非等效平行機台問題旨在多部功能相似機台，可同時進行加工且不會互相影響，而不同機台的加工效率不盡相同。針對此問題實務上多以人工進行排程，但需要考量的限制及條件繁複，再加上急/插單等突發狀況，人工作業勢難以應付。有鑑於此，本篇研究在考量諸多實務限制條件下，建構一個以模擬退火法(Simulated Annealing)為基礎，結合變鄰域下降法(Variable Neighborhood Descent )之啟發式演算法，針對排程問題，以最小化最晚完工時間(Minimum Makespan)以及符合Burn-In機台加工比例為目標，期能找出符合實務需求之優化排程，研究中考量之限制條件包括每日工時上限、機台可行性、設置時間、Burn In級距限制等。實證結果表明，本研究所提出的方法能解決商業求解軟體無法在短時間內求解之中大型規模問題，且能透過調整參數的方式，適應不同的生產條件，並在有限的時間內求得優化解。

The unrelated parallel machine scheduling problem aims to assign jobs to independent machines with sequence-dependent setup times so that the makespan is minimized. When many practical considerations are introduced, solving the resulting problem is challenging, especially when problems of realistic sizes are of interest. In this study, in addition to the conventional objective of minimizing the makespan, we further consider the burn-in (B/I) procedure that is required in practice; we need to ensure that the scheduling results satisfy the B/I ratio constrained by the equipment. To solve the resulting complicated problem, we propose a population-based simulated annealing algorithm embedded with a variable neighborhood descent technique. Empirical results show that the proposed solution strategy outperforms a commonly used commercial optimization package. It can find the optimal solution for small problem instances and is scalable to solve problem instances of realistic sizes in a limited time.

1. INTRODUCTION----------------------- 1
1.1 Research background-------------- 1
1.2 Research motivation-------------- 1
1.3 Research purpose and method------ 2
1.4 Research framework--------------- 2
2. LITERATURE REVIEW------------------ 5
2.1 Single operation----------------- 5
2.1.1 Single machine scheduling------ 6
2.1.2 Parallel machine scheduling---- 6
2.1.2.1 Unrelated parallel machines-- 7
2.1.2.2 Identical parallel machines-- 10
2.2 Multiple operations-------------- 11
2.2.1 Flow shop scheduling problem--- 12
2.2.2 Job shop scheduling problem---- 12
2.2.3 Open shop scheduling problem--- 13
2.3 Summary-------------------------- 13
3. MATHEMATICAL FORMULATION----------- 16
4. SOLUTION APPROACH------------------ 23
4.1 Initial solution----------------- 23
4.2 Algorithm steps------------------ 24
4.2.1 Initialization----------------- 24
4.2.2 Neighborhood search------------ 24
4.2.3 Incumbent solution updating---- 26
4.2.4 Termination-------------------- 27
4.3 Summary-------------------------- 27
5. NUMERICAL EXPERIMENTS-------------- 29
5.1 Parameter calibration------------ 29
5.2 Validation----------------------- 31
5.3 Practical application scenarios-- 34
6. CONCLUDING REMARKS----------------- 38
6.1 Conclusion and contribution------ 38
6.2 Future work---------------------- 38
REFERENCES----------------------------- 40

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