IDEAS home Printed from https://ideas.repec.org/a/spr/joptap/v106y2000i2d10.1023_a1004667028547.html
   My bibliography  Save this article

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
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1023/A:1004667028547
    File Function: Abstract
    Download Restriction: Access to the full text of the articles in this series is restricted.
    File URL: https://libkey.io/10.1023/A:1004667028547?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    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.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Houmin Yan & Xun Yu Zhou & G. Yin, 1999. "Approximating an Optimal Production Policy in a Continuous Flow Line: Recurrence and Asymptotic Properties," Operations Research, INFORMS, vol. 47(4), pages 535-549, August.
    2. Xiang Li, 2017. "Optimal procurement strategies from suppliers with random yield and all-or-nothing risks," Annals of Operations Research, Springer, vol. 257(1), pages 167-181, October.
    3. B. Khoury, 2009. "A discrete approach to designing optimal hedging-point control policies for production-inventory systems with general stochastic behavior," Computational Management Science, Springer, vol. 6(4), pages 399-409, October.
    4. B C Giri & T Dohi, 2005. "Exact formulation of stochastic EMQ model for an unreliable production system," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 56(5), pages 563-575, May.
    5. Jingfu Huang & Gaoke Wu & Yiju Wang, 2021. "Retailer’s Emergency Ordering Policy When Facing an Impending Supply Disruption," Sustainability, MDPI, vol. 13(13), pages 1-21, June.
    6. 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.
    7. Gharbi, A. & Pellerin, R. & Sadr, J., 2008. "Production rate control for stochastic remanufacturing systems," International Journal of Production Economics, Elsevier, vol. 112(1), pages 37-47, March.
    8. Om Prakash & A.R. Roy & A. Goswami, 2014. "Stochastic manufacturing system with process deterioration and machine breakdown," International Journal of Systems Science, Taylor & Francis Journals, vol. 45(12), pages 2539-2551, December.
    9. Peymankar, Mahboobe & Dehghanian, Farzad & Ghiami, Yousef & Abolbashari, Mohammad Hassan, 2018. "The effects of contractual agreements on the economic production quantity model with machine breakdown," International Journal of Production Economics, Elsevier, vol. 201(C), pages 203-215.
    10. Owen Q. Wu & Hong Chen, 2010. "Optimal Control and Equilibrium Behavior of Production-Inventory Systems," Management Science, INFORMS, vol. 56(8), pages 1362-1379, August.
    11. Harun Öztürk, 2021. "Optimal production run time for an imperfect production inventory system with rework, random breakdowns and inspection costs," Operational Research, Springer, vol. 21(1), pages 167-204, March.
    12. Kenné, Jean-Pierre & Gharbi, Ali, 2018. "Production and replacement policies for a deteriorating manufacturing system under random demand and qualityAuthor-Name: Ouaret, Samir," European Journal of Operational Research, Elsevier, vol. 264(2), pages 623-636.
    13. Sevgen, Arya & Sargut, F. Zeynep, 2019. "May reorder point help under disruptions?," International Journal of Production Economics, Elsevier, vol. 209(C), pages 61-69.
    14. Brian Tomlin, 2006. "On the Value of Mitigation and Contingency Strategies for Managing Supply Chain Disruption Risks," Management Science, INFORMS, vol. 52(5), pages 639-657, May.
    15. Giri, B. C. & Dohi, T., 2004. "Optimal lot sizing for an unreliable production system based on net present value approach," International Journal of Production Economics, Elsevier, vol. 92(2), pages 157-167, November.
    16. Cheng, T.C.E. & Gao, Chunyan & Shen, Houcai, 2011. "Production planning and inventory allocation of a single-product assemble-to-order system with failure-prone machines," International Journal of Production Economics, Elsevier, vol. 131(2), pages 604-617, June.
    17. Rivera-Gómez, Héctor & Gharbi, Ali & Kenné, Jean-Pierre & Montaño-Arango, Oscar & Hernandez-Gress, Eva Selene, 2016. "Production control problem integrating overhaul and subcontracting strategies for a quality deteriorating manufacturing system," International Journal of Production Economics, Elsevier, vol. 171(P1), pages 134-150.
    18. 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.
    19. Liu, John J. & Yang, Ping, 1996. "Optimal lot-sizing in an imperfect production system with homogeneous reworkable jobs," European Journal of Operational Research, Elsevier, vol. 91(3), pages 517-527, June.
    20. Hajji, A. & Mhada, F. & Gharbi, A. & Pellerin, R. & Malhamé, R., 2011. "Integrated product specifications and productivity decision making in unreliable manufacturing systems," International Journal of Production Economics, Elsevier, vol. 129(1), pages 32-42, January.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:spr:joptap:v:106:y:2000:i:2:d:10.1023_a:1004667028547. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Sonal Shukla or Springer Nature Abstracting and Indexing (email available below). General contact details of provider: http://www.springer.com .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.