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Optimal Maintenance Policy and Sale Date of a Machine

Author

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  • Gerald L. Thompson

    (Carnegie-Mellon University)

Abstract

A machine is to be bought, used for productive purposes for a length of time, and then sold. It is possible to do preventive maintenance while the machine is being used, if desired, in order to slow down the degradation of the machine's capability. The value of owning the machine is the sum of the discounted value of its production while it is owned plus its discounted value when sold. In this paper a modification of a model due to B. Naslund for the problem is discussed. Using Pontryagin's maximum principle, the problem is treated as one of optimal control with the control variables being the use or nonuse of preventive maintenance and the selection of the sale date. It is shown that the optimal maintenance policy is bang-bang, and methods for finding the optimal sale date are determined. Simply examples show the various kinds of solutions that can be obtained with varying assumptions concerning the actual functions used in the model.

Suggested Citation

  • Gerald L. Thompson, 1968. "Optimal Maintenance Policy and Sale Date of a Machine," Management Science, INFORMS, vol. 14(9), pages 543-550, May.
    • Handle: RePEc:inm:ormnsc:v:14:y:1968:i:9:p:543-550
    DOI: 10.1287/mnsc.14.9.543
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    Citations

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    Cited by:

    1. George Bitros & Elias Flytzanis, 2004. "Utilization and Maintenance in a Model with Terminal Scrapping," Macroeconomics 0411016, University Library of Munich, Germany.
    2. Bitros, George C., 2009. "The Theorem of Proportionality in Mainstream Capital Theory: An Assessment of its Conceptual Foundations," MPRA Paper 17436, University Library of Munich, Germany.
    3. Dimitrios Koumparoulis, 2011. "The Proportionality Hypothesis in Capital Theory: an Assessment of the Literature," EuroEconomica, Danubius University of Galati, issue 27, pages 27-39, February.
    4. George C. Bitros & Elias Flytzanis, 2003. "A Rehabilitation of Economic Replacement Theory," Macroeconomics 0303009, University Library of Munich, Germany.
    5. Mason, Robin, 2004. "Dividends, safety and liquidation when liabilities are long-term and stochastic," European Economic Review, Elsevier, vol. 48(6), pages 1179-1210, December.
    6. P F Lesse & J R Roy, 1987. "Optimal Replacement and Maintenance of Urban Infrastructure," Environment and Planning A, , vol. 19(8), pages 1115-1121, August.
    7. 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.
    8. 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.
    9. Wallace J. Hopp & Sung‐Chi Wu, 1988. "Multiaction maintenance under markovian deterioration and incomplete state information," Naval Research Logistics (NRL), John Wiley & Sons, vol. 35(5), pages 447-462, October.
    10. George Bitros, 2010. "The theorem of proportionality in contemporary capital theory: An assessment of its conceptual foundations," The Review of Austrian Economics, Springer;Society for the Development of Austrian Economics, vol. 23(4), pages 367-401, December.
    11. Mark G. Tang, 1993. "A stochastic machine maintenance and sale problem: Results with different production functions," Naval Research Logistics (NRL), John Wiley & Sons, vol. 40(5), pages 677-696, August.
    12. Kim, Bowon & Park, Sangsun, 2008. "Optimal pricing, EOL (end of life) warranty, and spare parts manufacturing strategy amid product transition," European Journal of Operational Research, Elsevier, vol. 188(3), pages 723-745, August.
    13. Marcel Savioz, 1990. "Investment and Maintenance in the Aviation Industry," Swiss Journal of Economics and Statistics (SJES), Swiss Society of Economics and Statistics (SSES), vol. 126(I), pages 17-38, March.

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