Optimal Maintenance and Replacement of Extraction Machinery
Journal of Systems Science and Systems Engineering, Vol. 17, No. 4, 2008
16 Pages Posted: 6 May 2008 Last revised: 8 Mar 2014
Date Written: May 1, 2008
This paper considers a problem of optimal preventive maintenance and replacement schedule of equipment devoted to extracting resources from known deposits. Typical examples are oil drills, mine shovels, etc. At most one replacement of the existing machinery by a new one is allowed. The problem is formulated as an optimal control problem subject to the state constraint that the remaining deposit at any given time is nonnegative. We show that the optimal preventive maintenance, production rates, and the replacement and salvage times of the existing machinery and the new one, if required, can be obtained by solving sequentially a series of free-end-point optimal control problems. Moreover, an algorithm based on this result is developed and used to solve two illustrative examples.
Keywords: maintenance and replacement, optimal control, the maximum principle, extraction, mining equipment, extraction machinery
JEL Classification: M11, C61
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