CNC加工排程問題是一種典型的彈性零工式生產排程問題（FJSSP），其複雜度已被證明為NP-hard。儘管有很多關於FJSSP的研究，但CNC加工排程問題的實際應用還沒有得到太多關注，相關論文也很有限。實際上，CNC加工產業存在幾個關鍵特徵，可能對排程問題產生很大影響，分別是製程彈性、多資源限制和批量調度。製程彈性允許產品通過其任何可替代製程完成，可理解為產品能透過不同順序的不同工序步驟完成生產。另外還應注意，由於不同機台的加工能力不同，導致不同製程的良率可能彼此不同。此時製程規劃和排程的整合變得致關重要。除了機台之外，夾治具也是用於生產產品的主要資源。雖然在產能規劃階段期間夾治具的數量處於足夠的水平，但由於若干產品同時需要相同的夾治具，規劃人員有時會遇到夾治具短缺。因此，需要適當的排程來避免這種情況。而批量調度的用意為讓作業（批）可以被分成許多較小的作業（子批），使得相同作業的前後工序步驟因分成多批而可以重疊，通常用於提高生產效率。
本研究旨在建立一個整合訂單資訊、在製品資訊（WIP）和上述CNC加工產業特徵且基於混合式多目標基因演算法（HMOGA）結合局部搜索的排程系統。HMOGA的最佳參數組合由實驗設計決定，且通過計算分析來檢驗局部搜索的有效性。最後採用公司的實際數據來驗證所提出的方法。結果表明，本研究開發的排程系統在現實世界的CNC加工問題中表現良好。

CNC machining scheduling problem is a classical flexible job shop scheduling problem (FJSSP) which has been proven to be NP-hard. Although lots of research works on FJSSP, applications for real-world CNC machining scheduling problem have not received much attention and the related papers are limited. In reality, several critical characteristics exist in CNC machining industry and can cause great impact on the scheduling problem, which are process plan flexibility, multiple resource constraints and lot streaming respectively. Process plan flexibility allows a product to be finished by any of its alternative process plans with different required operations under different processing sequence. It should also be noticed that yield rates of process plans are possibly different to each other because of the different processing capability of machines. So, the integration of process planning and scheduling becomes important. On top of machine, fixture is also a main resource used to produce the products. Even though the quantity of fixture is at a sufficient level during capacity planning stage, planners sometimes encounter fixture shortage owing to several products requiring the same fixture at the same time. Consequently, a proper scheduling is needed to avoid this situation. And lot streaming describes a job (lot) can be split into a number of smaller jobs (sublots) so that successive operations of the same job can be overlapped, and is often used to enhance production efficiency.
This research aims to establish a scheduling system integrating order information, work in process (WIP) information and the abovementioned characteristics for CNC machining scheduling industry based on a hybrid multi-objective genetic algorithm (HMOGA) combined with local search. The best parameter combination of HMOGA is decided by design of experiment, and the effectiveness of local search is checked through computational analysis. Lastly, real data from a company will be adopted to verify the proposed method. The result shows that the scheduling system developed by this research performs well in the real-world CNC machining scheduling problem.

摘要…………………………………………………………………………………………………………………………..I
Abstract…………………………………………………………………………………………………………………….II
致謝…………………………………………………………………………………………………………………........IV
Contents…………………………………………………………………………………………………………………..VI
List of Tables…………………………………………………………………………………………………………….IX
List of Figures……………………………………………………………………………………………………………X
Chapter 1: Introduction…………………………………………………………………………………………….1
1.1 Background and Motivation………………………………………………………………………………..1
1.2 Research Objective………………………………………………………………………………………………6
1.3 Research Method………………………………………………………………………………………………..7
1.4 Organization of Thesis…………………………………………………………………………………………8
Chapter 2: Literature Review…………………………………………………………………………………..10
2.1 Scheduling in CNC Machining Industry………………………………………………………………10
2.2 Framework of Scheduling System………………………………………………………………………14
2.3 Integration of Process Planning and Scheduling…………………………………………………17
2.4 Scheduling with Multiple Resource Constraints…………………………………………………20
2.5 Lot Streaming……………………………………………………………………………………………………23
2.6 Multi-objective Evolutionary Algorithm for Scheduling Problem……………………….25
2.7 Contribution of the Research…………………………………………………………………………….29
Chapter 3: Problem Definition…………………………………………………………………………………36
3.1 Problem Statement……………………………………………………………………………………………36
3.2 Notations and Assumptions………………………………………………………………………………42
3.3 Mathematical Formulation………………………………………………………………………………..46
Chapter 4: Methodology…………………………………………………………………………………………51
4.1 Scheduling System Framework………………………………………………………………………….51
4.2 Fundamental Database and Data Pre-treatment for scheduling…………………………52
4.2.1 Database used in the Scheduling System………………………………………………………..52
4.2.2 Data Pre-treatment………………………………………………………………………………………..54
4.3 Process Plan Treatment Module (PPTM)……………………………………………………………57
4.4 Order Priority Module (OPM)……………………………………………………………………………59
4.5 Hybrid Multi-objective Genetic Algorithm (HMOGA)…………………………………………60
4.5.1 Framework of the Proposed HMOGA……………………………………………………………..62
4.5.2 Encoding and Decoding Schema…………………………………………………………………….63
4.5.3 Initial Population Generation………………………………………………………………………….69
4.5.4 Fitness Evaluation…………………………………………………………………………………………..76
4.5.5 Selection ………………………………………………………………………………………………………..76
4.5.6 Crossover……………………………………………………………………………………………………….77
4.5.7 Mutation………………………………………………………………………………………………………..86
4.5.8 Local Search……………………………………………………………………………………………………91
4.5.9 Next Population Generation……………………………………………………………………………94
Chapter 5: Computational Analysis ……………………………………………………………………….103
5.1 Execution Environment of the Scheduling System……………………………………………103
5.2 Convergent Situation of HMOGA…………………………………………………………………….104
5.3 Design of Experiment for HMOGA Parameter Setting………………………………………109
5.3.1 Significant Parameters for HMOGA……………………………………………………………….109
5.3.2 Best Parameter Combination for HMOGA…………………………………………………….113
5.3.3 Solutions under the Best Parameter Combination Setting…………………………….115
5.4 Performance Comparison for Different Algorithm……………………………………………125
5.5 Analysis of Objective Values at Different Maximum Sublot Quantity……………….128
Chapter 6: Conclusion……………………………………………………………………………………………130
Reference………………………………………………………………………………………………………………133
Appendix………………………………………………………………………………………………………………147
Appendix A: Real Case Dataset for Computational Analysis…………………………………..147
Appendix B: Experimental Observation for ANOVA……………………………………………….159
Appendix C: Test Case used to Compare Different Algorithms……………………………….168

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