Just in time vs. all in sync: An analysis of two types of synchronization in a minimal model of machine activity in industrial production

The notion of synchronization in logistics is distinct from that encountered in the natural sciences and, in particular, in physics where synchronization rather means that the different parts of the system operate in unison. In logistics, synchronization is often associated with a ‘just in time’ paradigm in supply and production systems. A perfect logistics synchronization therefore is that the activity in a process triggers activity in a neighboring process without delay or queuing. Globally, this type of synchronization can be envisioned as a wave of activity running through the logistics chain. Our goal is a deeper theoretical understanding of these two types of synchronization, i.e. physics synchronization and logistics synchronization, as well as their interplay in the context of production systems where both types may coexist. We employ a minimal model of propagating excitations (representing machine activity) in a graph (representing a production network where each node is a machine). We evidence a strong change in the relationship between the two types of synchronization as a function of two parameters: the machine setup time and the random machine activation representing scheduling conflicts. Comparison of numerical results with pair-approximation mean-field predictions gives mechanistic insights into the synchronization behavior. Using robustness against network connectivity failures as a performance indicator, we find that, depending on the dynamical regime and network architecture, both logistics and physics synchronization can serve as easy-to-measure indicators of systemic performance.