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Optimal Maintenance Policy and Sale Date of a Machine

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  • Gerald L. Thompson

    (Carnegie-Mellon University)

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    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.

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    File URL: http://dx.doi.org/10.1287/mnsc.14.9.543
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    Bibliographic Info

    Article provided by INFORMS in its journal Management Science.

    Volume (Year): 14 (1968)
    Issue (Month): 9 (May)
    Pages: 543-550

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    Handle: RePEc:inm:ormnsc:v:14:y:1968:i:9:p:543-550

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    Cited by:
    1. Mason, Robin, 1997. "Dividends, Safety and Liquidation when Liabilities are Long-term and Stochastic," Cambridge Working Papers in Economics 9731, Faculty of Economics, University of Cambridge.
    2. George C. Bitros & Elias Flytzanis, 2003. "A Rehabilitation of Economic Replacement Theory," Macroeconomics 0303009, EconWPA.
    3. George Bitros & Elias Flytzanis, 2004. "Utilization and Maintenance in a Model with Terminal Scrapping," Macroeconomics 0411016, EconWPA.
    4. repec:ise:isegwp:wp182008 is not listed on IDEAS
    5. 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.
    6. 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.
    7. George Bitros, 2010. "The theorem of proportionality in contemporary capital theory: An assessment of its conceptual foundations," The Review of Austrian Economics, Springer, vol. 23(4), pages 367-401, December.

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