In this book, continuum models of re-entrant production systems are developed that treat the ?ow of products in analogy to traffic ?ow. Specifically, the dynamics of material ?ow through a re - entrant factory via a parabolic conservation law is modeled describing the product density and ?ux in the factory. The basic idea underlying the approach is to obtain transport coefficients for ?uid dynamic models in a multiscale setting simultaneously from Monte Carlo simulations and actual observations of the physical system, i.e. a production factory. Since partial differential equation (PDE) - conservation laws are successfully used for modeling the dynamical behavior of product ?ow in manufacturing systems, a highly re-entrant manufacturing systems is modeled using a diffusive PDE. It is demonstrated that PDE models are preferable to simulate large and complex production systems, because they are accurate, fast, and amenable themselves to optimization, which is a quite important advantage for a mathematical model. The work brings out an almost universally applicable tool to provide rough estimates of the behavior of complex production systems in non-equilibrium regimes.

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