Advertisement

Springer Nature is making SARS-CoV-2 and COVID-19 research free. View research | View latest news | Sign up for updates

Monotonicity of optimal flow control for failure-prone production systems

  • 46 Accesses

  • 17 Citations

Abstract

In this paper, we consider the problem of the optimal flow control for a production system with one machine which is subject to failures and produces one part type. In most previous work, it has been assumed that the machine has exponential up and down times, i.e., its state process is a Markov process. The system considered in our study has general machine up and down times. Our main result is establishing monotone properties for the optimal control policy.

This is a preview of subscription content, log in to check access.

References

  1. 1.

    Olsder, G. J., andSuri, R.,The Optimal Control of Parts Routing in a Manufacturing System with Failure-Prone Machines, Proceedings of the 19th IEEE Conference on Decision and Control, pp. 722–727, 1980.

  2. 2.

    Rishel, R.,Dynamic Programming and Minimum Principles for Systems with Jump Markov Distributions, SIAM Journal on Control, Vol. 29, pp. 338–371, 1975.

  3. 3.

    Kimemia, J. G., andGershwin, S. B.,An Algorithm for the Computer Control of Production in Flexible Manufacturing Systems, IIE Transactions, Vol. 15, pp. 353–362, 1983.

  4. 4.

    Akella, R., andKumar, P. R.,Optimal Control of Production Rate in a Failure-Prone Manufacturing System, IEEE Transactions on Automatic Control, Vol. 31, pp. 116–126, 1986.

  5. 5.

    Bielecki, T., andKumar, P. R.,Optimality of Zero-Inventory Policies for Unreliable Manufacturing Systems, Operations Research, Vol. 36, pp. 532–541, 1988.

  6. 6.

    Caramanis, M., andLiberopoulos, G.,Perturbation Analysis for the Design of Flexible Manufacturing Systems Flow Controllers, Operations Research, Vol. 40, pp. 1107–1125, 1992.

  7. 7.

    Caramanis, M., andSharifnia, A.,Near-Optimal Manufacturing Flow Controller Design, International Journal of Flexible Manufacturing System, Vol. 3, pp. 321–336, 1991.

  8. 8.

    Gershwin, S. B., Akella, R., andChoong, Y. F.,Short-Term Production Scheduling of an Automated Manufacturing Facility, IBM Journal of Research and Development, Vol. 29, pp. 392–400, 1985.

  9. 9.

    Sharifnia, A.,Optimal Production Control of a Manufacturing System with Machine Failures, IEEE Transactions on Automatic Control, Vol. 33, pp. 620–625, 1988.

  10. 10.

    Boukas, E. K., andHaurie, A.,Manufacturing Flow Control and Preventive Maintenance: A Stochastic Control Approach, IEEE Transactions on Automatic Control, Vol. 35, pp. 1024–1031, 1990.

  11. 11.

    Sethi, S., Soner, H. M., Zhang, Q., andJiang, J.,Turnpike Sets in Stochastic Production Planning Problems, Proceedings of the 29th IEEE Conference on Decision and Control, pp. 590–595, 1990.

  12. 12.

    Hu, J. Q., andXiang, D.,Structural Properties of Optimal Production Controllers in Failure-Prone Manufacturing Systems, IEEE Transactions on Automatic Control, Vol. 39, pp. 640–643, 1994.

  13. 13.

    Liberopoulos, G.,Flow Control of Failure-Prone Manufacturing Systems: Control Design Theory and Applications, PhD Thesis, Manufacturing Engineering Department, Boston University, 1992.

  14. 14.

    Hu, J. Q., Vakili, P., andYu, Y. G.,Optimality of Hedging Point Policies in the Production Control of Failure-Prone Manufacturing Systems, IEEE Transactions on Automatic Control, Vol. 39, pp. 1875–1880, 1994.

  15. 15.

    Liberopoulos, G., andCaramanis, M.,Production Control of Manufacturing Systems with Production Rates Dependent Failure Rate, IEEE Transactions on Automatic Control, Vol. 39, pp. 889–895, 1994.

  16. 16.

    Hu, J. Q., andXiang, D.,A Queueing Equivalence to Optimal Control of a Manufacturing System with Failures, IEEE Transactions on Automatic Control, Vol. 38, pp. 499–502, 1993.

  17. 17.

    Hu, J. Q., andXiang, D.,Optimal Control for Systems with Deterministic Production Cycles, IEEE Transactions on Automatic Control, Vol. 40, pp. 782–786, 1995.

  18. 18.

    Tu, F. S., Song, D. P. andLou, S. X. C.,Preventive Hedging Point Control Policy, Technical Report, Faculty of Management Studies, University of Toronto, 1992.

  19. 19.

    Tsitsiklis, J. N.,Convexity and Characterization of Optimal Policies in a Dynamic Routing Problem, Journal of Optimization Theory and Applications, Vol. 44, pp. 105–136, 1984.

  20. 20.

    Asmussen, S.,Applied Probability and Queues, John Wiley and Sons, New York, New York, 1987.

Download references

Author information

Additional information

This work was partially supported by the National Science Foundation under Grants DDM-9215368 and EDI-9212122. The authors thank two anonymous reviewers for helpful comments and suggestions.

Communicated by W. B. Gong

Rights and permissions

Reprints and Permissions

About this article

Cite this article

Hu, J.Q., Xiang, D. Monotonicity of optimal flow control for failure-prone production systems. J Optim Theory Appl 86, 57–71 (1995). https://doi.org/10.1007/BF02193461

Download citation

Key Words

  • Failure-prone production systems
  • optimal flow control
  • hazard rate function
  • monotonicity