随机恶化系统的基于状态的生产:最优政策与学习

Collin Drent, Melvin Drent, Joachim Arts
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引用次数: 0

摘要

问题的定义:生产系统在使用过程中会随机恶化,最终可能发生故障,从而导致在计划维护时刻产生高昂的维护成本。这种劣化行为受系统生产率的影响。虽然生产率越高,收入越多,但系统的劣化速度也可能越快。因此,应该对生产进行动态控制,以权衡两次维护之间的恶化和收入积累。我们所研究的系统,其生产与劣化之间的关系是已知的,且每个系统都相同;而对于不同的系统,这种关系是不同的,需要即时学习。决策问题是在计划的维护时刻(运行)和维护时刻(战术)之间的最佳间隔时间内找到最佳生产政策。方法/结果:对于已知生产劣化关系的系统,我们将运行决策问题视为连续时间马尔可夫决策过程,并证明最优策略具有直观的单调性。我们还提出了 "砰砰 "政策最优化的充分条件,并部分描述了最优区间长度的结构,从而实现了运营决策问题和战术决策问题的高效联合优化。对于在生产-劣化关系中表现出多变性的系统,我们提出了一种贝叶斯程序来学习任何生产政策下的未知劣化率。数值研究表明,在各种情况下,(i) 与静态生产相比,基于条件的生产可将利润提高 50%;(ii) 与最先进的顺序方法相比,整合基于条件的生产和维护决策可将利润提高 21%;(iii) 我们的贝叶斯方法(尤其是在 "砰砰 "机制中)的表现接近于了解每个系统的生产-劣化关系的 Oracle 政策。管理意义:生产应根据实时状态监测进行动态调整,战术维护计划应预测并整合这些运营决策。我们提出的框架可帮助管理者以最佳方式做到这一点:这项工作得到了 Nederlandse Organisatie voor Wetenschappelijk Onderzoek [Grant 439.17.708] 的支持:在线附录见 https://doi.org/10.1287/msom.2022.0473 。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
Condition-Based Production for Stochastically Deteriorating Systems: Optimal Policies and Learning
Problem definition: Production systems deteriorate stochastically due to use and may eventually break down, resulting in high maintenance costs at scheduled maintenance moments. This deterioration behavior is affected by the system’s production rate. Although producing at a higher rate generates more revenue, the system may also deteriorate faster. Production should thus be controlled dynamically to tradeoff deterioration and revenue accumulation in between maintenance moments. We study systems for which the relation between production and deterioration is known and the same for each system and systems for which this relation differs from system to system and needs to be learned on-the-fly. The decision problem is to find the optimal production policy given planned maintenance moments (operational) and the optimal interval length between such maintenance moments (tactical). Methodology/results: For systems with a known production-deterioration relation, we cast the operational decision problem as a continuous time Markov decision process and prove that the optimal policy has intuitive monotonic properties. We also present sufficient conditions for the optimality of bang-bang policies, and we partially characterize the structure of the optimal interval length, thereby enabling efficient joint optimization of the operational and tactical decision problem. For systems that exhibit variability in their production-deterioration relations, we propose a Bayesian procedure to learn the unknown deterioration rate under any production policy. Numerical studies indicate that on average across a wide range of settings (i) condition-based production increases profits by 50% compared with static production, (ii) integrating condition-based production and maintenance decisions increases profits by 21% compared with the state-of-the-art sequential approach, and (iii) our Bayesian approach performs close, especially in the bang-bang regime, to an Oracle policy that knows each system’s production-deterioration relation. Managerial implications: Production should be adjusted dynamically based on real-time condition monitoring and the tactical maintenance planning should anticipate and integrate these operational decisions. Our proposed framework assists managers to do so optimally.Funding: This work was supported by the Nederlandse Organisatie voor Wetenschappelijk Onderzoek [Grant 439.17.708].Supplemental Material: The online appendix is available at https://doi.org/10.1287/msom.2022.0473 .
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