在工業工程領域中，同時優化維護與零件庫存管理策略可以有效平衡系統的可用性與降低成本，因而獲得了顯著的關注，然而，現有研究通常存在局限性，主要集中於單一故障模式、忽略了機會性維護以及在更換維護期間未考慮供應商庫存狀態的問題。
為了彌合這些差距，本研究深入探討了複雜系統中基於預測性維護和零件庫存的聯合優化，該系統包括兩種不同的故障模式，並考慮了兩種情境：機會性維護和常規性維護情境，採用哪種維修情境取決於機台是否有硬失效，零件的退化過程使用伽馬過程來建模，透過感測器持續監測其衰退情形，當零件衰退值超過閾值時，會實施不完美維護或更換維護；此外，研究亦考慮了兩種故障模式之間的相互作用。由於庫存策略中供應商的選擇在整個聯合決策模型中也發揮著關鍵作用，本文探討了關於原廠設備製造商和售後市場供應商的選擇，為了增強庫存模型的現實性和適用性，引入了一個隨機變數—供應商連續可用性和不可用性之時間間隔，其反映了供應鏈動態運作的情況，從而使模型更貼近實際情境。由於現代製造系統的高度複雜性和零件退化的隨機性，本研究提出了以模擬最佳化演算法來尋找最佳的零件庫存政策、機會性維護和常規性維護的零件衰退閾值以及零件供應商的選擇，同時使用基於分位數的估計方法估計系統可靠性的機會性限制式，並進行數值研究以驗證所提出的模型和解決方法能有效且高效地找到最佳的維護成本。

The simultaneous optimization of maintenance activities and inventory management for spare parts in industrial engineering has gained significant traction due to its ability to effectively balance system availability and cost. However, existing research often has limitations, primarily focusing on single failure modes, overlooking the issue of opportunistic maintenance and the consideration of supplier inventory status during replacement maintenance.
To bridge these gaps, this study delves into the joint optimization of predictive maintenance and parts inventory for complex system that encompasses two distinct failure modes. Two scenarios are considered, opportunistic maintenance and routine maintenance, based on whether the machines experience
hard failures. The degradation process of the parts is modeled using a gamma process, and continuous monitoring of their degradation levels is facilitated through sensors. When a part surpasses the threshold, imperfect maintenance or replacement maintenance are implemented. Furthermore, the study considers the interaction between the two failure modes. Additionally, the choice of suppliers plays a crucial role in shaping the entire joint decision model. This paper explores considerations regarding both original equipment manufacturers (OEM suppliers) and aftermarket suppliers. To enhance the realism and applicability of the inventory model, a random variable has been introduced, representing the time interval between successive availability and unavailability of suppliers. This inclusion reflects a more nuanced understanding of supply chain dynamics, thereby aligning the model more closely with practical scenarios. In light of the high degree of complexity in modern manufacturing systems and the profound stochasticity in component degradation, a simulation optimization method is proposed to find the optimal component inventory policy, degradation level thresholds of components for both opportunistic maintenance and routine maintenance and the selection of parts suppliers. The simulation-based optimization algorithm effectively solves the proposed model, simultaneously addressing the chance constraint of system reliability by using quantile-based approach. A numerical study is conducted to verify that the proposed model and solution method can find the optimal maintenance cost effectively and efficiently. Furthermore, the influence of critical factors in the model on the optimal policy is analyzed for deriving useful managerial insights.

Broek, M. A. U. H., Teunter, R. H., De Jonge, B., & Veldman, J. (2021). Joint condition-based maintenance and load-sharing optimization for two-unit systems with economic dependency. European Journal of Operational Research, 295(3), 1119-1131.

Civicioglu, P. (2013). Backtracking search optimization algorithm for numerical optimization problems. Applied Mathematics and computation, 219(15), 8121-8144.

Colledani, M., Magnanini, M. C., & Tolio, T. (2018). Impact of opportunistic maintenance on manufacturing system performance. CIRP Annals, 67(1), 499-502.

Darendeliler, A., Claeys, D., Khatab, A., & Aghezzaf, E. H. (2020). Joint optimization of dynamic lot-sizing and condition-based maintenance. In 9th International Conference on Operations Research and Enterprise Systems (pp. 151-158). SCITEPRESS–Science and Technology Publications

Do, P., Scarf, P., & Iung, B. (2015). Condition-based maintenance for a two-component system with dependencies. IFAC-PapersOnLine, 48(21), 946-951.

Falkner, C. H. (1968). Jointly optimal inventory and maintenance policies for stochastically failing equipment. Operations Research, 16(3), 587-601.

Hao, S., & Yang, J. (2018). Reliability analysis for dependent competing failure processes with changing degradation rate and hard failure threshold levels. Computers & Industrial Engineering, 118, 340-351.

He, Y., Liu, F., Cui, J., Han, X., Zhao, Y., Chen, Z., ... & Zhang, A. (2019). Reliability-oriented design of integrated model of preventive maintenance and quality control policy with time-between-events control chart. Computers & Industrial Engineering, 129, 228-238.

Huang, J. F. (2011). Application of reliability centered maintenance in a hydrocracker. Advanced Materials Research, 317, 1837-1842.

Jia, C., & Zhang, C. (2020). Joint optimization of maintenance planning and workforce routing for a geographically distributed networked infrastructure. IISE Transactions, 52(7), 732-750.

Kleijnen, J. P. (2014). Simulation-optimization via Kriging and bootstrapping: a survey. Journal of Simulation, 8, 241-250.

Kuhnle, A., Jakubik, J., & Lanza, G. (2019). Reinforcement learning for opportunistic maintenance optimization. Production Engineering, 13, 33-41.

