臺灣博碩士論文加值系統

本研究探討經濟生產批量包含機器當機(AR)及不完美的重工程序之最佳生產週期。傳統的經濟生產批量假設生產過程是完美的(無不良品)，也就是生產過程不發生變異，與實際情況較為不符合。因為在生產過程中機器可能會因時間而產生劣化，甚至是當機或故障的情況都有可能會發生，這些情況都會導致不良品的產生。除了機器劣化的因素之外，生產過程也可能因為其他原因產生出不良品。業界對於不良品的處理有兩種方式，一是採取重工嘗試修復，二是直接作為報廢品處理。
本研究假設在正常生產週期時，生產之機器假設具隨機性當機的機會，以AR(abort/resume)作為機器維修後的處理方式，即當機器維修完成後繼續原先未完成之生產週期。正常生產週期完成後，緊接著進行不良品之重工程序。而重工程序假設為不完美的，會產生一定比例的重工失敗品(即報廢品)。除此以外，本研究針對這些假設發展出數學模式，其模式以總存貨成本最小化來求得最佳生產週期。最後提出實例來做驗證，並對其參數做敏感度分析，期望整個模式能較符合實際情況。

This research considers the optimal cycle time for an EPQ model with machine breakdowns (AR-policy) and imperfect rework process. The classic EPQ model assumes production process is perfect, but perfect production process is unrealistic. For instance, as machine operation time getting longer, the status of production equipment may start to shift from stable condition to unstable, due to many different known or unknown factors. Most of the times, defective items produced as well as machine breakdowns are inevitable. In the real-life situation, they have two ways to deal with the defective items. One is to rework the defective items and the other is scrap the items.

This study assumes that machine breakdowns is random variable follows a known probability density function. In the regular production process, when machine breakdown occurs, the AR-policy is adopted. Once the machine is fixed and restored, it will continue the regular production process for the remaining uptime. All defective items are reworked immediately in the same production cycle when regular process ends. The rework process is assumed to be imperfect, a portion of the reworked items failed and become the scrap items. In this thesis, a mathematical model is developed to minimize the overall inventory costs and to derive the optimal cycle time. A numerical example with sensitivity analysis is provided to demonstrate its practical usages.

中文摘要 I
Abstract II
誌謝 III
表目錄 VI
圖目錄 VII
第一章 緒論 1
1.1研究動機與目的 2
1.2研究範圍的界定 2
1.3研究方法與流程 3
第二章 文獻探討 5
2.1傳統的經濟訂購批量與經濟生產批量模式 5
2.2 不良品相關文獻探討 6
2.2.1 重工及不良品相關文獻 6
2.2.2 重工及不良品含報廢品相關文獻 7
2.2.2.1 不允許缺貨相關之研究 7
2.2.2.2 允許缺貨相關之研究 7
2.3 機器當機相關文獻探討 8
第三章 經濟生產週期建構 11
3.1 問題描述及符號假設 11
3.2 生產模式架構與基本假設 14
3.2.1 生產模式架構 14
3.2.2 基本假設 15
3.3 Case1：在生產週期內發生當機 15
3.4 Case2：在生產週期內沒發生當機 19
3.5 整合Case1和Case2 並假設發生當機之機率為隨機性機率分配 22
3.6 機器發生當機之機率為指數分配 23
3.6.1 證明此成本函數存在最小值 24
3.6.2 求其最佳生產週期 24
3.6.3 公式驗證 26
3.7機器發生當機之機率為均勻分配 27
3.7.1 證明此成本函數存在最小值 28
3.7.2 求其最佳生產週期 28
3.7.3 公式驗證 29
第四章 實例驗證與敏感度分析 31
4.1 實例1驗證（當機器當機之機率分配為指數分配） 31
4.1.1 檢驗此成本函數是否存在最小值 32
4.1.2 求出其估計值來得出最佳生產週期 32
4.1.3 平均當機間隔時間變動與期望成本的關係 33
4.1.4 報廢率變動與期望成本和生產週期的關係 34
4.1.5 不良率變動與期望成本和生產週期的關係 35
4.1.6 藉由不良率與報廢率的變動來討論期望成本的關係 36
4.2 實例2驗證（當機器當機之機率分配為指數分配） 37
4.2.1 檢驗此成本函數是否存在最小值 38
4.2.2 求出其估計值來得出最佳生產週期 38
4.2.3 平均當機間隔時間變動與期望成本的關係 39
4.2.4 報廢率變動與期望成本和生產週期的關係 40
4.2.5 不良率變動與期望成本和生產週期的關係 41
4.2.6 藉由不良率與報廢率的變動來討論期望成本的關係 42
第五章 結論與未來方向 43
5.1 有無當機之影響(當機之分配為指數分配和無當機做比較) 43
5.1.1 不良率變動對期望成本與生產週期之影響 43
5.1.2 重工報廢率變動對期望成本與生產週期之影響 44
5.2 當機策略不同之影響(AR型及NR型做比較) 45
5.2.1 當機間隔時間變動對期望成本之影響 45
5.2.2 不良率變動對期望成本與生產週期之影響 46
5.2.3 重工報廢率變動對期望成本與生產週期之影響 47
5.3 當機之機率分配之影響(以指數和均勻分配做比較) 48
5.4 結論與未來方向 49
5.4.1 未來方向 51
參考文獻 52
附錄A A-1
附錄B B-1
附錄C C-1
附錄D D-1
附錄E E-1
附錄F F-1
附錄G G-1

