June  2016, 9(2): 407-427. doi: 10.3934/krm.2016.9.407

Parameter extraction of complex production systems via a kinetic approach

1. 

Intel Corporation, Assembly & Test Technology Development, 5000 W. Chandler Blvd, Chandler, AZ 85226, United States

2. 

Department of Mathematics and Statistics, Arizona State University, Tempe, AZ 85287-1804

3. 

Ondokuz Mayis University, Department of Mathematics, Samsun, 55139, Turkey

Received  May 2015 Revised  November 2015 Published  March 2016

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.
Citation: Ali K. Unver, Christian Ringhofer, M. Emir Koksal. Parameter extraction of complex production systems via a kinetic approach. Kinetic and Related Models, 2016, 9 (2) : 407-427. doi: 10.3934/krm.2016.9.407
References:
[1]

D. Armbruster, D. Marthaler and C. Ringhofer, A mesoscopic approach to the simulation of semiconductor supply chains,, Proceedings of the International Conference on Modeling and Analysis of Semiconductor Manufacturing (MASM2002) (eds. G. Mackulak et al.), (): 365. 

[2]

D. Armbruster, D. Marthaler and C. Ringhofer, Kinetic and fluid model hierarchies for supply chains, SIAM J. on Multiscale Modeling, 2 (2003), 43-61. doi: 10.1137/S1540345902419616.

[3]

D. Armbruster and C. Ringhofer, Thermalized kinetic and fluid models for re-entrant supply chains, SIAM J. Multiscale Modeling and Simulation, 3 (2005), 782-800. doi: 10.1137/030601636.

[4]

D. Armbruster, C. Ringhofer and T. Jo, Continuous models for production flows, in Proceedings of the 2004 American Control Conference, Boston, 4589-4594.

[5]

J. Banks, J. Carson and B. Nelson, Discrete Event System Simulation, Prentice Hall, 1999.

[6]

S. Brush, Kinetic Theory, Pergamon Press, 1972.

[7]

C. Cercignani, Boltzmann Equation and its Applications, Applied Mathematical Sciences, 67, 1988. doi: 10.1007/978-1-4612-1039-9.

[8]

G. Fishman, Discrete-Event Simulation, Springer-Verlag, New York, 2001. doi: 10.1007/978-1-4757-3552-9.

[9]

D. Helbing, Traffic and related self-driven many-particle systems, Reviews of Modern Physics, 73 (2001), 1067-1141. doi: 10.1103/RevModPhys.73.1067.

[10]

J. Nocedal and S. Wright, Numerical Optimization, 2nd edition, Springer-Verlag, New York, 2006.

[11]

A. Unver and C. Ringhofer, Estimation of transport coefficients in re-entrant factory models, 15th IFAC Symposium on System Identification, SYSID France, (2009), 705-710.

[12]

A. Unver, C. Ringhofer and D. Armbruster, A hyperbolic relaxation model for product flow in complex production networks, AIMS Procceedings, (2009), 790-799.

[13]

A. Unver, Observation Based PDE Models for Stochastic Production Systems, Thesis (Ph.D.), Arizona State University, 2008.

show all references

References:
[1]

D. Armbruster, D. Marthaler and C. Ringhofer, A mesoscopic approach to the simulation of semiconductor supply chains,, Proceedings of the International Conference on Modeling and Analysis of Semiconductor Manufacturing (MASM2002) (eds. G. Mackulak et al.), (): 365. 

[2]

D. Armbruster, D. Marthaler and C. Ringhofer, Kinetic and fluid model hierarchies for supply chains, SIAM J. on Multiscale Modeling, 2 (2003), 43-61. doi: 10.1137/S1540345902419616.

[3]

D. Armbruster and C. Ringhofer, Thermalized kinetic and fluid models for re-entrant supply chains, SIAM J. Multiscale Modeling and Simulation, 3 (2005), 782-800. doi: 10.1137/030601636.

[4]

D. Armbruster, C. Ringhofer and T. Jo, Continuous models for production flows, in Proceedings of the 2004 American Control Conference, Boston, 4589-4594.

[5]

J. Banks, J. Carson and B. Nelson, Discrete Event System Simulation, Prentice Hall, 1999.

[6]

S. Brush, Kinetic Theory, Pergamon Press, 1972.

[7]

C. Cercignani, Boltzmann Equation and its Applications, Applied Mathematical Sciences, 67, 1988. doi: 10.1007/978-1-4612-1039-9.

[8]

G. Fishman, Discrete-Event Simulation, Springer-Verlag, New York, 2001. doi: 10.1007/978-1-4757-3552-9.

[9]

D. Helbing, Traffic and related self-driven many-particle systems, Reviews of Modern Physics, 73 (2001), 1067-1141. doi: 10.1103/RevModPhys.73.1067.

[10]

J. Nocedal and S. Wright, Numerical Optimization, 2nd edition, Springer-Verlag, New York, 2006.

[11]

A. Unver and C. Ringhofer, Estimation of transport coefficients in re-entrant factory models, 15th IFAC Symposium on System Identification, SYSID France, (2009), 705-710.

[12]

A. Unver, C. Ringhofer and D. Armbruster, A hyperbolic relaxation model for product flow in complex production networks, AIMS Procceedings, (2009), 790-799.

[13]

A. Unver, Observation Based PDE Models for Stochastic Production Systems, Thesis (Ph.D.), Arizona State University, 2008.

