The stochastic opportunistic replacement problem, part III: improved bounding procedures

Efraim Laksman (), Ann-Brith Strömberg () and Michael Patriksson ()
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Efraim Laksman: Chalmers University of Technology and University of Gothenburg
Ann-Brith Strömberg: Chalmers University of Technology and University of Gothenburg
Michael Patriksson: Chalmers University of Technology and University of Gothenburg

Annals of Operations Research, 2020, vol. 292, issue 2, No 7, 733 pages

Abstract: Abstract We consider the problem to find a schedule for component replacement in a multi-component system, whose components possess stochastic lives and economic dependencies, such that the expected costs for maintenance during a pre-defined time period are minimized. The problem was considered in Patriksson et al. (Ann Oper Res 224:51–75, 2015b), in which a two-stage approximation of the problem was optimized through decomposition (denoted the optimization policy). The current paper improves the effectiveness of the decomposition approach by establishing a tighter bound on the value of the recourse function (i.e., the second stage in the approximation). A general lower bound on the expected maintenance cost is also established. Numerical experiments with 100 simulation scenarios for each of four test instances show that the tighter bound yields a decomposition generating fewer optimality cuts. They also illustrate the quality of the lower bound. Contrary to results presented earlier, an age-based policy performs on par with the optimization policy, although most simple policies perform worse than the optimization policy.

Keywords: Stochastic programming; Mixed binary linear optimization; Maintenance optimization; Stochastic opportunistic replacement problem; 90C11; 90C15; 90B25 (search for similar items in EconPapers)
Date: 2020
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DOI: 10.1007/s10479-019-03278-z

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