生產計劃(Production Planning)是指在有限的可用生產資源下，為了盡可能即時滿足客戶訂單與最小化成本等，對生產系統中的材料、機器設備和勞動力進行配置的計劃。為了考慮線性規劃生產計劃(Linear Programming Production Planning, LPPP)模型中的前置時間(Lead Time)效應並解決所謂的循環議題，現有文獻提出了兩類方法。一種是迭代模擬方法的線性規劃模型；另一個是清理函數(Clearing Function, CF)方法。然而，現有這兩種方法在求解過程中都忽略了在製品(Work-in-process, WIP)在週期的端點所產生的工作量(Workload)，如此一來可能會造成計劃和模擬（實際）情況之間的偏差。因此，為了精確建立週期的產能限制式，本文研究了在週期邊界仍在加工中的在製品工作量。
在週期中的在製品批次是指那些無法在同一個週期中完工的批次，而在製品批次的加工時間會造成不同週期的產能負荷。在週期邊界前的加工時間應消耗在該邊界前的週期產能，在週期邊界後的加工時間應消耗在該邊界後的週期產能。因此，在製品的批次工作量在不同週期的分布由加工時間（輸入與輸出的時間間隔）與週期的長度決定。一段週期的工作量是週期邊界前後所造成的在製品批次工作量與同時在該週期輸入與輸出的批次工作量所組成。本研究透過模擬實驗來測試與驗證此建模技巧是否有效，而由於相較於清理函數之數學模型容易求解，因此應用本研究提出之建模技術之模型較清理函數節省了87%的時間且表現良好。

Production planning makes the decisions related to the allocation of various resources, such as materials, machines and labor, in a production system to fulfill customer orders as on-time as possible with the objective of minimizing costs under limited available resources. To consider lead time effects in linear programming production planning (LPPP) models or to solve the so called circularity issue, two classes of approaches were proposed in existing literatures. One is LP simulation iteration approaches; the other one is clearing function (CF) approaches. However, these two classes of existing approaches ignore the workload generated by the work-in-process (WIP) at the boundaries of periods, which may cause deviations between planned outs and simulation/actual outs. Hence, to properly model the capacity constraints in periods, this study accurately calculates the workloads in the periods that account for the processing of WIP at a period boundary.
WIP lots at period boundaries refer to those lots that cannot complete in the same period. The processing time of a WIP lot contributes to the workloads of various periods. The portion of the processing time before the boundary should charge the capacity of the periods before the boundary, and the portion of the processing time after the boundary should charge the capacity of the periods after the boundary. Hence, the workload of a period consists of those from the WIP lots at the beginning and ending boundaries of the period, plus those from the lots both inputted and outputted in the period. The distributions of a WIP lot to various periods is determined by the relationship between processing time (input-output time lag) and period length. This study tests and validates the effectiveness of the proposed modeling technique by simulation experiments. This study performs well and saves 87% of the computation time of CF because of lower difficulty for solving mathematical model.

摘要 I
Abstract II
TABLE OF CONTENTS IV
LIST OF FIGURES VI
LIST OF TABLES VI
1. Introduction 1
1.1. Linear programming production planning 1
1.2. Lead time issue in production planning 4
1.3. Motivations of this study 6
2. Literature Review 9
2.1. Production planning model with iterative method 9
2.2. Production planning model with clearing function method 11
3. Method 16
3.1. Input-output relation modeling technique 16
3.2. Capacity-constrained parameter calculation 20
3.3. Input-output-relation-constrained parameter calculation 33
3.4. LPPP model 36
4. Experiments and result analysis 41
4.1. Parameters setting 42
4.1.1. Parameters of constraints for LPPP 42
4.1.2. Parameters for simulation 47
4.2. Experiment design 48
4.2.1. Simulation model 48
4.2.2. Experimental procedure 49
4.3. Result and analysis 50
4.3.1. Calculation of experiment responses 50
4.3.2. Calculation of objective value 52
4.3.3. Experiment results 53
4.3.4. Factor analysis 55
5. Conclusion and future research 61
Reference 63

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