Cybernetic Control in a Supply Chain: Wave Propagation and Resonance

The cybernetic control and management of production can be improved by an understanding of the dynamics of the supply chains for the production organizations. This paper describes an attempt to better understand the dynamics of a linear supply chain through the application of the normal mode analysis technique of physics. A model is considered in which an organization’s response to a perturbation from the steady state is affected by the inertia which the company naturally exhibits. This inertia determines how rapidly an organization can respond to deviations from the steady state of its own inventories and those of the two organizations immediately preceding and following it in the chain. The model equations describe the oscillatory phenomena of the naturally occurring normal modes in the chain, in which waves of deviations from the steady state situation travel forward and backwards through the chain. It would be expected that the most effective cybernetic control occurs when resonant interventions cause either amplification or damping of the deviations from the steady state.