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Hierarchical Production Control in Dynamic Stochastic Jobshops with Long-Run Average Cost

Author

Listed:
  • S. P. Sethi

    (University of Texas at Dallas)

  • H. Zhang

    (Academia Sinica)

  • Q. Zhang

    (University of Georgia)

Abstract

We consider a production planning problem for a dynamic jobshop producing a number of products and subject to breakdown and repair of machines. The machine capacities are assumed to be finite-state Markov chains. As the rates of change of the machine states approach infinity, an asymptotic analysis of this stochastic manufacturing systems is given. The analysis results in a limiting problem in which the stochastic machine availability is replaced by its equilibrium mean availability. The long-run average cost for the original problem is shown to converge to the long-run average cost of the limiting problem. The convergence rate of the long-run average cost for the original problem to that of the limiting problem together with an error estimate for the constructed asymptotic optimal control is established.

Suggested Citation

  • S. P. Sethi & H. Zhang & Q. Zhang, 2000. "Hierarchical Production Control in Dynamic Stochastic Jobshops with Long-Run Average Cost," Journal of Optimization Theory and Applications, Springer, vol. 106(2), pages 231-264, August.
    • Handle: RePEc:spr:joptap:v:106:y:2000:i:2:d:10.1023_a:1004667028547
    DOI: 10.1023/A:1004667028547
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    References listed on IDEAS

    as
    1. Chand Samaratunga & Suresh P. Sethi & Xun Yu Zhou, 1997. "Computational Evaluation of Hierarchical Production Control Policies for Stochastic Manufacturing Systems," Operations Research, INFORMS, vol. 45(2), pages 258-274, April.
    2. T. Bielecki & P. R. Kumar, 1988. "Optimality of Zero-Inventory Policies for Unreliable Manufacturing Systems," Operations Research, INFORMS, vol. 36(4), pages 532-541, August.
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