Kinetic and fluid models for supply chains supporting policy attibutes

We consider a supply chain consisting of a sequence of buffer queues and processors with certain throughput times and capacities. In a previous work, we have derived a hyperbolic conservation law for the part density and flux in the supply chain. In the present paper, we introduce internal variables (named attributes: e.g. the time to due-date) and extend the previously defined model into a kinetic-like model for the evolution of the part in the phase-space (degree-of-completion, attribute). We relate this kinetic model to the hyperbolic one through the moment method and a ’monokinetic’ (or single-phase) closure assumption. If instead multi-phase closure assumptions are retained, richer dynamics can take place. In a numerical section, we compare the kinetic model (solved by a particle method) and its two-phase approximation and demonstrate that both behave as expected.