本研究在製造商不良品不完美重工生產系統下以數學模式建構出整合購買者存貨持有成本的兩個存貨模式。模式(一)為製造商於生產時間t1內生產足夠多個購買者於生產時間t1及重工時間t2之良品需求量後立即配送一次，重工完成後定量多次配送至多個購買者的存貨模式，本模式假設製造商於正常生產過程會產生不良品，且不良品皆可重工，而不良品在重工修復期間亦有報廢品產生；模式(二)為製造商在共同週期下生產多樣產品並多次配送的存貨模式，而本模式假設生產之不良品完全報廢；兩模式在配送方面，由於基本經濟生產批量(EPQ)假設需求為連續配送的，但實務上並不符合實際情況，因此製造商將產品配送至購買者時使用定量批次的配貨方式。接著分別建構模式(一)、(二)之數學模式且皆整合製造商與購買者存貨持有成本，使總成本最小化，並分別探討「最佳生產批量與最佳配送次數」及「最佳生產時間與最佳配送次數」之最佳化決策。最後以數值例子作驗證，並對相關參數做敏感度分析與模式之比較，期望本研究之模式能夠因應實務之情況，提供業界作為實務應用與決策上之參考。

This research develops two mathematical models with buyer’s inventory holding costs under the imperfect production system. They are (1) EPQ model with (n+1) deliveries strategy to multiple-buyers. This model also assumes have failure ratio in rework of defective items. (2) Multi-item production system with scrap and multi-delivery policy under rotation cycle policy. Traditional EPQ model assumes that the demand for the shipment is continuous, but it is not realistic. Therefore, the delivery of products often adopts multiple fixed quantity shipments. Total costs include manufacturer and buyer of inventory costs, and the objective is to minimize the total costs. Optimal lot size and best delivery policy are derived for Model 1. Optimal production time and number of deliveries are obtained for Model 2. Finally, numerical examples are provided for validation and sensitivity analysis demonstrates its applicability.

中文摘要 i
Abstract ii
誌謝 iii
目錄 iv
表目錄 vii
圖目錄 viii
第一章 緒論 1
1.1 研究動機與目的 1
1.2 研究範圍與界定 2
1.3 研究方法 3
1.4 研究流程與架構 4
第二章 文獻探討 7
2.1 經濟訂購批量(EOQ)與經濟生產批量(EPQ) 7
2.2 整合製造商和購買者相關之文獻 9
2.2.1 單一製造商vs單一購買者相關文獻 10
2.2.2 單一製造商vs多個購買者相關文獻 11
2.3 不良品、重工及報廢品之相關文獻 12
2.3.1 不良品與重工相關文獻 12
2.3.2 不良品重工及報廢品相關文獻 16
2.4 多樣產品相關之文獻 18
2.5 多次配送相關文獻 19
第三章 數學模式建構 22
3.1 建構模式(一)之整合購買者存貨成本數學模式最佳化 22
3.1.1 模式(一)之建構描述與參數符號說明 22
3.1.2 模式(一)公式推導 25
3.2 建構模式(二)之整合購買者存貨成本數學模式最佳化 34
3.2.1 模式(二)之建構描述與參數符號說明 34
3.2.2 模式(二)公式推導 36
第四章 數值驗證與敏感度分析 42
4.1 模式(一)之數值例子 42
4.1.1模式(一)之數值驗證與敏感度分析 43
4.1.2模式(一)與先前研究之比較 48
4.2 模式(二)之數值例子 60
4.2.1 模式(二)數值驗證與敏感度分析 61
4.2.2 模式(二)多樣產品之使用率比較 65
第五章 結論與建議 68
5.1 兩模式分析之結論 68
5.1.1 模式(一)之結論 68
5.1.2 模式(二)之結論 70
5.2 本研究對產業之貢獻 71
5.2.1 模式(一)之貢獻 71
5.2.2 模式(二)之貢獻 71
5.3 未來研究方向 71
參考文獻 73
【附錄A】模式(一)之製造商於配送時間內存貨公式推導 A-1
【附錄B】模式(一)之購買者存貨持有公式推導 B-1
【附錄C】模式(一)之(Q,n+1)模式公式推導 C-1
【附錄D】模式(二)之製造商於配送時間內存貨推導 D-1
【附錄E】模式(二)之購買者存貨持有公式推導 E-1
【附錄F】模式(二)之(T,n)模式公式推導 F-1
【附錄G】比例週期之相關概念 G-1

