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Replacement Decisions with Maintenance Under Uncertainty: An Imbedded Optimal Control Model

Author

Listed:
  • Ali Dogramaci

    (Department of Industrial Engineering, Bilkent University, Ankara 06800, Turkey)

  • Nelson M. Fraiman

    (Graduate School of Business, Columbia University, New York, New York 10027)

Abstract

How should a manager make replacement decisions for a chain of machines over time if each is maintained by an optimal control model addressing uncertainty of machine breakdowns? A network representation of the problem involves arcs with interdependent costs. A solution algorithm is presented and replacement considerations under technological change are incorporated into a well-known optimal control model for maintenance under uncertainty (that of Kamien and Schwartz 1971). The method is illustrated by an example.

Suggested Citation

  • Ali Dogramaci & Nelson M. Fraiman, 2004. "Replacement Decisions with Maintenance Under Uncertainty: An Imbedded Optimal Control Model," Operations Research, INFORMS, vol. 52(5), pages 785-794, October.
    • Handle: RePEc:inm:oropre:v:52:y:2004:i:5:p:785-794
    DOI: 10.1287/opre.1040.0133
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    References listed on IDEAS

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    1. Suresh P. Sethi, 2021. "Optimal Control Theory," Springer Texts in Business and Economics, Springer, edition 4, number 978-3-030-91745-6, August.
    2. Abraham Mehrez & Gad Rabinowitz & Eli Shemesh, 2000. "A Discrete Maintenance and Replacement Model under Technological Breakthrough Expectations," Annals of Operations Research, Springer, vol. 99(1), pages 351-372, December.
    3. Cyrus Derman, 1962. "On Sequential Decisions and Markov Chains," Management Science, INFORMS, vol. 9(1), pages 16-24, October.
    4. Morton I. Kamien & Nancy L. Schwartz, 1971. "Optimal Maintenance and Sale Age for a Machine Subject to Failure," Management Science, INFORMS, vol. 17(8), pages 495-504, April.
    5. S. P. Sethi & T. E. Morton, 1972. "A mixed optimization technique for the generalized machine replacement problem," Naval Research Logistics Quarterly, John Wiley & Sons, vol. 19(3), pages 471-481, September.
    6. Gerald L. Thompson, 1968. "Optimal Maintenance Policy and Sale Date of a Machine," Management Science, INFORMS, vol. 14(9), pages 543-550, May.
    7. Morton Klein, 1962. "Inspection--Maintenance--Replacement Schedules Under Markovian Deterioration," Management Science, INFORMS, vol. 9(1), pages 25-32, October.
    8. Wallace J. Hopp & Suresh K. Nair, 1991. "Timing replacement decisions under discontinuous technological change," Naval Research Logistics (NRL), John Wiley & Sons, vol. 38(2), pages 203-220, April.
    9. Suresh Chand & Suresh Sethi, 1982. "Planning horizon procedures for machine replacement models with several possible replacement alternatives," Naval Research Logistics Quarterly, John Wiley & Sons, vol. 29(3), pages 483-493, September.
    10. S. Bylka & S. Sethi & G. Sorger, 1992. "Minimal forecast horizons in equipment replacement models with multiple technologies and general switching costs," Naval Research Logistics (NRL), John Wiley & Sons, vol. 39(4), pages 487-507, June.
    11. P. Sethi & N. A. Derzko & L. P. Lehoczky, 1996. "Erratum To “A Stochastic Extension Of The Miller‐Modigliani Framework”1," Mathematical Finance, Wiley Blackwell, vol. 6(4), pages 407-408, October.
    12. Suresh Chand & Vernon Ning Hsu & Suresh Sethi, 2002. "Forecast, Solution, and Rolling Horizons in Operations Management Problems: A Classified Bibliography," Manufacturing & Service Operations Management, INFORMS, vol. 4(1), pages 25-43, September.
    13. Kordonsky, Kh. B. & Gertsbakh, I. B., 1993. "Choice of the best time scale for system reliability analysis," European Journal of Operational Research, Elsevier, vol. 65(2), pages 235-246, March.
    14. Suresh Sethi & Suresh Chand, 1979. "Planning Horizon Procedures for Machine Replacement Models," Management Science, INFORMS, vol. 25(2), pages 140-151, February.
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    Cited by:

    1. Alain Bensoussan & Suresh P. Sethi, 2007. "The Machine Maintenance and Sale Age Model of Kamien and Schwartz Revisited," Management Science, INFORMS, vol. 53(12), pages 1964-1976, December.
    2. A. Bensoussan & Q. Feng & S. P. Sethi, 2022. "Integrating equipment investment strategy with maintenance operations under uncertain failures," Annals of Operations Research, Springer, vol. 317(2), pages 353-386, October.
    3. Borgonovo, E., 2010. "The reliability importance of components and prime implicants in coherent and non-coherent systems including total-order interactions," European Journal of Operational Research, Elsevier, vol. 204(3), pages 485-495, August.
    4. Nguyen, T.P. Khanh & Yeung, Thomas G. & Castanier, Bruno, 2013. "Optimal maintenance and replacement decisions under technological change with consideration of spare parts inventories," International Journal of Production Economics, Elsevier, vol. 143(2), pages 472-477.
    5. Michael Jong Kim & Viliam Makis, 2013. "Joint Optimization of Sampling and Control of Partially Observable Failing Systems," Operations Research, INFORMS, vol. 61(3), pages 777-790, June.
    6. Mellal, Mohamed Arezki, 2020. "Obsolescence – A review of the literature," Technology in Society, Elsevier, vol. 63(C).
    7. Öner, K.B. & Kiesmüller, G.P. & van Houtum, G.J., 2015. "On the upgrading policy after the redesign of a component for reliability improvement," European Journal of Operational Research, Elsevier, vol. 244(3), pages 867-880.

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