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Revealing instabilities in a generalized triadic supply network: a bifurcation analysis

Ritterskamp, Daniel; Demirel, Guvan; MacCarthy, Bart; Rudolf, Lars; Champneys, Alan; Gross, Thilo

Authors

Daniel Ritterskamp

Guvan Demirel

Bart MacCarthy

Lars Rudolf

Alan Champneys

Thilo Gross



Abstract

Supply networks are exposed to instabilities and thus a high level of risk. To mitigate this risk, it is necessary to understand how instabilities are formed in supply networks. In this paper, we focus on instabilities in inventory dynamics that develop due to the topology of the supply network. To be able to capture these topology-induced instabilities, we use a method called generalized modeling, a minimally specified modeling approach adopted from ecology. This method maps the functional dependencies of production rates on the inventory levels of different parts and products, which are imposed by the network topology, to a set of elasticity parameters. We perform a bifurcation analysis to investigate how these elasticities affect the stability. First, we show that dyads and serial supply chains are immune to topology-induced instabilities. In contrast, in a simple triadic network, where a supplier acts as both a first and a second tier supplier, we can identify instabilities that emerge from saddle-node, Hopf, and global homoclinic bifurcations. These bifurcations lead to different types of dynamical behavior, including exponential convergence to and divergence from a steady state, temporary oscillations around a steady state, and co-existence of different types of dynamics, depending on initial conditions. Finally, we discuss managerial implications of the results.

Journal Article Type Article
Publication Date Jul 30, 2018
Print ISSN 1054-1500
Electronic ISSN 1089-7682
Publisher AIP Publishing
Peer Reviewed Peer Reviewed
Volume 28
Issue 7
Article Number 073103
APA6 Citation Ritterskamp, D., Demirel, G., MacCarthy, B., Rudolf, L., Champneys, A., & Gross, T. (2018). Revealing instabilities in a generalized triadic supply network: a bifurcation analysis. Chaos, 28(7), doi:10.1063/1.5026746. ISSN 1054-1500
DOI https://doi.org/10.1063/1.5026746
Publisher URL https://aip.scitation.org/doi/10.1063/1.5026746

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