考慮平行機台故障率與健康狀態的預防性維修與生產排程之決策研究

Abstract

在工業 4.0 的潮流以及物聯網的時代下，我們有足夠的資料預測機台的健康狀況。若機台狀況變差，加工將會產生延遲時間。因此在排程的同時必須考慮延遲時間及機台狀況的變化。本研究將在此生產環境下研究如何同時規劃平行機台之預防性維修時間，以及工作加工順序，並且最小化期望總完工時間。 本研究首先提出一數學規劃模型來解決此排程問題，將機台年齡影響工作加 工與延遲時間考慮進去，並同時考慮預防性維修對機台年齡的影響等因素，以求得最佳生產排程，使得期望總完工時間最小。由於此模型為混整數非線性數學規劃模型，當問題規模增大後，將無法在有限時間內求得最佳解，因此本研究提出兩個啟發式演算法，針對中小型問題，本研究提出兩階段啟發式演算法，在有限時間內，求得品質優良的區域最佳解，而針對大規模問題，本研究提出雙啟發式演算法，能夠快速的求得品質優良的可行解。 最後，本研究進行數值分析，以分析模型與演算法之求解效率，首先針對各參數對最佳預防性維修週期的影響進行分析，確保兩階段啟發式演算法能夠有效的分配工作至各機台，接著進行問題規模的分析，在有限的工作數之下，兩階段啟發式演算法皆能有效率的求得品質優良的解，而對於雙啟發式演算法，由數值分析證實當工作數達到 50 時，仍然能求出品質優良的可行解，除了能夠有效分配預防性 維修時間外，也能有效率的排序預防性週期區間內的工作。

Due to Industrial 4.0 and Internet of Things, we have enough information to predict the machine health. If the machine condition becomes worse, the process will need additional processing time. Therefore, the additional processing time and the machine failure rate must be considered simultaneously when scheduling. Based on these conditions, this study tries to find the optimal preventive maintenance and jobs schedule on parallel machines, while minimize the expected total completion time. This study first proposed a mathematical programming model to solve this scheduling problem, considering failure rate, the age of machine and additional processing time, trying to minimize the expected completion time. Since this model is a mixed-integer nonlinear mathematical programming model, when the problem size increases, it will not be able to find the optimal solution in a finite computation time. Therefore, this study proposed two heuristic algorithms. For middle scale problem, we proposed two-phase heuristic algorithm, which obtains a local optimal solution with good quality in limited computation time. On the other hand, for large scale problem, we proposed double heuristic algorithm, which efficiently find a feasible solution. Lastly, this study conducted numerical analysis to analyze the efficiency of the model and algorithm. The result reveals that the two-stage algorithm can effectively assign jobs to each machine and obtain the solution with high quality. Besides, double heuristic algorithm can efficiently solve the problem with 50 jobs.