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Multiscale analysis of re-entrant production lines: An equation-free approach

Author

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  • Zou, Y.
  • Kevrekidis, I.G.
  • Armbruster, D.

Abstract

The computer-assisted modeling of re-entrant production lines, and, in particular, simulation scalability, is attracting a lot of attention due to the importance of such lines in semiconductor manufacturing. Re-entrant flows lead to competition for processing capacity among the items produced, which significantly impacts their throughput time (TPT). Such production models naturally exhibit two time scales: a short one, characteristic of single items processed through individual machines, and a longer one, characteristic of the response time of the entire factory. Coarse-grained partial differential equations for the spatio-temporal evolution of a “phase density” were obtained through a kinetic theory approach in Armbruster and Ringhofer [Thermalized kinetic and fluid models for re-entrant supply chains, SIAM J. Multiscale Modeling Simul. 3(4) (2005) 782–800.] We take advantage of the time scale separation to directly solve such coarse-grained equations, even when we cannot derive them explicitly, through an equation-free computational approach. Short bursts of appropriately initialized stochastic fine-scale simulation are used to perform coarse projective integration on the phase density. The key step in this process is lifting: the construction of fine-scale, discrete realizations consistent with a given coarse-grained phase density field. We achieve this through computational evaluation of conditional distributions of a “phase velocity” at the limit of large item influxes.

Suggested Citation

  • Zou, Y. & Kevrekidis, I.G. & Armbruster, D., 2006. "Multiscale analysis of re-entrant production lines: An equation-free approach," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 363(1), pages 1-13.
  • Handle: RePEc:eee:phsmap:v:363:y:2006:i:1:p:1-13
    DOI: 10.1016/j.physa.2006.01.043
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    Cited by:

    1. Dong, Ming & He, Fenglan, 2012. "A new continuous model for multiple re-entrant manufacturing systems," European Journal of Operational Research, Elsevier, vol. 223(3), pages 659-668.

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