Continuous models for production flows

We model high volume, multi-stage continuous production flow through a re-entrant factory. We approximate production volume through a continuous density variable and production stages through a continuous completion variable. Ideas from traffic modeling and gas dynamics are adapted to generate a hierarchy of PDE models. All of these models are variations of nonlinear nonlocal hyperbolic conservation laws. They allow extremely fast and accurate simulations. Large scale discrete event simulation based on an INTEL factory are presented. The data are analyzed to generate a parameterization for the PDE model of this factory. A diffusion coefficient is determined by looking at the spread of throughput times in a factory run at steady state.