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研究生:歐陽炳昌
研究生(外文):Bing-Chang OuYang
論文名稱:線性需求下整合性生產存貨模式之最佳批量
論文名稱(外文):An optimal batch size for integrated production-inventory model with a linear trend in demand
指導教授:黃惠民黃惠民引用關係饒忻饒忻引用關係
指導教授(外文):Hui-Ming WeeHsin Rau
學位類別:博士
校院名稱:中原大學
系所名稱:工業工程研究所
學門:工程學門
學類:工業工程學類
論文種類:學術論文
論文出版年:2007
畢業學年度:95
語文別:英文
論文頁數:73
中文關鍵詞:整合性生產補貨模式整合性生產存貨模式線性需求經濟補貨批量模式經濟生產批量模式
外文關鍵詞:integrated production- replenishment for a manufacturinproduction modelreplenishment modelintegrated production-inventory modellinear trend in demand
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由於產品需求有淡旺季的現象,過去許多生產或存貨研究的文獻合理地將需求假設為線性函數,且在過去三十年來,大多數文獻皆著重在生產或補貨問題中之最佳解與啟發式演算法的研究,此現象暗示著這類問題的演算法仍有改善空間。
本論文先檢視過去線性需求文獻的演算法,進而提出演算法的改進與其他領域的應用。首先本文將需求為線性函數文獻歸為三類:經濟補貨批量模式、經濟生產批量模式及整合性生產補貨模式。再針對此三種存貨模式個別地提出演算法的改進,簡化過去文獻的複雜運算,本文亦提供完整理論證明彌補過去文獻保留的推測及數值驗證,由結果證實本研究所發展的演算法也是最佳解。
此外,我們還將所發展的演算法延伸到供應鏈管理上單一買賣雙方的應用,發展一個整合性生產存貨模式並提供完整理論證明,驗證本研究建議的模式亦是最佳解,同時也提出範例說明本研究的整合性生產存貨模式與供應鏈整合的重要性。
Due to the usual business cycle of boom and slack, the demand pattern has been assumed to be a reasonably linear trend for production or inventory problems in the literature. In the past three decades, many efforts have made to determine the optimal solution for both production and replenishment problems with a linear trend in demand. However most studies have remained focused on the fundamental methodology and heuristic method development. This implies that a powerful algorithm for these problems is still needed.
In this dissertation, we first provide a simple and accurate algorithm to obtain optimal solutions for previous researches including the replenishment model, production model and integrated production-replenishment for a manufacturing system. Our algorithm is very simple and no complex mathematical calculations such as a cubic equation or power function are required for determining the optimal schedule. In addition, we also develop a general equation to determine the optimal production or replenishment schedule for these three models. The purpose of this study was to provide demonstrations of applicability and completely theoretical proofs to relax some conjectures from previous studies. From the results, we validate that our proposed algorithm is also an optimal solution.
In addition, when considering a supply chain environment, we present an integrated production-inventory model with a linear trend in demand. It is assumed that a vendor makes a single product and supplies it to a buyer with a non-periodic and just-in-time (JIT) replenishment model. The objective is to minimize the joint total cost incurred by the vendor and the buyer. We also provide complete theoretical demonstrations to verify that the Hessian matrix with total cost is positive definite, the solution of the production schedule for a specified production cycles is unique and that the total cost of the production cycles is a convex function of the production cycles. Furthermore, we also show that the performance of integrated consideration in the joint total cost is better than the performance of an independent decision for the buyer or vendor.
中文摘要 i
英文摘要 ii
誌謝 iii
中文目錄 iv
英文目錄 vi
表目錄 viii
圖目錄 ix

第一章 緒論
1.1 研究背景與目的 1
1.2 研究範圍 2
1.3 論文架構 3

第二章 文獻探討
2.1 線性需求之補貨模式 5
2.2 線性需求之生產模式 6
2.3 線性需求之生產補貨模式 6
2.4 線性需求相關文獻摘要 7
2.5 整合性生產存貨模式 8

第三章 模式描述
3.1 緒論 9
3.2 通用假設與符號描述 9
3.3 模式描述 10

第四章 補貨模式
4.1 緒論 11
4.2 數學模式 11
4.2.1 單一線性需求之最佳解 11
4.2.2 雙線性需求之啟發式演算法 13
4.3 求解程序 16
4.4 數值範例 18
4.5 小結 22

第五章 生產模式
5.1 緒論 24
5.2 數學模式 24
5.3 求解程序 28
5.4 數值驗證 30
5.5 小結 332

第六章 整合性生產補貨模式
6.1 緒論 34
6.2 數學模式 35
6.3 模式比較 38
6.4 求解程序 39
6.5 數值驗證 41
6.5.1 補貨模式 41
6.5.2 生產模式 41
6.5.3 整合性生產補貨模式 44
6.6 小結 45

第七章 整合性生產存貨模式
7.1 緒論 50
7.2 數學模式 50
7.3 求解程序 55
7.4 數值範例 57
7.5 小結 61

第八章 結論與未來研究方向
8.1 結論 68
8.2 未來研究方向 69

參考文獻 70

LIST OF TABLES
Table Page
Table 2-1 Summary of Various models with a linear trend in demand 8
Table 4-1 Parameters of 25 numerical examples for a single-piece linear model 18
Table 4-2 Results for the comparison of examples in Table 4-1 20
Table 4-3 Optimal replenishment schedule comparison for Example No.1 shown
in Table 4-4 21
Table 4-4 Parameters of 7 numerical examples for the piecewise-linear model 21
Table 4-5 Costs comparison between the proposed algorithm and two
single-piece models shown in Table 4-4 22
Table 4-6 Replenishment schedules comparison of the proposed algorithm and
two single-piece models for Example No.1 shown in Table 4-3 22
Table 5-1 Validations for linearly increasing demand 31
Table 5-2 Total cost for various iterations for Example 5-1 31
Table 5-3 Validations for linearly decreasing demand 32
Table 6-1 Demonstrations for the replenishment model and production model 43
Table 6-2 New example and demonstrations for the integration productionreplenishment
model 45
Table 7-1 Optimal solutions for various P in Example 7-1 57
Table 7-2 Comparison of various costs for the vendor and buyer with various n
in Example 7-1 (P = 2000) 58
Table 7-3 Optimal solutions for various P in Example 7-2 59
Table 7-4 Comparison of various costs for the vendor and buyer with various n
in Example 7-2 (P = 2000) 60
Table 7-5 Comparison of optimal solutions for various viewpoints (P = 2000) 61

LIST OF FIGURES
Figure Page
Figure 1-1 Schematic of a generic supply chain 2
Figure 1-2 The configuration of this dissertation 3
Figure 4-1 The kth replenishment period across stages one and two in the
piecewise linear model 14
Figure 5-1 Number of production cycles n against the total cost W(n) for
Example 5-1 32
Figure 5-2 Number of production cycles n against the total cost W(n) for
Example 5-2 with H = 5 33
Figure 6-1 Number of production cycles n against the total cost W(n) for
Example 6-6 with P = 500 44
Figure 7-1 The inventory level for the vendor and the buyer 52
Figure 7-2 Comparison of various costs for the vendor and the buyer with n in
Example 7-1 (P = 2000) 58
Figure 7-3 Comparison of various costs for the vendor and the buyer with n in
Example 7-2 (P = 2000) 60
Figure 7-4 The inventory level for Cv(n, tp0, Hp) and Cv(n+1, τp0, Hp) 65
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