本研究探討一類源自半導體濕製程（wet etching）材料管理情境之彈性零工式排程問題（Flexible Job-shop Scheduling Problem， FJSP）。在此環境中，作業需依據 recipe 使用特定化學材料，且機台可加工集合（machine eligibility）會隨材料配置而動態改變。為貼近 chemical bath的實務運作，本研究以 machine period 描述機台在一段期間內所載入的材料組合與可用狀態；在 period 期間，材料同時受到使用時間上限（useful lifetime）與可用量（quantity）之雙重限制，並於 period closure（材料更換）時產生可量化之剩餘材料浪費。相較於既有研究多偏向僅考量單一材料限制（僅時間或僅用量），本研究聚焦於同時納入「時間＋用量」雙重可行性（dual-feasibility），以刻畫更真實的 time–waste trade-off。 本研究建立一個雙目標（bi-objective）模型，同時最小化最大完工時間（makespan， C_max）與總加權材料浪費（total weighted material waste， TWMW）。為處理 operation assignment、sequencing、material configuration 以及 parallel batching 的高度耦合，本研究提出以圖模型為核心的整合式表示法，並設計可同時處理跨機台指派與機台內排序調整之 branching；在 batching 設定下，材料消耗採 batch-level 計算方式以避免重複計算，並使 TWMW 的計算與 period closure 機制保持一致。為提升搜尋效率與解集合品質，本研究採用 recovering beam search（RBS）作為主要搜尋架構，結合節點篩選與評估機制以控制樹狀展開規模，並以 Pareto dominance 維護非支配解集合以產生具代表性的 Pareto front。最後，透過計算實驗評估所提方法在不同問題規模與限制強度下之表現，驗證本研究在雙目標權衡、材料限制一致性與計算效率上的方法論價值。;This study investigates a flexible job-shop scheduling problem (FJSP) motivated by semiconductor wet etching operations with material-management considerations. In the studied environment， each operation requires recipe dependent chemical materials， and machine eligibility changes dynamically with the material configuration. To reflect the practical logic of chemical baths/material packages， the planning horizon of each machine is partitioned into machine periods， where a period represents the loaded material set and its availability status. Within a period， material feasibility is jointly constrained by both useful lifetime (time-driven) and quantity (consumption-driven) limits. When a period is closed due to material replacement， the remaining materials generate measurable waste. While related studies often consider only one type of material constraint (either lifetime or quantity)， this thesis focuses on a dual-feasibility setting that simultaneously models both constraints to better capture the time–waste trade-off in wet-etch operations. A bi-objective formulation is proposed to minimize the makespan (C_max) and the total weighted material waste (TWMW). To address the strong coupling among operation assignment， sequencing， material configuration， and parallel batching， the study develops an integrated graph-based representation and designs branching that can jointly handle reassignment across machines and resequencing on machines. Under batching， material usage is accounted for at the batch level to avoid double counting， ensuring that TWMW remains consistent with the period-closure mechanism. To efficiently explore the large solution space and to generate a representative set of trade-off solutions， the proposed approach adopts recovering beam search (RBS) as the main search backbone， incorporating node screening and evaluation to control tree expansion. A non-dominated archive based on Pareto dominance is maintained to construct a high-quality Pareto front for the two objectives. Finally， computational experiments are conducted across different instance scales and constraint intensities to assess the effectiveness of the proposed framework in balancing the bi-objective trade-off， maintaining material-consistency， and achieving practical computational efficiency.
