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研究生:林鳳玉
研究生(外文):Feng-Yu Lin
論文名稱:不完美品質之生產系統下探討經濟生產批量模式-應用代數方法求解
論文名稱(外文):The Economic Production Quantity Model with Random Scrap Items Derived Algebraically
指導教授:邱元錫邱元錫引用關係
指導教授(外文):Yuan-Shyi Chiu
學位類別:碩士
校院名稱:朝陽科技大學
系所名稱:工業工程與管理系碩士班
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:2005
畢業學年度:93
語文別:中文
論文頁數:54
中文關鍵詞:隨機不良率代數方法求解經濟生產批量
外文關鍵詞:Algebraic derivationRandom scrap rateProduction
相關次數:
  • 被引用被引用:2
  • 點閱點閱:453
  • 評分評分:
  • 下載下載:1
  • 收藏至我的研究室書目清單書目收藏:0
本研究主要發展出利用代數方法求解經濟生產批量(EPQ)及經
濟訂購批量(EOQ)的相關問題。其中包含兩個主題,(1)傳統EPQ模
式中,不完美品質生產系統隨機產生不良品,在允許缺貨的條件下,
應用代數法推導出最佳生產數量、最大允許缺貨欠撥水準及最小總成
本。(2)在傳統EPQ模式中,不完美品質生產系統隨機產生不良品,
在不允許缺貨的條件下,應用代數法推導出最佳生產數量及最小總成
本。
傳統的EPQ/EOQ模式中,都是將期望成本函數做一次及二次
微分,若二次微分大於零,則表示函數有極小值存在。再將一次微
分令為零,進而求解。但近幾年來已有文獻提出在不使用微分的條
件下,利用代數方法針對傳統的EPQ模式及傳統的EOQ模式做推
導求解。本研究延續該文獻之方法中所假設的條件:隨機產生不良
品,而後發展出其他相關議題,其中包括在不完美品質生產系統下,
不良品採全數報廢處理,分別針對允許缺貨及不允許缺貨兩種情況
對數量及成本做探討。期望幫助不瞭解或不會微積分的實務工作者
能應用類似的代數方法解得其相關生產數量及其最佳期望總成本。
This study proposes an algebraic method for solving imperfect quality economic production quantity (EPQ) model. It includes the following two subjects: (1) the EPQ model with random scrap items and shortages are permitted and backordered; (2) the EPQ model with random scrap items and no shortages are allowed. Algebraic derivations are used in each case, in order to obtain the optimal production operating policies that minimize the overall production-inventory costs.
Traditional approaches for deriving optimal production lot size are by using the differential calculus on the production-inventory cost function with the need to prove optimality first. Recent articles proposed the algebraic approach to the solution of classic economic order quantity (EOQ) and economic production quantity (EPQ) model without reference to the use of derivatives. This paper extends it to a finite production rate model taking the backlogging and random scrap rate into consideration. This study demonstrates that optimal production lot size for the aforementioned model can be derived algebraically and the expected overall production-inventory costs can be obtained immediately as well.
The results of this thesis are verified with prior works of the same models and when scrap rate equals to zero, it is identical to the optimal lot-size equations given by the classic EPQ models. Numerical examples demonstrate their practical usages.
目 錄
摘 要 I
目 錄 II
圖 目 錄 IV
表 目 錄 V
符 號 目 錄 VI
第一章 緒論 1
1.1 研究動機與目的 2
1.2 研究範圍與界定 2
1.3 研究方法 3
1.4 研究架構與流程 4
第二章 文獻探討 6
2.1典型經濟訂購/生產批量模式 6
2.2無不良品之存貨模式的相關文獻 8
2.3具不良品之存貨模式的相關文獻 9
2.4允許缺貨及欠撥模式之相關文獻 9
2.5傳統EPQ及EOQ之解法探討 10
第三章 代數方法應用於存貨模式之求解 13
3.1代數方法應用於典型EOQ模式之發展 14
3.2代數方法應用於典型EPQ模式之發展 16
3.3本研究探討之主題一:不完美品質之EPQ模式在不允許缺貨條件下之代數解 19
3.4本研究探討之主題二:不完美品質之EPQ模式在允許缺貨條件下之代數解 26
第四章 實例驗証與分析 38
4.1.1不允許缺貨模式 38
4.1.2允許缺貨模式 40
4.2.1不允許缺貨模式 44
4.2.2允許缺貨模式 46
第五章 結論與未來研究方向 49
5.1 結論 49
5.2 未來研究方向 50
參考文獻 52
參考文獻
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