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A numerical study of Markov decision process algorithms for multi-component replacement problems
European Journal of Operational Research ( IF 6.4 ) Pub Date : 2021-07-10 , DOI: 10.1016/j.ejor.2021.07.007
Jesper Fink Andersen 1 , Anders Reenberg Andersen 1 , Murat Kulahci 1, 2 , Bo Friis Nielsen 1
Affiliation  

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 system has a K-out-of-N reliability structure, and components deteriorate according to a multivariate gamma process with Lévy copula dependence. The TBM and CBM models are formulated as Markov Decision Processes (MDPs), and optimal policies are found using dynamic programming. Solving the CBM model requires 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 requirements for systems with independent component deterioration increase at a slower rate than for systems with stochastic dependence.



中文翻译:

多分量置换问题马尔可夫决策过程算法的数值研究

我们提出了基于时间的维护 (TBM) 和基于状态的维护 (CBM) 的统一建模框架,用于优化多组件系统中的更换。所考虑的系统具有ķ-在......之外-ñ可靠性结构和组件根据具有 Lévy copula 依赖的多元 gamma 过程劣化。TBM 和 CBM 模型被制定为马尔可夫决策过程 (MDP),并使用动态规划找到最优策略。求解 CBM 模型需要将连续恶化过程离散化。因此,我们研究了获得接近最优策略所需的离散化水平。我们的结果表明,比文献中先前建议的更粗略的离散化水平就足够了,这表明动态规划是多组件系统优化的一种可行方法。当通过修改策略迭代的优化实现解决时,我们通过 MDP 模型大小限制的经验结果进一步证明了这一点。TBM 模型通常可以用比 CBM 模型更多的组件来求解,因为前者具有更稀疏的状态转换结构。在独立分量恶化的特殊情况下,可以在运行时有效地计算转移概率。这大大降低了内存需求。对于这种情况,当在算法的并行实现中使用十个处理器时,我们也实现了十倍的加速。总而言之,我们的结果表明,具有独立组件劣化的系统的计算需求增加的速度比具有随机相关性的系统慢。这大大降低了内存需求。对于这种情况,当在算法的并行实现中使用十个处理器时,我们也实现了十倍的加速。总而言之,我们的结果表明,具有独立组件劣化的系统的计算需求增加的速度比具有随机相关性的系统慢。这大大降低了内存需求。对于这种情况,当在算法的并行实现中使用十个处理器时,我们也实现了十倍的加速。总而言之,我们的结果表明,具有独立组件劣化的系统的计算需求增加的速度比具有随机相关性的系统慢。

更新日期:2021-07-10
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