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研究生:蔣其軒
研究生(外文):Chi-Hsuan Chiang
論文名稱:利用共同週期法求解不完美生產系統下可變動生產速率之經濟批量排程問題
論文名稱(外文):The common cycle approach to the ELSP problem with imperfect production processes and flexible production rates
指導教授:張秀雲張秀雲引用關係
指導教授(外文):Shiow-Yun Chang
學位類別:碩士
校院名稱:國立成功大學
系所名稱:工業與資訊管理學系碩博士班
學門:商業及管理學門
學類:其他商業及管理學類
論文種類:學術論文
論文出版年:2007
畢業學年度:95
語文別:中文
論文頁數:68
中文關鍵詞:可變動生產速率共同週期法經濟批量排程問題不完美生產系統
外文關鍵詞:Flexible production ratesImperfect production processesCommon cycle approachesEconomic Lot Scheduling Problem
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本研究主要探討具有多餘產能的不完美生產系統下,可變動生產速率進行生產之經濟批量排程問題。在無限期規劃下,單一機器為了最小化總生產成本而對多種產品所進行的生產排序問題即為所謂的經濟批量排程問題。本研究考慮生產系統同時具有操控狀態及失控狀態兩種模式,並假設在操控狀態下所生產的產品皆符合品管的要求。而經由長期的生產過程,此生產系統會根據指數分配由操控狀態轉移至失控狀態。在失控狀態下將會生產固定且已知比例的瑕疵品,但此生產系統可藉由維修由失控狀態轉回至操控狀態,並假設機器在生產開始前必定處於操控狀態下,分別考慮在不進行檢驗下、連續檢驗政策下與定期檢驗下的不完美生產系統之單位時間期望總成本模式。
除了上述假設之外,本研究再考量此生產系統可利用多餘的閒置時間降低生產速率來進行生產。之前多位學者已研究過降低生產速率可有效的減低生產期間的存貨成本,使總成本達到最佳。因此本研究將考慮不完美生產系統中,可變動生產速率之經濟批量排程問題,並利用共同週期法對此模式進行求解與性質分析。
求解後發現,在不進行檢驗的不完美生產系統中,可變動生產速率之經濟批量排程問題之最佳共同生產週期,將因模式增加了品質成本項而比完美生產系統時短。在連續檢驗政策的不完美生產系統中,可變動生產速率之經濟批量排程問題若不存在機器的閒置時間,則其最佳共同生產週期將會與完美系統中可變動生產速率之經濟批量排程問題具有相同的最佳解。在定期檢驗政策下,定期檢驗次數將與生產時間成正比。
In this paper, we consider the Economic Lot Scheduling Problem (ELSP) with imperfect production processes and assume the single facility is underutilized to produce with the flexible production rates. It is assumed that there are two states: “in-control” and “out-of-control” in the production processes. The production facility starts in the in-control state producing items of acceptable quality. However, the facility may shift at a random time to the out-of-control state with the exponential distributions and begins to produce a fixed fraction of nonconforming items. If the process is found to be in the out-of-control state, we could restore it to the in-control state and suppose that the restoration time is negligible. We study the imperfect process without restoration, the imperfect process with continuous review system and the imperfect process with periodic review system respectively.
Traditionally, the production rate was chosen according to the maximum capacity of the machine. However, recently it was suggested that when machines are underutilized, we could slowdown the production rate and take up the idle time to lower inventory holding costs. We consider the production facility with the flexible production rate to take up the idle time rather than the rigid approach because the flexible way always has lower cost under the common cycle policy.
Consequently, we discovered and proved several propositions. 1. The ELSP in the imperfect production process without restoration is a Convex Programming Problem. 2. In the imperfect production process with continuous review system, there is no machine idle time in the optimal solutions of some cases, and the optimal solutions of these cases are the same as those of the perfect production process. 3. In the imperfect production process with periodic review system, the inspected times increase as the production time increases. Some numerical examples are used to illustrate our propositions.
中文摘要……………………………………………………………i
Abstract……………………………………………………………ii
致謝…………………………………………………………………iv
目錄…………………………………………………………………v
表目錄………………………………………………………………viii
圖目錄………………………………………………………………ix

第一章 緒論…………………………………………………………1
1.1 研究動機與目的…………………………………………………1
1.2 研究範圍與假設…………………………………………………2
1.3 研究架構與流程…………………………………………………2

第二章 文獻探討……………………………………………………4
2.1 經濟批量排程問題常見的解法…………………………………4
2.1.1 獨立解法………………………………………………………5
2.1.2 共同週期法……………………………………………………6
2.1.3 基本週期法……………………………………………………7
2.1.4 延伸基本週期法………………………………………………7
2.2 降低生產速率的生產方法………………………………………9
2.2.1 固定低速率法…………………………………………………9
2.2.2 彈性速率法……………………………………………………10
2.3 不完美生產系統下的經濟批量問題……………………………12

第三章 模式建構……………………………………………………15
3.1 問題描述、基本假設與符號定義………………………………15
3.1.1 問題描述………………………………………………………15
3.1.2 基本假設………………………………………………………17
3.1.3 符號定義………………………………………………………18
3.2 模式推導…………………………………………………………19
3.2.1 不檢驗政策……………………………………………………20
3.2.2 連續檢驗政策…………………………………………………24
3.2.3 定期檢驗政策…………………………………………………25
3.3 模式性質之驗證與求解…………………………………………31
3.3.1 性質之驗證……………………………………………………31
3.3.2 模式之求解……………………………………………………40

第四章 數值分析……………………………………………………46
4.1 模式分析與結果…………………………………………………46
4.1.1 範例說明………………………………………………………47
4.1.2 完美生產系統下之經濟批量排程問題………………………49
4.1.3 不進行檢驗下之經濟批量排程問題…………………………50
4.1.4 連續檢驗政策下之經濟批量排程問題………………………52
4.1.5 定期檢驗政策下之經濟批量排程問題………………………54
4.2 模式之敏感度分析………………………………………………55
4.3 小結………………………………………………………………60

第五章 結論與未來研究方向………………………………………63
5.1 研究成果…………………………………………………………63
5.2 未來研究方向……………………………………………………63

參考文獻………………………………………………………………65
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」,國立成功大學工業管理研究所碩士論文,中華民國九十一年六月。
林育壯,「不可靠生產系統再生產點與固定生產批量存貨模式」,國立成功大學工業與資訊管理研究所碩士論文,中華民國九十三年六月。
張孝裕,「倉儲受限下可變動生產速率之兩產品經濟批量排程問題」,國立成功大學工業與資訊管理學系碩士論文,中華民國九十五年八月。
洪維恩,「數學運算大師 - Mathematica 5」,旗標出版股份有限公司,中華民國九十五年八月。
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