We develop continuum models of re-entrant factory production systems that treat the flow of products in analogy to traffic flow. Specifically, we model the dynamics of material flow through a re-entrant factory via a parabolic conservation law describing the product density and flux in the factory. We first extract the transport coefficients, in particular, velocity and diffusion coefficients of the particles in the production system using discrete event simulation (DES). Since PDE-conservation laws are successfully used for modeling the dynamical behavior of product flow in manufacturing systems, we model the manufacturing system using a diffusive partial differential equation (PDE). The specifics of the production process enter into the velocity and diffusion coefficient of the conservation law. The resulting nonlinear parabolic conservation law model allows fast and accurate simulations.