表目錄
表1-1 模式(一)與模式(二)之基本假設比較表 2
表2-1 EOQ與EPQ模式之基本假設比較表 8
表2-2 本研究與主要文獻比較表 21
表3-1 模式(一)之參數符號說明表 23
表3-2 模式(二)之參數符號說明表 34
表4-1 模式(一)之數值假設表 42
表4-2 模式(一)之敏感度分析事項表 44
表4-3 模式(一)與先前研究之比較事項表 49
表4-4 兩模式於重工後配送次數相同之列表 49
表4-5 兩模式的總配送次數相同之列表 51
表4-6 兩模式分別最佳解之列表 52
表4-7 模式(二)之數值假設表 60
表4-8 模式(二)之敏感度分析事項表 62
表5-1 模式(一)與先前研究比較之結果表 69
表5-2 製造商配送決策之決策條件列表 69
表G-1 比例週期數值假設表 G-1
表G-2 模式(二)之共同週期與比例週期成本表 G-3
圖目錄
圖1-1 研究流程與架構圖 5
圖3-1 模式(一)之單一製造商對多個購買者示意圖 23
圖3-2 模式(一)之製造商良品存貨圖 26
圖3-3 模式(一)之製造商不良品存貨圖 28
圖3-4 模式(一)之製造商報廢品存貨圖 29
圖3-5 模式(一)之顧客端之良品存貨圖 29
圖3-6 模式(二)之製造商良品存貨圖 36
圖3-7 模式(二)之製造商不良品存貨圖 38
圖3-8 模式(二)之顧客端良品存貨圖 38
圖4-1 模式(一)之配送次數與多種成本之關係圖 45
圖4-2 模式(一)之不良率、報廢率對多種成本之關係圖 45
圖4-3 模式(一)之不良率、報廢率對最佳生產批量之關係圖 46
圖4-4 模式(一)之不良率、報廢率對最佳期望年總成本之關係圖 46
圖4-5 模式(一)之不良率、報廢率對最佳生產批量之曲面圖 47
圖4-6 模式(一)之不良率、報廢率對最佳期望年總成本之曲面圖 47
圖4-7 模式(一)之配送次數、生產批量對期望年總成本之曲面圖 48
圖4-8 兩模式於重工後配送次數相同且不含生產成本之比較 50
圖4-9 兩模式於重工後配送次數相同之多種相關成本比較圖 50
圖4-10 兩模式的總配送次數相同且不含生產成本之成本比較圖 51
圖4-11 兩模式的總配送次數相同之多種相關成本比較 52
圖4-12 兩模式分別最佳解且不含生產成本之成本比較圖 53
圖4-13 兩模式分別最佳解之多種相關成本比較圖 54
圖4-14 兩模式分別最佳解之總運送成本比較圖 54
圖4-15 兩模式分別最佳解之總持有成本比較圖 55
圖4-16 分析(1).(2)結果與兩模式最佳解且不含生產成本比較圖 55
圖4-17 供應鏈環境下之製造商配送決策問題 56
圖4-18 製造商在配送決策上之分析圖 57
圖4-19 購買者數與最佳配送次數之關係圖 58
圖4-20 購買者數與最佳生產批量之關係圖 58
圖4-21 購買者數與最佳年期望總成本之關係 59
圖4-22 平均固定運送成本與最佳期望年總成本之關係 59
圖4-23 模式(二)推導步驟 61
圖4-24 模式(二)之配送次數與多種成本之關係圖 63
圖4-25 模式(二)之平均不良率與多種成本之關係圖 63
圖4-26 模式(二)之平均不良率與個別生產批量之關係圖 64
圖4-27 模式(二)之平均不良率對最佳期望年總成本之關係圖 64
圖4-28 模式(二)之配送次數、生產時間對期望年總成本之曲面圖 65
圖4-29 模式(二)之單一產品與多樣產品比較圖 66
圖4-30 模式(二)之單一產品與多樣產品使用率比較圖 67
圖5-1 模式(二)多樣產品在共同週期下生產之存貨模型圖 70
圖5-2 五樣產品之共同週期與比例週期成本比較圖 72
圖G-1 五樣產品之共同週期與比例週期成本比較圖 G-4

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