Parameter Extraction of Complex Production Systems via a Kinetic Approach

Abstract

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 conser- vation law is modeled describing the product density and ux in the factory. The basic idea underlying the approach is to obtain transport coeficients for uid dynamic models in a multi-scale setting simultaneously from Monte Carlo simulations and actual observations of the physical system, i.e. the factory. Since partial difeerential equation (PDE) conservation laws are successfully used for modeling the dynamical behavior of product ow in manufacturing systems, a re-entrant manufacturing system is modeled using a discusive PDE. The specifics of the production process enter into the velocity and discusion coeficients of the conservation law. The resulting nonlinear parabolic con- servation law model allows fast and accurate simulations. With the traffic ow-like PDE model, the transient behavior of the discrete event simulation (DES) model according to the averaged in ux, which is obtained out of discrete event experiments, is predicted. The work brings out an almost universally ap- plicable tool to provide rough estimates of the behavior of complex production systems in non-equilibrium regimes. © American Institute of Mathematical Sciences.