We consider an optimization model for determining optimal opportunistic maintenance (that is, component replacement) schedules when data is deterministic. This problem generalizes that of Dickman, Epstein, and Wilamowsky  and is a natural starting point for the modelling of replacement schedules when component lives are non-deterministic. We show that this basic opportunistic replacement problem is NP-hard. We show that the convex hull of the set of feasible replacement schedules is full-dimensional, and that all the necessary inequalities also are facet-inducing. We show that when maintenance occasions are fixed, the remaining problem can be stated as a linear program; when maintenance costs are monotone with time, the latter is solvable through a greedy procedure. Results from a series of case studies performed in the areas of aircraft engine and wind turbine maintenance are also reported. These illustrate the advantages of utilizing opportunistic maintenance activities based on a complete optimization model, as compared to simpler policies.
Department of Mathematical Sciences, Chalmers University of Technology and Department of Mathematical Sciences, University of Gothenburg, Gothenburg, Sweden. Report, May 2011.