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1.	Laksman, Efraim, 1983, et al. (author) The stochastic opportunistic replacement problem, part III: improved bounding procedures 2020 In: Annals of Operations Research. - : Springer Science and Business Media LLC. - 1572-9338 .- 0254-5330. ; 292:2, s. 711-733 Journal article (peer-reviewed)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, 2015), 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.

Laksman, Efraim, 1983, et al. (author)
The stochastic opportunistic replacement problem, part III: improved bounding procedures
2020
In: Annals of Operations Research. - : Springer Science and Business Media LLC. - 1572-9338 .- 0254-5330. ; 292:2, s. 711-733
Journal article (peer-reviewed)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, 2015), 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.

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