生產計劃在公司中扮演著一個重要的腳色，其透過最適當地分配不同資源去達到顧客需求，同時最大化利潤或最小化成本。較為廣泛使用的生產計劃方法是線性規劃生產計劃(linear programming production planning, LPPP)。然而，前置時間所造成的循環議題(lead time circularity issue)往往影響了傳統的線性規劃生產計劃模型的準確性。為了解決前置時間循環議題，現有文獻中有兩個主要的研究方向，其中包含模擬迭代方法的線性規劃模型和清理函數(clearing function, CF)方法。
本研究主要針對三維清理函數(three-dimensional CF)方法與考慮在週期端點在製品(work-in-process, WIP)的建模方法兩個模型。然而，即使這些模型表現很好，先前文獻指出當生產前置時間越長，兩個模型的表現越差。因此，本研究主要目的是去探討規劃期長度與生產前置時間之間關係如何影響兩個模型的表現。本研究將規劃期長度與生產前置時間的比例關係設成因子執行實驗。實驗中兩個模型用來解不同問題案例，模擬則是用來計算模擬產量，而模擬產量將用來比較規劃產量去驗證線性規劃生產計劃模型的準確性。

Production planning plays an important role for a company. It optimally allocates different types of resources to meet customer’s demand by maximizing the profit or minimizing the cost. The widely-used approach in production planning is linear programming production planning (LPPP). However, lead time circularity issue usually affects the accuracy of traditional LPPP models. To deal with the lead time issue, there are two main research directions of approaches in existing literatures, including LP simulation iteration approach and clearing function approach.
This study focuses on the two models, three-dimensional (3D) clearing function approach and modeling approach considering the WIP at the boundaries of period. However, although these two models perform well, previous works seem to point out that the longer production lead time, the worse these two models perform. Therefore, the main focus of this study is to investigate how the relationship of planning period length and production lead time affects the performance of the two models. This study sets the ratio of planning period length to production lead time as a control factor to conduct the experiments. The two models are used to solve various problem instances and simulations are used to calculate simulated outs, which are then compared with planned outs in order to provide the accuracy of the LPPP models.

摘要 i
Abstract ii
目錄 iii
圖目錄 v
表目錄 vi
1. 緒論 1
1.1. 線性規劃生產模型相關術語 1
1.2. 生產計劃的前置時間議題 2
1.3. 動機 5
2. 文獻探討 6
2.1. 生產計劃模型迭代法 6
2.2. 利用清理函數的生產計劃模型 8
2.3. 規劃期邊界在製品批量計算生產計劃模型 11
3. 方法 12
3.1. 3D清理函數法 12
3.1.1. 資料點蒐集 14
3.1.2. 平面分段表面擬合 15
3.1.3. 平面參數計算 19
3.1.4. 平面刪減 19
3.1.5. 輸入、產出相關限制式參數計算 19
3.1.6. 3D LPPP模型 22
3.2. BWIPL 建模方法 24
3.2.1. 產能限制式參數計算 25
3.2.2. 輸入產出相關限制式參數計算 35
3.2.3. BWIPL 模型 35
3.3. 影響LPPP模型的平均前置時間與規劃期長度之間關係 39
4. 實驗與結果分析 40
4.1. 參數 41
4.1.1. LPPP模型的參數 41
4.1.2. 模擬參數 46
4.2. 實驗 47
4.2.1. 模擬模型 47
4.2.2. 實驗流程 48
4.3. 模型表現計算 50
4.3.1. 差異評估計算 50
4.3.2. 目標值計算 53
4.4. 實驗結果與分析 53
4.4.1. 差異評估 54
4.4.2. 目標值 57
5. 結論與未來研究 60
文獻參考 61
附錄A 63

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