[1]

Jean-Michel Coron, Matthias Kawski, Zhiqiang Wang. Analysis of a conservation law modeling a highly re-entrant manufacturing system. Discrete and Continuous Dynamical Systems - B, 2010, 14 (4) : 1337-1359. doi: 10.3934/dcdsb.2010.14.1337

[2]

Ciro D'Apice, Peter I. Kogut, Rosanna Manzo. On optimization of a highly re-entrant production system. Networks and Heterogeneous Media, 2016, 11 (3) : 415-445. doi: 10.3934/nhm.2016003

[3]

K. F. C. Yiu, L. L. Xie, K. L. Mak. Analysis of bullwhip effect in supply chains with heterogeneous decision models. Journal of Industrial and Management Optimization, 2009, 5 (1) : 81-94. doi: 10.3934/jimo.2009.5.81

[4]

Ciro D'Apice, Peter I. Kogut, Rosanna Manzo. On relaxation of state constrained optimal control problem for a PDE-ODE model of supply chains. Networks and Heterogeneous Media, 2014, 9 (3) : 501-518. doi: 10.3934/nhm.2014.9.501

[5]

Afaf Bouharguane. On the instability of a nonlocal conservation law. Discrete and Continuous Dynamical Systems - S, 2012, 5 (3) : 419-426. doi: 10.3934/dcdss.2012.5.419

[6]

Ciro D'Apice, Rosanna Manzo. A fluid dynamic model for supply chains. Networks and Heterogeneous Media, 2006, 1 (3) : 379-398. doi: 10.3934/nhm.2006.1.379

[7]

R.G. Duran, J.I. Etcheverry, J.D. Rossi. Numerical approximation of a parabolic problem with a nonlinear boundary condition. Discrete and Continuous Dynamical Systems, 1998, 4 (3) : 497-506. doi: 10.3934/dcds.1998.4.497

[8]

Alberto Bressan, Graziano Guerra. Shift-differentiabilitiy of the flow generated by a conservation law. Discrete and Continuous Dynamical Systems, 1997, 3 (1) : 35-58. doi: 10.3934/dcds.1997.3.35

[9]

Alberto Bressan, Khai T. Nguyen. Conservation law models for traffic flow on a network of roads. Networks and Heterogeneous Media, 2015, 10 (2) : 255-293. doi: 10.3934/nhm.2015.10.255

[10]

Robert I. McLachlan, G. R. W. Quispel. Discrete gradient methods have an energy conservation law. Discrete and Continuous Dynamical Systems, 2014, 34 (3) : 1099-1104. doi: 10.3934/dcds.2014.34.1099

[11]

Julien Jimenez. Scalar conservation law with discontinuous flux in a bounded domain. Conference Publications, 2007, 2007 (Special) : 520-530. doi: 10.3934/proc.2007.2007.520

[12]

Yanzhao Cao, Song Chen, A. J. Meir. Analysis and numerical approximations of equations of nonlinear poroelasticity. Discrete and Continuous Dynamical Systems - B, 2013, 18 (5) : 1253-1273. doi: 10.3934/dcdsb.2013.18.1253

[13]

Gabriella Bretti, Ciro D’Apice, Rosanna Manzo, Benedetto Piccoli. A continuum-discrete model for supply chains dynamics. Networks and Heterogeneous Media, 2007, 2 (4) : 661-694. doi: 10.3934/nhm.2007.2.661

[14]

Pierre Degond, Maximilian Engel. Numerical approximation of a coagulation-fragmentation model for animal group size statistics. Networks and Heterogeneous Media, 2017, 12 (2) : 217-243. doi: 10.3934/nhm.2017009

[15]

G. Acosta, Julián Fernández Bonder, P. Groisman, J.D. Rossi. Numerical approximation of a parabolic problem with a nonlinear boundary condition in several space dimensions. Discrete and Continuous Dynamical Systems - B, 2002, 2 (2) : 279-294. doi: 10.3934/dcdsb.2002.2.279

[16]

John R. Tucker. Attractors and kernels: Linking nonlinear PDE semigroups to harmonic analysis state-space decomposition. Conference Publications, 2001, 2001 (Special) : 366-370. doi: 10.3934/proc.2001.2001.366

[17]

Raimund Bürger, Stefan Diehl, María Carmen Martí. A conservation law with multiply discontinuous flux modelling a flotation column. Networks and Heterogeneous Media, 2018, 13 (2) : 339-371. doi: 10.3934/nhm.2018015

[18]

Darko Mitrovic. Existence and stability of a multidimensional scalar conservation law with discontinuous flux. Networks and Heterogeneous Media, 2010, 5 (1) : 163-188. doi: 10.3934/nhm.2010.5.163

[19]

Jing Shi, Tiaojun Xiao. Store assistance and coordination of supply chains facing consumer's return. Journal of Industrial and Management Optimization, 2016, 12 (3) : 991-1007. doi: 10.3934/jimo.2016.12.991

[20]

Tsan-Ming Choi. Quick response in fashion supply chains with dual information updating. Journal of Industrial and Management Optimization, 2006, 2 (3) : 255-268. doi: 10.3934/jimo.2006.2.255

2020 Impact Factor: 1.432

Metrics

  • PDF downloads (162)
  • HTML views (0)
  • Cited by (0)

[Back to Top]