A review of continuum models for production flows involving a large number of items and a large number of production stages is presented. The basic heuristic model is based on mass conservation and state equations for the relationship between the cycle time and the amount of work in progress in a factory. Heuristic extensions lead to advection diffusion equations and to capacity limited fluxes. Comparisons between discrete event simulations, factory data, numerical solutions of the heuristic PDEs and queuing network models are made. A first principle model based on the Boltzman equation for a probability density of a production lot, evolving in time and production stages is shown to lead to an advection diffusion equation.