Lu, C., Xu, T. X., & Cong, L. H. (2019). Condition-based maintenance decision based on inverse gaussian deterioration process under the condition of regular detection and maintenance. Journal of Intelligent & Fuzzy Systems, 37(4), 5767-5775.

Maria, A. (1997, December). Introduction to modeling and simulation. In Proceedings of the 29th conference on Winter simulation (pp. 7-13).

Marseguerra, M., Zio, E., & Podofillini, L. (2002). Condition-based maintenance optimization by means of genetic algorithms and Monte Carlo simulation. Reliability Engineering & System Safety, 77(2), 151-165.

Mild, P., & Salo, A. (2009). Combining a multiattribute value function with an optimization model: An application to dynamic resource allocation for infrastructure maintenance. Decision Analysis, 6(3), 139-152.

Mishra, A. K., Shrivastava, D., & Vrat, P. (2020). An opportunistic group maintenance model for the multi-unit series system employing Jaya algorithm. Opsearch, 57, 603-628.

Moustapha, M., Sudret, B., Bourinet, J. M., & Guillaume, B. (2016). Quantile-based optimization under uncertainties using adaptive Kriging surrogate models. Structural and multidisciplinary optimization, 54, 1403-1421.

Olde Keizer, M. C. A., R. H. Teunter, and J. Veldman (2017). Joint condition-based maintenance and inventory optimization for systems with multiple components. European Journal of Operational Research, 257(1), 209–222.

Parlar, M., & Berkin, D. (1991). Future supply uncertainty in EOQ models. Naval Research Logistics (NRL), 38(1), 107-121.

Rafiee, K., Feng, Q., & Coit, D. W. (2017). Reliability analysis and condition‐based maintenance for failure processes with degradation‐dependent hard failure threshold. Quality and Reliability Engineering International, 33(7), 1351-1366.

Rao, R. V., & More, K. C. (2017). Optimal design and analysis of mechanical draft cooling tower using improved Jaya algorithm. International Journal of Refrigeration, 82, 312-324.

Sleptchenko, A., & van der Heijden, M. (2016). Joint optimization of redundancy level and spare part inventories. Reliability Engineering & System Safety, 153, 64-74.

Shafiee, M., Finkelstein, M., & Bérenguer, C. (2015). An opportunistic condition-based maintenance policy for offshore wind turbine blades subjected to degradation and environmental shocks. Reliability Engineering & System Safety, 142, 463-471.

Song, M., Zhang, Y., Yang, F., Wang, X., Guo, G. (2023). Maintenance policy of degradation components based on the two-phase Wiener process. Eksploatacja i Niezawodność – Maintenance and Reliability, 25(4).

Taghipour, S., Banjevic, D., & Jardine, A. K. (2010). Periodic inspection optimization model for a complex repairable system. Reliability Engineering & System Safety, 95(9), 944-952.

Tessema, B., & Yen, G. G. (2006, July). A self adaptive penalty function based algorithm for constrained optimization. In 2006 IEEE international conference on evolutionary computation (pp. 246-253). IEEE.

Tian, Z., Jin, T., Wu, B., & Ding, F. (2011). Condition based maintenance optimization for wind power generation systems under continuous monitoring. Renewable Energy, 36(5), 1502-1509.

Valet, A., Altenmüller, T., Waschneck, B., May, M. C., Kuhnle, A., & Lanza, G. (2022). Opportunistic maintenance scheduling with deep reinforcement learning. Journal of Manufacturing Systems, 64, 518-534.

Van Horenbeek, A., Buré, J., Cattrysse, D., Pintelon, L., & Vansteenwegen, P. (2013). Joint maintenance and inventory optimization systems: A review. International Journal of Production Economics, 143(2), 499-508.

Van Horenbeek, A., & Pintelon, L. (2013). A dynamic predictive maintenance policy for complex multi-component systems. Reliability Engineering & System Safety, 120, 39-50.

Vu, H. C., Grall, A., Fouladirad, M., & Huynh, K. T. (2021). A predictive maintenance policy considering the market price volatility for deteriorating systems. Computers & Industrial Engineering, 162, 107686.

Wang, J., & Zhu, X. (2021). Joint optimization of condition-based maintenance and inventory control for a k-out-of-n: F system of multi-state degrading components. European Journal of Operational Research, 290(2), 514-529.

Yan, T., Lei, Y., Li, N., Pintelon, L., & Dewil, R. (2023). Joint optimization of maintenance and spare parts inventory for multi-unit systems with a generalized structure. Journal of Manufacturing Science and Engineering, 145(4), 041001.

Zhang, J., Zhao, X., Song, Y., & Qiu, Q. (2022). Joint optimization of condition-based maintenance and spares inventory for a series–parallel system with two failure modes. Computers & Industrial Engineering, 168, 108094.

Zhang, J. X., Ma, Y. Z., & Zhu, L. Y. (2016). Multiobjective simulation optimization using stochastic kriging. In Proceedings of the 22nd International Conference on Industrial Engineering and Engineering Management 2015: Core Theory and Applications of Industrial Engineering (Volume 1) (pp. 81-91). Atlantis Press.

Zhang, Y., Jin, Z., & Mirjalili, S. (2020). Generalized normal distribution optimization and its applications in parameter extraction of photovoltaic models. Energy Conversion and Management, 224, 113301.

Zhang, Y., Chi, A., & Mirjalili, S. (2021). Enhanced Jaya algorithm: A simple but efficient optimization method for constrained engineering design problems. Knowledge-Based Systems, 233, 107555.

Zhang, Y. (2021). Neural network algorithm with reinforcement learning for parameters extraction of photovoltaic models. IEEE Transactions on Neural Networks and Learning Systems, 34(6), 2806-2816.