Physics, stability, and dynamics of supply networks
- 7 December 2004
- journal article
- research article
- Published by American Physical Society (APS) in Physical Review E
- Vol. 70 (6), 066116
- https://doi.org/10.1103/physreve.70.066116
Abstract
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 nonlinear behavior is different, the linearized set of coupled differential equations is formally related to those of mechanical or electrical oscillator networks. Supply networks possess interesting features due to their complex topology and directed links. We derive analytical conditions for absolute and convective instabilities. The empirically observed "bullwhip 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 damped or growing oscillations. We also show that regular distribution networks possess two negative eigenvalues only, but perturbations generate a spectrum of complex eigenvalues.Keywords
This publication has 20 references indexed in Scilit:
- Network-induced oscillatory behavior in material flow networks and irregular business cyclesPhysical Review E, 2004
- Modeling Dynamics of Information NetworksPhysical Review Letters, 2003
- Economic production as chemistryIndustrial and Corporate Change, 2003
- Modelling supply networks and business cycles as unstable transport phenomenaNew Journal of Physics, 2003
- Measuring and avoiding the bullwhip effect: A control theoretic approachEuropean Journal of Operational Research, 2003
- Transfer function analysis of forecasting induced bullwhip in supply chainsInternational Journal of Production Economics, 2002
- Statistical mechanics of complex networksReviews of Modern Physics, 2002
- Topological Evolution of Dynamical Networks: Global Criticality from Local DynamicsPhysical Review Letters, 2000
- Controlling chaos in a switched arrival systemSystems & Control Letters, 1995
- Deterministic chaos in the beer production‐distribution modelSystem Dynamics Review, 1988