臺灣博碩士論文加值系統

當面臨隨機需求時，本論文提出一般型與簡化型兩種最佳生產批量決策模式。模式中針對定速生產，但需求為卜瓦松過程之固定批量生產系統進行探討，其目標為最小化包含機器整備成本、存貨持有成本與因需求隨機性而衍生之缺貨成本等之單位時間期望總成本。其中，缺貨型態按缺貨產生時點區分為於生產期中因累積總需求量大於已生產完成量而產生的暫態缺貨，與於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。而依據缺貨型態之不同，將分別採用缺貨後補(暫態缺貨)與外包(週期缺貨)等不同之補貨政策加以因應，以滿足需求。
在生產速率大於平均需求速率的情況下，一般型最佳生產批量決策模式將暫態缺貨與週期缺貨對生產存貨系統所造成之影響同時納入模式中分析，其利用存貨水準、已生產完成量與累積總需求量間之關係，建構單位時間期望總成本模式，並可證得單位時間期望總成本之近似函數為生產批量之凸函數。另由演算實驗結果發現，相較於傳統經濟生產批量模式，一般型最佳化模式所得之最佳生產批量較大；且隨著平均需求速率與生產速率比值之增加，單位時間期望總成本的改善幅度顯著提升。其中，降低機器整備成本可大幅降低單位時間期望總成本。
在生產速率遠大於平均需求速率的情況下，產生瞬間缺貨與週期缺貨的發生機率微小，其效應假設可忽略不計，因此，簡化型最佳生產批量決策模式僅需考慮機器整備成本、存貨持有成本與暫態缺貨成本。在特定條件下，本研究證得簡化型最佳化模式之單位時間期望總成本的近似函數為生產批量之凸函數，且相較於傳統經濟生產批量模式，模式以較大之生產批量來因應隨機需求對生產存貨系統所造成之影響，並可顯著地降低單位時間期望總成本。
本研究為針對隨機需求而發展之固定生產批量下的最佳生產批量決策模式，綜合研究結果可發現，相較於傳統經濟生產批量模式，本論文所發展之模式可顯著降低生產存貨相關總成本，並顯示將需求不確定性納入決策模式中，可大幅提升生產存貨管理之決策品質。

In this thesis, an extended Economic Production Quantity (EPQ) model under stochastic demand is investigated, where a fixed lot sizing policy is implemented to reduce the complexity of production planning and inventory control, and outsourcing with a secondary facility is used to supplement the lot sizing policy and to cope with the random demand. The considered cost includes: setup cost for the batch production, inventory carrying cost, backorder cost when the demand cannot be met immediately during the production period, and outsourcing cost when the total demand is greater than the lot size in one replenishment cycle.
For the general case where production rate is larger than demand rate, both backorder and outsourcing may occur in one replenishment cycle. A per unit time expected cost model is developed. Under some mild conditions, it can be shown that the cost function is convex. The computational study has demonstrated that significant cost savings can be achieved by deploying the proposed production lot sizing policy with an outsourcing strategy when the mean demand rate is high.
For the simplified case where production rate is significantly larger than demand rate, the probability or the amount of outsourcing becomes negligible. A reduced per unit time expected cost model is developed. Under some mild conditions, the per unit time cost model is shown to be convex. Extensive computational tests have illustrated that the average cost reduction of the proposed model is significant when compared with that of the classical lot sizing policy.
The main contributions of this thesis are two folds. An extended EPQ model with two different operating strategies to deal with shortages is developed and analyzed. The computational tests have illustrated that the optimal lot sizes in the proposed models are consistently larger than the ones in the classical EPQ. The average cost reduction of the proposed models is significant when compared with those of the classical lot sizing policy. In addition, the impact of various parameters on the expected cost models and the lot sizing policies is illustrated.

摘要 I
誌謝 III
目錄 IV
表目錄 VI
圖目錄 VII
第一章 緒論 1
1.1 研究動機 2
1.2 研究目的 3
1.3 研究範圍與限制 3
1.4 研究架構 4
第二章 文獻回顧 5
2.1 古典經濟生產批量模式 5
2.1.1 需求為已知固定常數型系統 6
2.1.2 需求為已知不定型系統 7
2.2 延伸型經濟生產批量模式 7
2.2.1 不可靠生產型系統 8
2.2.2 不完美生產型系統 9
2.2.3 隨機需求型系統 10
2.3 可缺貨型經濟生產批量模式 11
2.3.1 缺貨後補型系統 11
2.3.2 銷售損失型系統 12
2.3.3 部分銷售損失型系統 13
第三章 生產批量模式發展 17
3.1 問題描述 17
3.2 生產期之期望成本分析 24
3.3 消耗期之期望成本分析 27
3.4 一般型最佳生產批量決策模式 30
3.5 簡化型最佳生產批量決策模式 33
第四章 演算實驗分析 39
4.1 演算法發展 39
4.2 一般型最佳生產批量決策模式之演算實驗 42
4.2.1 演算範例 42
4.2.2 演算實驗與分析 44
4.3 簡化型最佳生產批量決策模式之演算實驗 47
4.3.1 演算範例 47
4.3.2 演算實驗與分析 49
4.4 小結 51
第五章 研究成果與後續研究議題 52
5.1 研究成果 52
5.2 後續研究議題 53
參考文獻 54
附錄 59
附錄一：卜瓦松分配理論性質證明 59
附錄二：生產期中產生暫態缺貨之發生機率分析 64

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