Observation Based PDE Models for Stochastic Production Systems

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.