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系統識別號 U0026-0207201415250700
論文名稱(中文) 隨機需求下之再生產點與固定經濟生產批量模式
論文名稱(英文) An Economic Production Quantity Model With a Positive Re-setup Point Under Random Demand
校院名稱 成功大學
系所名稱(中) 工業與資訊管理學系
系所名稱(英) Department of Industrial and Information Management
學年度 102
學期 2
出版年 103
研究生(中文) 楊欽閔
研究生(英文) Chin-Ming Yang
學號 R38921120
學位類別 博士
語文別 中文
論文頁數 74頁
口試委員 指導教授-李賢得
口試委員-利德江
口試委員-王清正
口試委員-陳明德
口試委員-葉丁鴻
中文關鍵字 經濟生產批量  再生產點  安全存量  隨機需求 
英文關鍵字 Lot sizing  Economic production quantity  resetup point  safety stock  random demand 
學科別分類
中文摘要 本研究探討當面臨隨機性需求環境時,為切合實際需求環境,考慮顧客需求為卜瓦松過程的隨機變數,另外安全存量的設定,將有助於降低因需求隨機性而衍生之缺貨成本,並改善存貨管理績效,故以最小化單位時間期望總成本為目標,發展再生產點之最佳生產批量模式。其中,單位時間期望總成本包含整備成本、存貨持有成本與缺貨成本,而缺貨型態按缺貨產生時點區分為生產期中因累積總需求量加上安全存量大於已生產完成量而產生的暫態缺貨,與批量生產完成時因累積總需求量大於生產批量而產生的週期缺貨,缺貨政策將採用缺貨後補加以因應,以滿足需求。
本論文以隨機過程之重新報酬理論為基礎,建構單位時間期望總成本模式。在部分限制條件下,可證得單位時間期望總成本的近似函數為生產政策再生產點與生產批量二個決策變數之凸函數,並據以發展快速搜尋方法,求得最佳再生產點與生產批量。根據演算實驗結果發現,當需求速率與缺貨成本為高水準時,相較於傳統經濟生產批量模式,本論文所發展之生產批量模式可明顯降低單位時間期望總成本,其中,顯示考慮再生產點設定不僅可減低缺貨數量與缺貨機率,亦使單位時間期望總成本下降,大幅提升生產批量模式之決策品質。
本論文之具再生產點經濟生產批量存貨模式之數學模式十分複雜,為了解需求隨機性對生產批量模式與再生產點之影響,進行簡化模式之發展,將再生產點固定為零,並不考慮週期性缺貨,建立較簡潔之單位時間總成本表示式,以快速求得最小化單位時間期望總成本之最佳生產批量。在特定限制條件下,可證得單位時間期望總成本為生產批量之凸函數,根據演算實驗發現,在需求為隨機情況下,簡化型生產批量模式較傳統經濟生產批量模式的最佳生產批量大,且可顯著改善因採用傳統經濟生產批量模式所大幅增加的暫態缺貨成本,而使單位時間期望總成本下降。
英文摘要 In this paper, an extended Economic Production Quantity (EPQ) model is studied, where demand follows a random process. This study is motivated by an industrial case for precision machine assembly in the machinery industry. Both a positive resetup point s and a fixed lot size Q are implemented in this production control policy. The resetup point, i.e., the lowest inventory level to start the production, is adopted to minimize stock shortage during the replenishment cycle. The considered cost includes setup cost, inventory carrying cost, and shortage cost, where shortage may occur at the production stage and/or at the end of one replenishment cycle. Under some mild conditions, the expected cost per unit time can be shown to be convex with respect to decision parameters s and Q. Further computational study has shown that the proposed model outperforms the classical EPQ, when faced with random demand. In particular, a positive resetup point contributes to a significant portion of this cost savings when compared with that in the classical lot sizing policy.

To simplify the mathematical model, the resetup point s is fixed to zero, a per unit time expected cost model is developed and analyzed. Under some mild conditions, it can be shown that the lower/upper bounds of the expected cost model are convex. Computational experiments have demonstrated that the proposed lot sizing policy outperforms the classical EPQ model when demand is random. In particular, significant cost savings can be achieved when demand rate and/or charge per unit short per unit time are high.
論文目次 摘要 I
Abstract II
誌謝 V
目錄 VI
圖目錄 IX
表目錄 X
第一章 緒論 1
1.1 研究動機 1
1.2 研究目的 2
1.3 研究範圍與限制 3
1.4 研究架構與流程 3
第二章 文獻回顧 6
2.1 確定型經濟批量模式 6
2.1.1 需求速率為已知固定常數之經濟批量模式 6
2.1.2 需求為已知的動態經濟批量模式 8
2.2 不確定型生產系統經濟批量模式 8
2.2.1 不可靠生產系統之經濟批量模式 9
2.2.2 需求具隨機性之經濟批量模式 11
2.3 具安全存量(再生產點)之經濟批量模式 12
2.3.1 具前置時間之經濟批量模式 12
2.3.2 具安全存量之經濟批量模式 13
第三章 單位時間期望成本模式發展 16
3.1 問題描述 16
3.2 再生產點經濟生產批量存貨模式 21
3.2.1 再生產點模式期望生產週期時間分析 21
3.2.2 再生產點模式生產期之期望成本 22
3.2.3 再生產點模式消耗期之期望成本 26
3.2.4 再生產點模式單位時間期望成本模式之特性31
3.3 簡化型經濟生產批量存貨模式 35
3.3.1 簡化型模式期望生產週期時間分析 36
3.3.2 簡化型模式生產期之期望成本 37
3.3.3 簡化型模式消耗期之期望成本 39
3.3.4 簡化型模式單位時間期望成本模式之特性 41
第四章 演算實驗與比較 45
4.1 演算法發展 45
4.2 再生產點經濟生產批量存貨模式演算實驗 47
4.2.1 再生產點模式演算範例 47
4.2.2 再生產點模式演算實驗與分析 50
4.3 簡化型經濟生產批量存貨模式演算實驗 53
4.3.1 簡化型模式演算範例 54
4.3.2 簡化型模式演算實驗與分析 55
第五章 研究成果與未來研究方向 59
5.1 研究成果 59
5.2 未來研究方向 60
參考文獻 61
附錄 66
附錄一 卜瓦松分配理論性質證明 66
附錄二 演算法程式 70
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