| Continuum models of re-entrant production systems are developed that treat the flow of products in analogy to traffic flow. Specifically, the dynamics of material flow through a re-entrant factory via a parabolic conservation law is modeled describing the product density and flux in the factory. The basic idea underlying the approach is to obtain transport coefficients for fluid 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 differential equation (PDE) - conservation laws are successfully used for modeling the dynamical behavior of product flow in manufacturing systems, a re-entrant manufacturing system is modeled using a diffusive PDE. Firstly, the transport coefficients; namely, velocity and diffusion coefficients of the particles are extracted in the production system using discrete event simulation (DES). The specifics of the production process enter into the velocity and diffusion coefficients of the conservation law. The resulting nonlinear parabolic conservation law model allows fast and accurate simulations. With the traffic flow-like PDE model, the transient behavior of the DES model according to the averaged influx, which is obtained out of discrete event experiments, is predicted. As the PDE and DES models are compared in terms of WIP (Work in Progress) levels and fluxes as functions of time at each machine stage, the agreement of the two models is substantiated. In this dissertation, it is demonstrated that PDE models are preferable to simulate large and complex production systems, because they are accurate, fast, and can be optimized via constraint 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. |
