Physics, stability, and dynamics of supply networks

Area of Science:

• Operations Research
• Network Science
• Supply Chain Management

Background:

• Supply networks exhibit complex dynamics, including the bullwhip effect, which is poorly understood.
• Existing models often fail to capture the inherent physical transport and adaptation behaviors within supply chains.

Purpose of the Study:

• To model supply networks as physical transport problems governed by balance and production speed adaptation equations.
• To analyze the stability conditions and dynamic behavior of complex supply networks.
• To provide a theoretical explanation for the bullwhip effect and generalize it.

Main Methods:

• Treating supply networks as physical transport systems.
• Linearizing coupled differential equations governing network dynamics.
• Deriving analytical conditions for absolute and convective instabilities.
• Analyzing eigenvalues of the network structure.

Main Results:

• The linearized supply network equations are formally related to oscillator networks.
• Analytical conditions for absolute and convective instabilities were derived.
• The bullwhip effect is explained as a resonance-driven convective instability.
• Generalized instability analysis applies to arbitrary supply networks, revealing complex eigenvalues and oscillatory behavior.

Conclusions:

• Supply networks can be effectively modeled as physical transport systems.
• Network topology and resonance effects are key drivers of supply chain instabilities like the bullwhip effect.
• The derived framework provides a generalized understanding of supply network dynamics and stability.