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

Area of Science:

• Operations Research
• Supply Chain Management
• Ecology

Background:

• Supply networks face significant risks from inherent instabilities.
• Understanding the formation of these instabilities is crucial for risk mitigation.
• Inventory dynamics are particularly susceptible to disruptions caused by network structure.

Purpose of the Study:

• To investigate topology-induced instabilities in supply network inventory dynamics.
• To analyze how network structure influences supply chain stability.
• To identify specific network configurations that lead to instabilities.

Main Methods:

• Utilized generalized modeling, a minimally specified approach from ecology.
• Mapped functional dependencies of production rates on inventory levels using elasticity parameters.
• Performed bifurcation analysis to assess the impact of elasticities on stability.

Main Results:

• Dyads and serial supply chains demonstrate immunity to topology-induced instabilities.
• A simple triadic network, with a supplier serving multiple tiers, exhibits instabilities.
• Identified saddle-node, Hopf, and global homoclinic bifurcations in triadic networks.
• Observed diverse dynamical behaviors including convergence, divergence, oscillations, and co-existing dynamics.

Conclusions:

• Network topology significantly influences supply chain stability and risk.
• Triadic network structures introduce unique instability risks not present in simpler chains.
• Findings offer insights for managing supply chain dynamics and mitigating risks through network design.