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The opportunistic replacement problem: analysis and case studies

Torgny Almgren (Torgny.Almgren***at***volvo.com)
Niclas Andreasson (niclasa***at***chalmers.se)
Michael Patriksson (mipat***at***chalmers.se)
Ann-Brith Strömberg (anstr***at***chalmers.se)
Adam Wojciechowski (wojcadam***at***chalmers.se)

Abstract: 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 [21] 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.

Keywords: mixed binary linear programming, polyhedral analysis, complexity analysis, opportunistic maintenance, replacement problem, case studies

Category 1: Integer Programming ((Mixed) Integer Linear Programming )

Category 2: Applications -- OR and Management Sciences (Scheduling )

Citation: Department of Mathematical Sciences, Chalmers University of Technology and Department of Mathematical Sciences, University of Gothenburg, Gothenburg, Sweden. Report, May 2011.

Download: [PDF]

Entry Submitted: 01/22/2009
Entry Accepted: 01/22/2009
Entry Last Modified: 06/08/2011

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