過去研究最佳生產週期問題的學者，多假設製程為一完美製程。換言之，在製造過程中不會產生不良品。但從製程品質管制的角度來看，不良品的產生實際上是絕對無法避免的。因此，基於此原因且有別於過去的研究，本文假設製程為一不完美製程。然而，當製程為一不完美製程時，會因不良品的產生而增加額外成本，如：修復不良品成本與不良品造成的機會成本。所以，為了能降低不良品所帶來的額外機會成本，於是在製程中加入檢測的動作，期能透過檢測來減少不良品數，以降低不良品所增加的成本。
本文基於上述考量，考慮在某個製造設施，重複生產單一產品族的不完美製程下，建立一個數學模式，透過對該模式求解，找出最佳生產週期與檢測次數，以最小化總成本。在成本分析中，透過對成本項的觀察，分析其最佳解結構，發現本模式目標函數的最好平均成本曲線(the best average cost curve)為一片段凹性連續函數曲線(piece-wise continuous convex curve)，因此，在進行搜尋演算法的分析與設計時，透過片段凹性連續函數曲線所產生的接合點，以協助求取生產週期與檢測次數的最佳解。
於本文中，提出一組數據與隨機試驗的數據，以驗證本研究模式所得到的結果，作為生產管理決策於決定生產週期與檢測策略時的參考。

目錄
誌謝 IV
目錄 V
圖目錄 VI
表目錄 VIII
第一章 研究背景與目的 1
1.1研究背景與動機 1
1.2研究目的 1
1.3研究方法 2
1.4研究工具 2
1.5論文架構 2
第二章 文獻探討 4
2.1不完美製程的研究發展 4
2.2不完美製程上檢測的研究發展 6
2.3預備知識 7
第三章 數學模式與成本分析 9
3.1符號定義 9
3.2假設條件 10
3.3目標函數 11
1.設置成本 11
2.檢測成本 11
3.期望修復成本 11
4.期望機會成本 12
5.存貨持有成本 13
6.總生產成本 13
3.4數學模式 14
第四章 理論性質分析 16
4.1 圖形的觀察 16
4.2接合點 18
4.3片段凹性 20
第五章 演算法設計 24
5.1演算法的下界 24
5.2演算法的上界 27
5.3設計搜尋演算法 31
5.4演算法流程圖 32
第六章 數據驗證 34
6.1 數據實驗範圍 34
6.2 隨機數據實驗 36
第七章? 結論 40
7.1 研究貢獻 40
7.2 未來發展 40
附錄 A 41
A.1產品I修復期望成本 41
A.2產品I不良品機會成本 41
A.3產品I的存貨持有成本計算過程 42
參考文獻 44
圖目錄
圖 1.5.1 論文架構圖 3
圖 4.1.2 的最好平均成本曲線 18
圖4.1.1 圖形 17
圖5.4.1演算法流程圖 33
表目錄
表4.1.1各項參數數據 17
表6.2.1各項參數的數據表 36
表6.2.2兩種演算法所求出的最佳解 36
表6.2.3 針對產品數5,10,15,20進行分析 37
表6.2.4 針對設置成本進行分析 37
表6.2.5 針對設置成本進行分析 38
表6.2.6 針對修復成本進行分析 38
表6.2.7 針對不良率進行分析 38
表6.2 8 針對需求率進行分析 39
表6.2.9 針對存貨持有成本進行分析 39
表6.2.10 針對不良品成本進行分析 39

1. Ben-Daya, M., “The economic production lot-sizing problem with imperfect production process and imperfect maintenance”, International Journal of Production Economics, 76, (2002), 257-264.
2. Berg, M., Posner M.J.M., Zhao, H., “Production-inventory systems with unreliable machines”, Operations Research, 42, (1997), 111-118.
3. Cheng, T.C.E., “EPQ with process and quality assurance considerations”, Journal of the Operational Research Society, 42, (1991), 713-720.
4. Cheng, T.C.E., “An economic order quantity model with demand-dependent unit production cost and imperfect production process”, IIE Transactions, 23, (1991), 23-28.
5. Chung, K.J., “Bounds for production lot sizing with machine breakdowns”, Computers and Industrial Engineering, 32, (1997), 139-144.
6. Chung, K.J., Hou, K.L., “An optimal production run time with imperfect production process and allowable shortages”, Computers and Operations Research, 30, (2003), 483-490.
7. Das, T.K., Sarkar, S., “Optimal preventive maintenance in a production inventory system”, IIE Transactions, 31 , (1999), 537-551.
8. Federgruen, A., So, K.C., “Optimal maintenance policies for single-server queuing system subject to breakdowns”, Operations Research , (38), 1990, 330-343.