[1]Ben-Dayaa, M. , Nomana, S. M.and Harigab M., “Integrated inventory control and inspection policies with deterministic demand”, Computers & Operations Research 33 pp.1625–1638 (2006).

[2]Cheng, T. C. E., “An economic order quantity model with demand-dependent unit production cost and imperfect production process,” IIE Transactions, Vol. 23,No. 1, pp.23-28 (1991).

[3]Chiu S. W. and Dah-Chuan Gong., “Determining the optimal lot size for the finite production model with an imperfect rework process of defective items”, Journal of Information & Optimization Sciences, Vol.25, No.1,pp.105-119 (2004).

[4]Chiu Y. P., “Determining the optimal lot size for the finite production model with random defective rate, the rework process, and backlogging”, Engineering Optimization, Vol. 35, No. 4, pp.427-437 (2003).

[5]Chiu S.W, Dah-chuan Gong and Hui-Ming Wee, “Effects of random defective rate and imperfect Rework Process on economic production quantity model ”,Janpan Journal of Industrial & Applied mMathmatics,vol. 21, No.3, pp. 375-389 (2004).

[6]Chiu S. W. and Chiu Y. P., “An economic production quantity model with the rework process of repairable defective items”, Journal of information & optimization sciences, Vol. 24, No. 3, pp.569-582 (2003).

[7]Chiu Y. P. and Chiu S. W., “A finite production model with random defective rate and shortages allowed and backordered”, Journal of Information & Optimization Sciences, Vol. 24, pp.553-567 (2003).

[8]Chung, K. J. and Hou, K. L., “An optimal production run time with imperfect production processes and allowable shortages,” Computers & Operations Research, Vol. 30, pp.483-490 (2003).


[9]Chung, Kun-Jen “Approximations to production lot sizing with machine breakdowns”, Computers and Operations Research Vol.30,pp.1499-1507 (2003).

[10]Chung, Kun-Jen “Bounds for production lot sizing with machine breakdowns”, Computers & Industrial Engineering Vol. 32, pp. 139-144 (1997).

[11]Dohi, T., Yamada, Y., Kaio, N., Osaki, S., “ The optimal lot sizing for unreliable economic manufacturing model”. International Journal of Reliability, Quality and Safety Engineering 4 (4), 413–426 (1997).

[12]Ford. W. Harris, “How many parts to make at once?,” The Magazines of Management, Vol. 10,pp.135-152 (1913).

[13]Giri B.C., Yun W.Y “Optimal lot sizing for an unreliable production system under partial backlogging and at most two failures in a production cycle.” International Journal of Production Economics Volume: 92, Issue: 2, pp. 157-167 (2004).

[14]Giri, B.C.; Dohi, T. “Computational aspects of an extended EMQ model with variable production rate.” Computers and Operations Research Volume: 32, Issue: 12, pp. 3143-3161 (2005).

