生產計劃的主要目的在於滿足顧客需求並同時最佳化某項特定的績效指標，例如：最小化總成本或是最大化總收益。對於一個生產計劃系統來說，其基本的決定包括未來各期的原物料投入量以及完成品庫存水準和缺貨水準。
本研究專注於多維清理函數(clearing function)的生產計劃模型，此類模型被用來處理使用傳統生產計劃方法會遇到的前置時間所產生的問題(lead time circularity issue)。每種清理函數方法(clearing function approach)包含一種清理函數模型、一種資料點的蒐集方式、一種清理函數的擬和方法(linearization fitting)及一種生產計劃的線性規劃模型(LPPP model)。
本研究的主要目的在於提升清理函數生產計劃方法的準確性。本研究使用了兩種派工法則進行模擬實驗測試了五種二維以及一種三維的清理函數方法。實驗結果顯示，對於所有測試的清理函數方法，本研究提出的累計期限目標派工法則(cumulative period target dispatching rule)可以有效的降低實際模擬結果與生產計劃模型所求出結果之間的差異。在同時考慮準確性、目標值以及資料點蒐集的難易度下，使用三維清理函數方法配合累計期限目標派工法則(3D-CPT)的表現最為傑出。
為了提高模型所求出結果的準確性，本研究針對三維的清理函數方法測試了增加在製品工作量(WIP workloads)下限限制式的影響。根據實驗結果，三維清理函數方法結合下限限制式與累計期限目標派工法則可以進一步增加方法的準確性，平均單期單產品的計劃產出與模擬產出絕對差距比率小於百分之一。

The focus of production planning is to meet customer demands with the objective of optimizing a particular performance measure, normally total cost or revenue. The essential decisions of a production planning system are the raw material release quantities and finished good inventory/backorder levels of various products in future periods.
This study focuses on clearing function approaches which are used to deal with the lead time circularity issue faced by the traditional linear programming production planning (LPPP) models with fixed lead time parameters. Each clearing function approach involves several computation modules, including sample data points collection, piece/plane-wise linearization fitting, clear function parameters calculation, segment/plane reduction, and LPPP model.
The main purpose of this study is to increase the accuracy of release schedules obtained from LPPP models with clearing function approach. This study tests five two-dimensional clearing function approaches and one three-dimensional (3D) clearing function approach under two dispatching rules. The experiment result shows that the cumulative period target (CPT) dispatching rule suggested in this study can make the simulated outputs closer to the planned outputs from LPPP models. Considering the accuracy, objective value, and complexity of collect sample data points, 3D clearing function LPPP with CPT dispatching rule (3D-CPT) is suggested in this study.
In addition, this study shows that adding WIP workloads lower bound constraints to the LPPP model increases the accuracy of the planning results. According to the experiment results, 3D-CPT with WIP lower bound constraints provides a very good planning accuracy, less than 1% average absolute difference in monthly (28-day response period) outputs between production planning model and simulation.

摘要 I
Abstract II
TABLE OF CONTENTS III
LIST OF FIGURES VI
LIST OF TABLES VII
1. Introduction 1
1.1. Terminologies 1
1.2. Lead time issue in production planning 3
1.3. Two main approaches to overcome circularity issue 4
1.4. Motivations of this study 6
2. Literature review 8
2.1. Production planning model with iterative schemes 8
2.2. Production planning models with clearing functions 9
3. Methodology 11
3.1. O2D clearing function approach 12
3.1.1. Sample data points collection 12
3.1.2. Piece-wise linearization fitting 13
3.1.3. Segment parameters calculation 16
3.1.4. Segment reduction 16
3.1.5. LPPP models 17
3.2. M2D-V1 clearing function approach 21
3.2.1. Sample data points collection 22
3.2.2. Piece-wise linearization fitting 23
3.2.3. Segment parameters calculation 24
3.2.4. Segment reduction 24
3.2.5. Input coefficient calculation 24
3.2.6. M2D-V1 LPPP model 27
3.3. M2D-V2 clearing function approach 29
3.3.1. Sample data points collection 36
3.3.2. Piece-wise linearization fitting 37
3.3.3. Segment parameters calculation 37
3.3.4. Input coefficient calculation 37
3.3.5. LPPP model 37
3.4. 3D clearing function approach 38
3.4.1. Sample data points collection 38
3.4.2. Plane-wise surface fitting 40
3.4.3. Plane parameters calculation 47
3.4.4. Plane reduction 47
3.4.5. Input coefficient calculation 47
3.4.6. LPPP models 47
3.5. Execute the production planning results 51
3.5.1. Execute release decision from LPPP 51
3.5.2. Dispatching rules 52
4. Simulation experiments and result analysis 54
4.1. Experimental design 54
4.1.1. Constant input parameters 54
4.1.2. Control factors 56
4.1.3. Generation of a random problem 58
4.2. The simulation model 60
4.2.1. Collecting sample data points to generate clearing functions 61
4.2.2. Experimental procedure 63
4.3. Simulation result and analysis 65
4.3.1. Calculation of experiment responses 65
4.3.2. Experiment results of production management approaches 69
4.3.3. Analysis of 3D-CPT 73
4.3.4. Result of adding WIP workloads bound constraints on 3D approach 79
4.3.5. Computation time of piece/plane-wise models and LPPP models 81
5. Conclusion and future research 82
Reference 85

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