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A numerical study of Markov decision process algorithms for multi-component replacement problems
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DOI：10.1016/j.ejor.2021.07.007.png)
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Abstract
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We present a unified modeling framework for Time-Based Maintenance (TBM) and Condition-Based Maintenance (CBM) for optimization of replacements in multi-component systems. The considered sys-tem has a K-out-of -N reliability structure, and components deteriorate according to a multivariate gamma process with Levy copula dependence. The TBM and CBM models are formulated as Markov Decision Pro-cesses (MDPs), and optimal policies are found using dynamic programming. Solving the CBM model re-quires that the continuous deterioration process is discretized. We therefore investigate the discretization level required for obtaining a near-optimal policy. Our results indicate that a coarser discretization level than previously suggested in the literature is adequate, indicating that dynamic programming is a feasible approach for optimization in multi-component systems. We further demonstrate this through empirical results for the size limit of the MDP models when solved with an optimized implementation of modified policy iteration. The TBM model can generally be solved with more components than the CBM model, since the former has a sparser state transition structure. In the special case of independent component deterioration, transition probabilities can be calculated efficiently at runtime. This reduces the memory requirements substantially. For this case, we also achieved a tenfold speedup when using ten processors in a parallel implementation of algorithm. Altogether, our results show that the computational require-ments for systems with independent component deterioration increase at a slower rate than for systems with stochastic dependence. (c) 2021 Elsevier B.V. All rights reserved.
Keywords:
Maintenance
Dynamic programming
Multi-component system
Markov decision process
Numerical study
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