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A State Aggregation Approach to Manufacturing Systems Having Machine States with Weak and Strong Interactions

Author

Listed:
  • J. Jiang

    (University of Toronto, Toronto, Canada)

  • S. P. Sethi

    (University of Toronto, Toronto, Canada)

Abstract

A hierarchical approach to control a manufacturing system, subject to multiple machine states modeled by a Markov process with weak and strong interactions, is suggested. The idea is to aggregate strongly interacting or high transition probability states within a group of states and consider only the transition between these groups for the analysis of the system in the long run. We show that such an aggregation results in a problem of reduced size, whose solution can be modified in a simple way to obtain an asymptotically optimal feedback solution to the original problem. Also, an example is solved to illustrate the results developed in the paper.

Suggested Citation

  • J. Jiang & S. P. Sethi, 1991. "A State Aggregation Approach to Manufacturing Systems Having Machine States with Weak and Strong Interactions," Operations Research, INFORMS, vol. 39(6), pages 970-978, December.
    • Handle: RePEc:inm:oropre:v:39:y:1991:i:6:p:970-978
    DOI: 10.1287/opre.39.6.970
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    Cited by:

    1. Q. Zhang & G. Yin & E. K. Boukas, 1997. "Controlled Markov Chains with Weak and Strong Interactions: Asymptotic Optimality and Applications to Manufacturing," Journal of Optimization Theory and Applications, Springer, vol. 94(1), pages 169-194, July.
    2. Parpas, Panos & Webster, Mort, 2014. "A stochastic multiscale model for electricity generation capacity expansion," European Journal of Operational Research, Elsevier, vol. 232(2), pages 359-374.
    3. S. P. Sethi & H. Yan & H. Zhang & Q. Zhang, 2002. "Optimal and Hierarchical Controls in Dynamic Stochastic Manufacturing Systems: A Survey," Manufacturing & Service Operations Management, INFORMS, vol. 4(2), pages 133-170.
    4. S. P. Sethi & Q. Zhang, 1998. "Near Optimization of Dynamic Systems by Decomposition and Aggregation," Journal of Optimization Theory and Applications, Springer, vol. 99(1), pages 1-22, October.

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