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Optimal Production Planning in a Stochastic Manufacturing System with Long-Run Average Cost

Author

Listed:
  • S. P. Sethi

    (University of Toronto)

  • W. Suo

    (University of Toronto)

  • M. I. Taksar

    (SUNY at Stony Brook)

  • Q. Zhang

    (University of Georgia)

Abstract

This paper is concerned with the optimal production planning in a dynamic stochastic manufacturing system consisting of a single machine that is failure prone and facing a constant demand. The objective is to choose the rate of production over time in order to minimize the long-run average cost of production and surplus. The analysis proceeds with a study of the corresponding problem with a discounted cost. It is shown using the vanishing discount approach that the Hamilton–Jacobi–Bellman equation for the average cost problem has a solution giving rise to the minimal average cost and the so-called potential function. The result helps in establishing a verification theorem. Finally, the optimal control policy is specified in terms of the potential function.

Suggested Citation

  • S. P. Sethi & W. Suo & M. I. Taksar & Q. Zhang, 1997. "Optimal Production Planning in a Stochastic Manufacturing System with Long-Run Average Cost," Journal of Optimization Theory and Applications, Springer, vol. 92(1), pages 161-188, January.
    • Handle: RePEc:spr:joptap:v:92:y:1997:i:1:d:10.1023_a:1022696215389
    DOI: 10.1023/A:1022696215389
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    References listed on IDEAS

    as
    1. 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.
    2. S. Sethi & H. M. Soner & Q. Zhang & H. Jiang, 1992. "Turnpike Sets and Their Analysis in Stochastic Production Planning Problems," Mathematics of Operations Research, INFORMS, vol. 17(4), pages 932-950, November.
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    Cited by:

    1. Barış Tan, 2019. "Production Control with Price, Cost, and Demand Uncertainty," OR Spectrum: Quantitative Approaches in Management, Springer;Gesellschaft für Operations Research e.V., vol. 41(4), pages 1057-1085, December.
    2. D. Beyer & S. P. Sethi, 1997. "Average Cost Optimality in Inventory Models with Markovian Demands," Journal of Optimization Theory and Applications, Springer, vol. 92(3), pages 497-526, March.
    3. Amir Ahmadi-Javid & Roland Malhamé, 2015. "Optimal Control of a Multistate Failure-Prone Manufacturing System under a Conditional Value-at-Risk Cost Criterion," Journal of Optimization Theory and Applications, Springer, vol. 167(2), pages 716-732, November.
    4. 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.
    5. Amir Ahmadi-Javid & Mohsen Ebadi, 2021. "Economic design of memory-type control charts: The fallacy of the formula proposed by Lorenzen and Vance (1986)," Computational Statistics, Springer, vol. 36(1), pages 661-690, March.

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