Optimal Maintenance and Replacement of Extraction Machinery

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

Suggested Citation: Suggested Citation

Sethi, Suresh and Yeh, Denny and Zhang, Rong and Jardine, Andrew, Optimal Maintenance and Replacement of Extraction Machinery (May 1, 2008). Journal of Systems Science and Systems Engineering, Vol. 17, No. 4, 2008, Available at SSRN: https://ssrn.com/abstract=1128287 or http://dx.doi.org/10.2139/ssrn.1128287