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Optimal Control of a Multistate Failure-Prone Manufacturing System under a Conditional Value-at-Risk Cost Criterion

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  • Amir Ahmadi-Javid

    (Amirkabir University of Technology)

  • Roland Malhamé

    (Ecole Polytechnique de Montréal)

Abstract

The aim of this paper is to establish the optimality of a hedging-point control policy in a multistate Markovian failure-prone manufacturing system with a risk-averse criterion that is defined as the conditional value-at-risk (CVaR) of the steady-state instantaneous running cost, where the system is subject to a constant single-product demand rate. An explicit expression for the optimal control policy is also obtained for the two-state case. The results are important from both theoretical and practical viewpoints. Indeed, the paper extends the well-known classical theoretical result on the optimality of hedging-point control policies under risk-neutral criteria, which are typically given by long-run average costs, and it develops a flexible and practical method for incorporating risk aversion into cost criteria. The approach presented here can be used to specify optimal control policies in similar manufacturing systems with CVaR criteria.

Suggested Citation

  • 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.
  • Handle: RePEc:spr:joptap:v:167:y:2015:i:2:d:10.1007_s10957-014-0668-6
    DOI: 10.1007/s10957-014-0668-6
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    References listed on IDEAS

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    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. Andrzej Ruszczyński & Alexander Shapiro, 2006. "Optimization of Convex Risk Functions," Mathematics of Operations Research, INFORMS, vol. 31(3), pages 433-452, August.
    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. Stanley Gershwin & Bariş Tan & Michael Veatch, 2009. "Production control with backlog-dependent demand," IISE Transactions, Taylor & Francis Journals, vol. 41(6), pages 511-523.
    5. Gürkan, G. & Karaesmen, F. & Ozdemir, O., 2007. "Optimal threshold levels in stochastic fluid models via simulation-based optimization," Other publications TiSEM 8af032bd-47a7-4363-9649-8, Tilburg University, School of Economics and Management.
    6. Philippe Artzner & Freddy Delbaen & Jean‐Marc Eber & David Heath, 1999. "Coherent Measures of Risk," Mathematical Finance, Wiley Blackwell, vol. 9(3), pages 203-228, July.
    7. Rockafellar, R. Tyrrell & Uryasev, Stanislav, 2002. "Conditional value-at-risk for general loss distributions," Journal of Banking & Finance, Elsevier, vol. 26(7), pages 1443-1471, July.
    8. 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.
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    Cited by:

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