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

Journal article
Authors Efraim Laksman
Ann-Brith Strömberg
Michael Patriksson
Published in Annals of Operations Research
ISSN 0254-5330
Publication year 2019
Published at Department of Mathematical Sciences
Language en
Links dx.doi.org/10.1007/s10479-019-03278...
Keywords Maintenance optimization, Mixed binary linear optimization, Stochastic opportunistic replacement problem, Stochastic programming
Subject categories Mathematics

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. © 2019, The Author(s).

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