Estimation of Transport Coefficients in Re-entrant Factory Models

Unver, Ali K.; Ringhofer, Christian

doi:10.3182/20090706-3-fr-2004.00117

Cited by 4 publications

(2 citation statements)

References 14 publications

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“…Extracting such a function out of real or simulation data is not obvious and subject to current research [27]. 2) As long as the clearing function is a monotone function of the load or the local density, the adjoint calculus will lead to similar equations as discussed in this paper and hence a optimized input function can be calculated easily.…”

Section: Discussionmentioning

confidence: 99%

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Control of Continuum Models of Production Systems

Marca

Armbruster

Herty

et al. 2010

IEEE Trans. Automat. Contr.

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Abstract-A production system which produces a large number of items in many steps can be modelled as a continuous flow problem. The resulting hyperbolic partial differential equation (PDE) typically is nonlinear and nonlocal, modeling a factory whose cycle time depends nonlinearly on the work in progress. One of the few ways to influence the output of such a factory is by adjusting the start rate in a time dependent manner. We study two prototypical control problems for this case: i) demand tracking where we determine the start rate that generates an output rate which optimally tracks a given time dependent demand rate and ii) backlog tracking which optimally tracks the cumulative demand. The method is based on the formal adjoint method for constrained optimization, incorporating the hyperbolic PDE as a constraint of a nonlinear optimization problem. We show numerical results on optimal start rate profiles for steps in the demand rate and for periodically varying demand rates and discuss the influence of the nonlinearity of the cycle time on the limits of the reactivity of the production system. Differences between perishable and non-perishable demand (demand versus backlog tracking) are highlighted.

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Section: Discussionmentioning

confidence: 99%

“…We now have the PDE, the coupling condition, and by examining directly, the terminal condition for the backlog problem as (respectively) (25) (26) (27) APPENDIX B CONJUGATE GRADIENT This appendix describes the details of the conjugate gradient numerical method used to find the minimizing influx .…”

Section: B Backlog Problemmentioning

confidence: 99%

Control of Continuum Models of Production Systems

Marca

Armbruster

Herty

et al. 2010

IEEE Trans. Automat. Contr.

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Modeling and Analysis of Reentrant Manufacturing Systems: Micro‐ and Macroperspectives

Dong

Yang

2011

Mathematical Problems in Engineering

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In order to obtain the better analysis of the multiple reentrant manufacturing systems (MRMSs), their modeling and analysis from both micro- and macroperspectives are considered. First, this paper presents the discrete event simulation models for MRMS and the corresponding algorithms are developed. In order to describe MRMS more accurately, then a modified continuum model is proposed. This continuum model takes into account the re-entrant degree of products, and its effectiveness is verified through numerical experiments. Finally, based on the discrete event simulation and the modified continuum models, a numerical example is used to analyze the MRMS. The changes in the WIP levels and outflux are also analyzed in details for multiple re-entrant supply chain networks. Meanwhile, some interesting observations are discussed.

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Parameter extraction of complex production systems via a kinetic approach

Unver

Ringhofer²,

Köksal

2016

KRM

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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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Estimation of Transport Coefficients in Re-entrant Factory Models

Cited by 4 publications

References 14 publications

Control of Continuum Models of Production Systems

Control of Continuum Models of Production Systems

Modeling and Analysis of Reentrant Manufacturing Systems: Micro‐ and Macroperspectives

Parameter extraction of complex production systems via a kinetic approach

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