Skip to main content

Optimal control of a failure prone manufacturing system with the possibility of temporary increase in production capacity

  • Part I Optimal Production Planning
  • Conference paper
  • First Online:

Part of the book series: Lecture Notes in Control and Information Sciences ((LNCIS,volume 214))

Abstract

Manufacturers have two general strategies to guard against uncertainties in the production or demand process: (a) building inventory to hedge against periods in which the production capacity is not sufficient to satisfy demand, and (b) temporarily increasing the production capacity, for example, by hiring temporary workers, adding overtime and/or extra shifts, or outsourcing part of the production. A production control problem is to strike a balance between the costs of building inventory, “buying” extra capacity, and backlogged demand. In this paper, we address this problem in the context of a single failure prone machine that produces a single part-type and show that the optimal control policy is a switching policy that is generally characterized by three switching levels.

Research was supported in part by the National Science Foundation under grants EID-9212122 and DDM-9215368.

This is a preview of subscription content, log in via an institution.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. R. Akella and P.R. Kumar, “Optimal Control of Production Rate in a Failure Prone Manufacturing System,” IEEE Transactions on Automatic Control, Vol. 31, No. 2, pp. 116–126, February 1986.

    Google Scholar 

  2. T. Bielecki and P.R. Kumar, “Optimality of Zero-Inventory Policies for Unreliable Manufacturing Systems,” Operations Research, Vol. 36, No. 4, pp. 532–541, July–August 1988.

    Google Scholar 

  3. M. Caramanis and A. Sharifnia, “Design of Near Optimal Flow Controllers for Flexible Manufacturing Systems,” Proceedings of the 3th ORSA/TIMS special Interest Conference on FMSA, Cambridge, MA, K.E. Steche and R. Suri eds. Elsevier Science Publishers B.V., Amsterdam.

    Google Scholar 

  4. M. Caramanis and G. Liberopoulos, “Perturbation Analysis for the Design of Flexible Manufacturing Systems Flow Controllers,” Operations Research, Vol. 40, No. 6, pp. 1107–1125, Nov.–Dec. 1992.

    Google Scholar 

  5. S. Gershwin, Manufacturing Systems Engineering, Prentice Hall, 1993.

    Google Scholar 

  6. S. Gershwin, Personal Communication, 1994.

    Google Scholar 

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

    Google Scholar 

  8. J.Q. Hu, “Production Rate Control for Failure Prone Production With No Backlog Permitted,” IEEE Transactions on Automatic Control, Vol.40, No.2, pp. 291–295, 1995.

    Google Scholar 

  9. J.Q. Hu, “A Queueing Approach to Manufacturing Flow Control Models,” Proceedings of the 34th IEEE Conference on Decision and Control, December 13–15, 1995.

    Google Scholar 

  10. J.Q. Hu, P. Vakili, and G.X. Yu, “Optimality of Hedging Point Policies in the Production Control of Failure Prone Manufacturing Systems,” IEEE Trans. on Automatic Control, Vol.39, No.9, pp.1875–1880, 1994.

    Google Scholar 

  11. J.Q. Hu and D. Xiang, “The Queueing Equivalence to a Manufacturing System with Failures,” IEEE Transactions on Automatic Control, 38, pp. 499–502, March, 1993.

    Google Scholar 

  12. J.Q. Hu and D. Xiang, “Structure Properties of Optimal Production Controllers of Failure Prone Manufacturing Systems,” IEEE Transactions on Automatic Control, Vol.39, No.3, pp. 640–643, 1994.

    Google Scholar 

  13. J.Q. Hu and D. Xiang, “Optimal Control for Systems with Deterministic Cycles,” IEEE Transactions on Automatic Control, Vol.40, No.4, pp. 782–786, 1994.

    Google Scholar 

  14. J.Q. Hu and D. Xiang, “Monotonicity of Optimal Flow Control for Failure Prone Production Systems,” Journal of Optimization Theory and Applications, Vol. 86, No.1, pp. 57–71, July 1995.

    Google Scholar 

  15. J. Lehoczky, S.P. Sethi, H.M. Soner, and M.I. Taksar, “An Asymptotic Analysis of Hierarchical Control of Manufacturing Systems under Uncertainty,” Mathematics of Operations Research, 16, pp. 594, 1991.

    Google Scholar 

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

    Google Scholar 

  17. G. Liberopoulos and M. Caramanis, “Production Control of Manufacturing Systems with Production Rate Dependent Failure Rates,” IEEE Trans. on Automatic Control, Vol. 39, No. 4, pp.889–895, 1994.

    Google Scholar 

  18. G. Liberopoupos and J.Q. Hu, “On the Order of Optimal Hedging Points in a Class of Manufacturing Flow Control Models,” IEEE Transactions on Automatic Control, Vol.40, No.2, pp. 282–286, 1995.

    Google Scholar 

  19. G.J. Olsder and R. Suri, “The Optimal Control of Parts Routing in a Manufacturing System with Failure Prone Machines,” Proceedings of the 19th IEEE Conference on Decision and Control, 1980.

    Google Scholar 

  20. R. Rishel, “Dynamic Programming and Minimum Principles for Systems with Jump Markov Distributions,” SIAM Journal of Control, Vol. 29, No. 2, February 1975.

    Google Scholar 

  21. S. Sethi, H. M. Soner, Q. Zhang, and J. Jiang, “Turnpike Sets and their Analysis in Stochastic Production Planning Problems,” Math. OR, Vol. 17, pp. 932–950, 1992.

    Google Scholar 

  22. S.P. Sethi and Q. Zhang, Hierarchical Decision Making in Stochastic Manufacturing Systems, Birkhauser, Boston, 1994.

    Google Scholar 

  23. A. Sharifnia, “Optimal Production Control of a Manufacturing System with Machine Failures,” IEEE Transactions on Automatic Control, Vol. AC-33, No. 7, pp. 620–625, July 1988.

    Google Scholar 

  24. G.X. Yu and P. Vakili, “Control of Manufacturing Systems with Production Dependent Machine Failures,” in Proceedings of 31st Annual Allerton Conference on Communication, Control, and Computing, Allerton, IL, 1993.

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Editor information

George Yin (Dr)Qing Zhang (Dr)

Rights and permissions

Reprints and permissions

Copyright information

© 1996 Springer-Verlag London Limited

About this paper

Cite this paper

Huang, L., Hu, JQ., Vakili, P. (1996). Optimal control of a failure prone manufacturing system with the possibility of temporary increase in production capacity. In: Yin, G., Zhang, Q. (eds) Recent Advances in Control and Optimization of Manufacturing Systems. Lecture Notes in Control and Information Sciences, vol 214. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0015113

Download citation

  • DOI: https://doi.org/10.1007/BFb0015113

  • Published:

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-76055-9

  • Online ISBN: 978-3-540-40949-6

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics