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Controlled Markov Chains with Weak and Strong Interactions: Asymptotic Optimality and Applications to Manufacturing

Author

Listed:
  • Q. Zhang

    (University of Georgia)

  • G. Yin

    (Wayne University)

  • E. K. Boukas

    (École Polytechnique de Montréal and GERAD)

Abstract

This paper deals with the asymptotic optimality of a stochastic dynamic system driven by a singularly perturbed Markov chain with finite state space. The states of the Markov chain belong to several groups such that transitions among the states within each group occur much more frequently than transitions among the states in different groups. Aggregating the states of the Markov chain leads to a limit control problem, which is obtained by replacing the states in each group by the corresponding average distribution. The limit control problem is simpler to solve as compared with the original one. A nearly-optimal solution for the original problem is constructed by using the optimal solution to the limit problem. To demonstrate, the suggested approach of asymptotic optimal control is applied to examples of manufacturing systems of production planning.

Suggested Citation

  • 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.
    • Handle: RePEc:spr:joptap:v:94:y:1997:i:1:d:10.1023_a:1022667905086
    DOI: 10.1023/A:1022667905086
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    References listed on IDEAS

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    1. 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.
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    Cited by:

    1. 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.

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