Physics, Stability and Dynamics of Supply Networks

Details Physics, Stability and Dynamics of Supply Networks Physics, Stability and Dynamics of Supply Networks

2004-05-11

arxiv.org/abs/cond-mat/0405230v1

Physical Review E 70, 066116 (2004)

Physics

Condensed Matter

Statistical Mechanics

For related work see http://www.helbing.org

Scientific paper

10.1103/PhysRevE.70.066116

We show how to treat supply networks as physical transport problems governed by balance equations and equations for the adaptation of production speeds. Although the non-linear behaviour is different, the linearized set of coupled differential equations is formally related to those of mechanical or electrical oscillator networks. Supply networks possess interesting new features due to their complex topology and directed links. We derive analytical conditions for absolute and convective instabilities. The empirically observed "bull-whip effect" in supply chains is explained as a form of convective instability based on resonance effects. Moreover, it is generalized to arbitrary supply networks. Their related eigenvalues are usually complex, depending on the network structure (even without loops). Therefore, their generic behavior is characterized by oscillations. We also show that regular distribution networks possess two negative eigenvalues only, but perturbations generate a spectrum of complex eigenvalues.

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