Parameter extraction of complex production systems via a kinetic approach

Ali K.  Unver; Christian Ringhofer; M. Emir  Koksal

doi:10.3934/krm.2016.9.407

Article Contents

2016, Volume 9, Issue 2: 407-427. Doi: 10.3934/krm.2016.9.407

This issue Previous Article Global solutions to the relativistic Vlasov-Poisson-Fokker-Planck system Next Article

Parameter extraction of complex production systems via a kinetic approach

1.
Intel Corporation, Assembly & Test Technology Development, 5000 W. Chandler Blvd, Chandler, AZ 85226
2.
Department of Mathematics and Statistics, Arizona State University, Tempe, AZ 85287-1804
3.
Ondokuz Mayis University, Department of Mathematics, Samsun, 55139

Received: May 2015

Revised: November 2015

Published: June 2016

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Abstract

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. 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 discrete event simulation (DES) model according to the averaged influx, which is obtained out of discrete event experiments, is predicted. 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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Mathematics Subject Classification: Primary: 65N35, 35K55; Secondary: 62P30.

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References

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