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A new continuous model for multiple re-entrant manufacturing systems

Author

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  • Dong, Ming
  • He, Fenglan

Abstract

The semiconductor manufacturing systems that involve a large number of products and many steps can be modeled through conservation laws for a continuous density variable on production processes. In this paper, the basic partial differential equation (PDE) models for single-product re-entrant manufacturing systems are proposed first. However, through the validation of numerical examples, the basic continuous models do not perform well for single-product re-entrant systems. Then, a new state equation that takes into account the re-entrant degree of a product is introduced to improve the basic continuous models. The applicability of the modified continuous model is illustrated through numerical examples. The influence of the influx variation on the outflux is also discussed. With the changes of influx, the outflux has a reverse phenomenon. Based on the new state equation, the continuous model for multi-product re-entrant systems with different priorities is established, and an example is provided to illustrate the applicability of the new continuous model.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:ejores:v:223:y:2012:i:3:p:659-668
    DOI: 10.1016/j.ejor.2012.07.002
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    References listed on IDEAS

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    1. Dieter Armbruster & Daniel E. Marthaler & Christian Ringhofer & Karl Kempf & Tae-Chang Jo, 2006. "A Continuum Model for a Re-entrant Factory," Operations Research, INFORMS, vol. 54(5), pages 933-950, October.
    2. J. G. Dai & G. Weiss, 1996. "Stability and Instability of Fluid Models for Reentrant Lines," Mathematics of Operations Research, INFORMS, vol. 21(1), pages 115-134, February.
    3. 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.
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