9. Goyal, S.K., “An integrated inventory model for a single product system”, Journal of Operational Research Society, 28, (1997) , 539-545.
10. Groenevelt, H., Pintelon, L., Seidmann, A., “A production lot sizing with machine breakdowns ” , Management Science , 38, (1992), 104-123.
11. Groenevelt, H., Pintelon, L., Seidmann, A., “Production batching with machine breakdowns and safety stocks”, Operations Research , 40, (1992), 959-971.
12. Harris, F.W., “How many parts to make at once”, Operations Research , 38, (1990), 947-950.
13. Hall, R., Zero Inventories, Dow Jones-Irwin, Homewood, IL(1983).
14. Johnson, L.A., and Montgomery, D., Operations Research in Production Planning, Scheduling and Inventory Control, New York: Wiley(1974).
15. Kim, C.H., Hong, Y., “A extended EMQ model for a failure prone machine with general lifetime distribution”, International Journal of Production Economics, 49, (1997), 215-223.
16. Khouja, M., Mehrez, A., “Economic production lot size model with variable production rate and imperfect quality”, Journal of the Operational Research Society, 45, (1994), 1405-1417.
17. Lee H. and Rosenblatt M., “ Simultaneous determination of production cycle and inspection schedules in a production system”, Management Science, 33, (1987), 1125-1136.
18. Lee, H.L., Rosenblatt, M.J., “A production and maintenance planning model with restoration cost dependent on detection delay”, IIE Transactions, 21, (1989), 368-375.
19. Lee, J.S., and Park, K.S., “Joint determination of production cycle and inspection intervals in a deteriorating production”, Journal of the Operational Research Society, 42, (1991), 775-783.
20. Lin, T.M., Tseng, S.T., Liou, M.J., “Optimal inspection schedule in the imperfect production system under general shift distribution”, Journal of the Chinese Institute of Industrial Engineers, 8, (2), (1991), 73-81.
21. Liou, M.J., Tseng, S.T., Lin, T.M., “The effects of inspection errors to the imperfect EMQ model”, IIE Transactions, 26, (1994), 42-51.
22. Lin, C.S., “Integrated production-inventory models with imperfect production processes and a limited capacity for raw materials”, Mathematical and Computer Modeling, 29, (1999), 81-89.
23. Liu, B., Cao, J., “Analysis of a production-inventory system with machine breakdowns and shutdowns”, Computers and Operations Research, 26, (1999), 73-91.
24. Lin, G.C., and Gong, D.C., “Simultaneous determination of production cycle and inspection production-inventory system with variable production rates”, Proceedings of The Fourth Asia-Pacific Industrial Engineering Management Systems Conference, December.18-20, 2002, Taipei, Taiwan.
25. Lin, C.S., Chen, C.H., and Kroll, D.E., “Integrated production-inventory models for imperfect production processes under inspection schedules”, Computers and Industrial Engineering, 44, (2003) , 633-650.
26. Makis, V., Fung, J., “An EMQ model with inspections and random machine failures”, Journal of the Operational Research Society, 49, (1998), 66-76.
27. Makis, V., “Optimal lot sizing and inspection policy for an EMQ model with imperfect inspections”, Naval Research Logistics, 45, (1998), 165-186.
28. Nahmias, S., Production and Operations Analysis , McGraw Hill , Singapore, (1997).
29. Porteus, E.L., “Optimal lot sizing, process quality improvement and setup cost reduction”, Operations Research, 34, ( 1986), 137-144.
30. Rogers, J., “A computational approach to the economic lot scheduling problem”, Management Science , 4, (1958), 264-291.
31. Rosenblatt, M.J., Lee, H.L., “Economic production cycle with imperfect production process”, IIE Transactions, 18, (1986), 48-55.
32. Silver, E.A., Pyke, F.D., Peterson, R., Inventory Management and Production Planning and Scheduling, Wilely, New York, (1998).
33. Tagaras, G., “An integrated cost model for joint optimization of process control and maintenance”, Journal of the Operational Research Society , 39, (1988), 757-766.
34. Tseng, S.T., “Optimal preventive maintenance policy for deteriorating production systems”, IIE Transactions, 28, (1996), 687-694.
35. Wang, C.H., Sheu, SH., “Simultaneous determination of the optimal production-inventory and product inspection policies for a deteriorating production system”, Computers and Operations Research, 28, (2001), 1093-1110.
36. Wang, C.H., Sheu, S.H., “Determining the optimal production-maintenance policy with inspection errors : using a Markov chain”, Computers and Operations Research, 30, (2003), 1-17.