為了最大化公司的利益，一個有效率的生產計劃必須決定未來各期的原物料購買量、產品開始生產量(production starts)、在製品量(WIP)及最終產品庫存水準(finished good inventory level)進而達到將有限資源產能分配到各種不同產品上的目的。
由於在傳統生產計劃方法上會有前置時間(lead time)產生的問題，本研究專注在線性規劃模型結合清理函數(clearing function)的方法。傳統清理函數是將產出量(output)定義為在製品量的函數並且取代在傳統生產計劃的線性規劃模型中的產能限制式，而本研究藉由一個新提出的概念而提出一種新的清理函數，此概念是將一期中的可開始生產量分為兩部分，第一部分為初始在製品水準，而此部分的工作量需求未達產能前，都可視為可開始生產量，而第二部分為在一期之中的到達量，此部分的可生產量被在本研究中新提出的清理函數所定義。在本研究中，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(fitting method)及一種生產計劃的線性規劃模型。本研究藉由模擬實驗測試了六種清理函數方法並比較其準確性。六種清理函數方法包含兩種現有的二維方法、一種新提出的二維方法及三種新提出的三維方法。實驗結果顯示第二版的改善後二維方法(M2D-V2)及第三版的三維方法(3D-V3)在可開始加工速率之派工法則(rate-based dispatching rule)下可以得到較好的準確度。而在第三版的三維方法運用可開始加工速率之派工法則(3D-V3-Rate)可以讓計劃產出(planned output)跟模擬產出(simulated output)的差距的絕對差距比率達到8.48%。

關鍵字：生產計劃、前置時間、清理函數、模擬

To maximize the profit of a company, an effective production planning system that allocates limited capacity of various resources among different products is essential. The function of production planning system is calculating raw material purchases, production starts, work-in-process quantities, and finished good inventory levels of all future periods within a planning horizon.
The lead time considerations in traditional production planning methods, such as material requirement planning (MRP) or linear programing production planning (LPPP) models, have major impact on the accuracy of the system. Hence, this study focuses on LPPP models adopting clearing functions, which can be used to replace classical capacity constraints. A traditional clearing function model describes the output in a period of a workstation as a function of the WIP level in the period of the workstation. It can be observed that the start workload in a period comes from two portion: one is initial WIP of the period; the other is arrival during the period. Initial WIP can be started for processing as long as their capacity requirement does not exceed the available capacity in the period. Whereas, the start workload causes by the arrival during the period should be defined by a nonlinear clearing function, which is empirically derived by the technique suggested in this study. Each clearing function approach in this study consists of several techniques, including a clearing function model, a data collection method, a fitting LP formulation, and a LPPP formulation. Six clearing function approaches are tested and compared in this study. The focus of this study is comparing the accuracy of various clearing function approaches through simulation experiments, which show 3D-V3 clearing function approaches with a rate-based dispatching rule performs the best and its absolute deviation between planned outputs and simulated outputs in a period is about 8.48%.
Key words: production planning, lead time, clearing function, simulation.

TABLE OF CONTENTS
摘要 I
Abstract II
TABLE OF CONTENTS III
LIST OF FIGURES VI
LIST OF TABLES VIII
1. Introduction 1
1.1. Lead time issue of traditional production planning methods 1
1.2. Two classes of approaches to deal with the vicious circle issue 3
1.3. Research motivation 4
2. Literature review 7
2.1. Production planning model with iterative method 8
2.2. Production planning model with clearing function 10
3. Clearing function approaches 11
3.1. O2D clearing function approach 12
3.1.1. Data point collection for building O2D clearing function 13
3.1.2. The procedure to filter original data points 14
3.1.3. Piece-wise linearization LP model 15
3.1.4. O2D LPPP model 18
3.2. M2D-V1 clearing function approach 21
3.2.1. Lead time effects in LPPP 22
3.2.2. Data point collection for building M2D-V1 clearing function 28
3.2.3. The procedure to filter original data points 29
3.2.4. Piece-wise linearization LP model 29
3.2.5. M2D-V1 LPPP model 30
3.3. M2D-V2 clearing function approach 33
3.3.1. Data point collection for building M2D-V2 clearing function 34
3.3.2. The procedure to filter original data points 35
3.3.3. Piece-wise linearization LP model 36
3.3.4. M2D-V2 LPPP model 36
3.4. 3D-V1 clearing function approach 37
3.4.1. Data point collection for building 3D clearing function 38
3.4.2. The procedure to filter original data points 38
3.4.3. Plane-wise linearization LP model 40
3.4.4. 3D-V1 LPPP model 45
3.5. 3D-V2 clearing function approach 48
3.5.1. Data point collection for building 3D clearing function 48
3.5.2. The procedure to filter original data points 48
3.5.3. Modified plane-wise linearization LP model 48
3.5.4. 3D-V2 LPPP model 49
3.6. 3D-V3 clearing function approach 49
3.6.1. Data point collection for building 3D clearing function 49
3.6.2. The procedure to filter original data points 50
3.6.3. Progressive plane-wise linearization LP model 50
3.6.4. 3D-V3 LPPP model 54
4. Simulation experiments and result analysis 55
4.1. Simulation Model 55
4.1.1. Collecting sample data points to calculate clearing function 56
4.1.2. Execute the release schedule from LPPP 57
4.2. Experimental design 58
4.2.1. The parameter for fitting model 58
4.2.2. Constant input parameters for generation of a random problem 59
4.2.3. Control factors for the experiment 61
4.2.4. Generation of a random problem 62
4.2.5. Experiment procedure 65
4.3. Simulation result and analysis 69
4.3.1. Calculation of experiment response 69
4.3.2. Experiment result for each production management approach 71
4.3.3. Control factor analysis for symbolic approach 74
4.3.4. Correlation between mean demand quantities and Response 2 79
5. Conclusion and future research 80
References 82

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