本研究旨在解決半導體製造中的排程問題，特別是涉及操作分配和材料分配的雙目標優化問題。目標是最小化完工時間（Makespan）與總加權材料浪費（Total Weighted Material Wasted; TWMW），考慮了決定哪些的材料組合要被裝載在機器上的材料分派(Material assignment)及平行批次處理(Parallel batching)的子問題，因此引入了一種結合材料分配多樣性與操作權重的解決方案，期望能找到符合需求之優化排程。在我們的排程問題中，機台可行性(Machine eligibility)並不是預先給定好的，會隨著面對不同的作業的配方(Recipe)，材料需求組合會有所變化，我們使用能夠表示批次處理的連結圖(Conjunctive graph)來表示操作順序，並引入材料分配機制來計算每種材料在不同機台間的分配機率。在初步解的構建過程中，結合了操作權重和材料分配策略，並通過遺傳算法（Genetic Algorithms; GA）進行優化，並在材料交叉操作中通過加權機制解決材料選擇的問題和基於材料使用機率的移除策略，期望進一步優化了材料分配的過程，再由非支配排序基因演算法(Non-dominated Sorting Genetic Algorithm II; NSGA-II)，去求得雙目標的柏拉圖前緣(Pareto front)，在每一次的迭代中找到適合留下來的子代，在有限的時間內求得優化解。;This study aims to address scheduling problems in semiconductor manufacturing, particularly focusing on the bi-objective optimization involving operation assignment and material assignment. The objectives are to minimize makespan and Total Weighted Material Wasted (TWMW). Sub-problems include determining the combinations of materials to be loaded onto machines (Material assignment) and managing Parallel Batching. To this end, a solution combining material allocation diversity and operation weighting is proposed, aiming to achieve optimized scheduling that meets specific requirements. In the context of our scheduling problem, machine eligibility is not predetermined; it dynamically changes with the recipes of different operations, leading to variations in material demand combinations. We employ a Conjunctive Graph capable of representing batch processing to depict operation sequences and introduce a material allocation mechanism to calculate the probabilities of assigning each material to different machines. During the construction of initial solutions, we integrate operation weighting and material allocation strategies, optimizing them through Genetic Algorithms (GA). In the material crossover operation, a weighted mechanism is used to resolve material selection issues, complemented by a removal strategy based on material usage probability, to further optimize the material allocation process. Subsequently, the Non-dominated Sorting Genetic Algorithm II (NSGA-II) is employed to obtain the Pareto front of the bi-objective problem, identifying suitable offspring at each iteration and achieving optimized solutions within a limited timeframe.