[15]Groenevelt, H., Pintelon, L., and Seidmann, A. “Production lot sizing with machine breakdowns. ” Management Science Vol. 38, pp.104-123 (1992).

[16]Groenevelt, H., Pintelon, L., and Seidmann, A. “Production batching with machine breakdowns and safety stocks”. Operations Research Vol. 40, pp.959-971 (1992).

[17]Hayek, P. A. and Salameh, M. K., “Production lot sizing with the reworking of imperfect quality items produced”, Production Planning and Control, Vol. 12,pp.584-590 (2001).



[18]Jamal, A.M.M.; Sarker, Bhaba R.; Mondal, Sanjay. “Optimal manufacturing batch size with rework process at a single-stage production system.” Computers and Industrial Engineering Volume: 47, Issue: 1, pp. 77-89 (2004).

[19]Kim, C.H., Hong, Y., “An extended EMQ model for a failure prone machine with general lifetime distribution.” International Journal of Production Economics 49, 215–223 (1997).

[20]Kim, C.H., Hong, Y., Kim, S.-Y., “An extended optimal lot sizing model with an unreliable machine. ”Production Planning and Control 8 (6), 577–585 (1997).

[21]Lee, H. L. “Lot sizing to reduce capacity utilization in production process with defective items, process corrections, and rework.” Management Science, 38(9), 1314–1328 (1992).

[22]Lee, H. L., & Rosenblatt, M. J. “Economic production cycles with imperfect production processes.” IIE Transactions,18(1), 48–55 (1986).

[23]Lin, Gary C. and Gong, D. C.,” On a production-inventory system of deteriorating items subject to random machine breakdowns with a fixed repair time.” Mathematical and Computer Modeling 43,pp.920-932 (2006).

[24]Liu, J. J. and Yang, p., “Optimal lot-sizing in an imperfect production system with homogeneous reworkable jobs”,European Journal of Operational Research, Vol. 91, pp.517-527 (1996).

[25]Rosenblatt, M.J. and Lee, H. L. , “Economic production cycles with imperfect production processes,” IIE Transactions, Vol. 18, pp. 48-55 (1986).

[26]Salameh, M.K. and Jaber, M.Y., “Economic production quantity model for items with imperfect quality”, International Journal of Production Economics, Vol. 64, pp.59-64 (2000).

[27]Schwaller, R.L., “EOQ under inspection costs”, Production and Inventory Management . Vol. 29, pp.22-24 (1988).

[28]Silver, E. A., “Establishing the order quantity when the amount received is uncertain.” INFOR, Vol. 14 , pp.32-39 (1976).

[29]Smith, S.A. and Agrawal, N., “Management of multi-item retail inventory systems with demand substitution”, Operation Research, Vol. 48, No. 1, pp. 50-64 (2000).

[30]Subramanyam, E. S. and Kumaraswamy, S., “EOQ formula under varying marketing policies and conditions,” IIE Transactions, Vol. 19, pp. 312-314 (1981).

[31]Tersine, R. J., Principles of Inventory and Materials Management, Prentice-Hall, New Jersey (1994).

[32]Wu, K.S. and Ouyang, L.Y., “(Q,r,L) Inventory model with defective items”, Computers and Industrial Engineering, Vol. 39, Iss. 1-2, pp. 173-185 (2001).

[33]鄭家昌，「不可靠生產系統之經濟批量模式－考慮瑕疵品及重製製程」，碩士論文，國立成功大學工業管理研究所，台南(2002)。

[34]蔡依齡，「允許部分欠撥下不完美生產系統之經濟批量」，碩士論文，私立真理大學管理科學研究所，台北(2003)。

[35]趙皇傑，「在含不良品重工修復程序之生產環境下的重要決策分析」，碩士論文，私立朝陽科技大學工業工程與管理所，台中(2004)。

[36]王珊翎，「含機器當機(NR)及重工不完美品質之生產系統下的最佳生產週期決策」，碩士論文，私立朝陽科技大學工業工程與管理所，台中(2005) 。

[37]賴俊宏，「在EPQ模式下含機器當機（AR）型及重工之最佳生產週期」，碩士論文，私立朝陽科技大學工業工程與管理所，台中(2005) 。