eguiluz, V.M.: Growing scale-free networks with small-world behavior. Phys. Rev. E 65(5), 057102 (2002)
Cardoso, S.R., Barbosa-Póvoa, A.P., Relvas, S., Novais, A.Q.: Resilience metrics in the assessment of complex supply-chains performance operating under demand uncertainty. Omega 56, 53–73 (2015)
Acknowledgements
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.
Author information
Authors and Affiliations
Corresponding author
Ethics declarations
Conflict of interest
No conflict of interest exists in the submission of this manuscript.
Rights and permissions
About this article
Cite this article
Wang, Y., Zhang, F. Modeling and analysis of under-load-based cascading failures in supply chain networks. Nonlinear Dyn 92, 1403–1417 (2018). https://doi.org/10.1007/s11071-018-4135-z
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s11071-018-4135-z