Modeling Supply Networks and Business Cycles as Unstable Transport Phenomena

Physical concepts developed to describe instabilities in traffic flows can be generalized in a way that allows one to understand the well-known instability of supply chains (the so-called ``bullwhip effect''). That is, small variations in the consumption rate can cause large variations in the production rate of companies generating the requested product. Interestingly, the resulting oscillations have characteristic frequencies which are considerably lower than the variations in the consumption rate. This suggests that instabilities of supply chains may be the reason for the existence of business cycles. At the same time, we establish some link to queuing theory and between micro- and macroeconomics.Comment: For related work see http://www.helbing.or

Chaos and complexity in a simple model of production dynamics

We consider complex dynamical behavior in a simple model of production dynamics, based on the Wiendahl’s funnel approach. In the case of continuous order flow a model of three parallel funnels reduces to the one-dimensional Bernoulli-type map, and demonstrates strong chaotic properties. The optimization of production costs is possible with the OGY method of chaos control. The dynamics changes drastically in the case of discrete order flow. We discuss different dynamical behaviors, the complexity and the stability of this discrete system

DYNAMICS BETWEEN ORDER AND CHAOS IN A SIMPLE REENTRANT MODEL OF PRODUCTION DYNAMICS

We consider a simple reentrant model of a manufacturing process, consisting of one machine at which two different types of items have to be processed. The model is completely deterministic: all delivery and processing times are fixed, and are generally incommensurate. Dependent on the arrival and processing times, a queue of waiting items grows, remains constant or disappears. We demonstrate that the dynamics of the system crucially depends on the queue type. Complexity is most observed for the case of growing queue. We characterize this dynamics between order and chaos with the T-entropy and the autocorrelation function