Planning of life-depleting preventive maintenance activities with replacements

Sergey S. Ketkov, Oleg A. Prokopyev () and Lisa M. Maillart
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Sergey S. Ketkov: HSE University
Oleg A. Prokopyev: University of Pittsburgh
Lisa M. Maillart: University of Pittsburgh

Annals of Operations Research, 2023, vol. 324, issue 1, No 47, 1483 pages

Abstract: Abstract We consider a system that generates a reward at some predefined decreasing rate as its virtual age increases. Periodic maintenance (PM) is performed to restore the system to as-good-as new condition, i.e., its virtual age is decreased to zero after each maintenance action. However, the system has a given deterministic initial lifetime and each maintenance action also results in a depletion of the remaining system’s lifetime. Whenever the lifetime expires, the system is replaced by a new identical one at some predefined cost. From the application perspective the considered setting is primarily motivated by the practice of battery-powered systems, e.g., sensors, that need to be remotely monitored. We formulate a general repair-replacement problem with an infinite time horizon, where we seek an optimal number of PM actions and an optimal PM interval. We describe global optimization techniques for solving a general case of the problem under some reasonably mild assumptions on the reward and lifetime depletion rates. For the special case of a constant lifetime depletion per each maintenance action, some analytic observations are provided. Finally, we also demonstrate that for sufficiently large replacement costs the infinite-horizon problem can be solved by leveraging the results for the related finite-horizon problem previously considered in the literature.

Keywords: Life-depleting preventive maintenance; Reward rate; Repair-replacement problem; Infinite-horizon model (search for similar items in EconPapers)
Date: 2023
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DOI: 10.1007/s10479-022-04767-4

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