大多數之平面切割問題限制切割方向須與原料邊線垂直或是平行，而在薄膜液晶顯示器(TFT-LCD)產業中，光學膜內之高分子排列角度為重要的產品規格，其影響到顯示器能否正確顯示明或暗之狀態，因此切割方向須依照產品之角度需求進行調整，導致過往多數之平面切割數學模式不適用。基於上述，本研究針對此類具角度限制之切割問題建構數學模式，且發展角度切割演算法，在滿足訂單之情形下，以最小化使用原料為目標，求解最佳之切割樣式與樣式使用次數。
本研究依據組合刀模切割製程之特性建構角度限制切割模式，接著將其分為三個數學模式，分別為單尺寸產品模式、訂單分配模式與樣式產生模式，並以列生成法串連三個模式，針對組合刀模切割製程，建立角度切割演算法，透過不同類型問題之測試，觀察其求解績效，並基於數值分析所得依據，接著針對多階段切割製程，提出最高利用決定法與截斷角度切割演算法，隨後透過不同訂單比較求解績效。
經過測試後發現於產品尺寸差異較大、訂單數差異較小時，使用組合刀模切割製程，可比多階段切割製程耗費較少的原料以滿足訂單需求，而針對多階段切割製程方面，於問題較小時，可以截斷角度切割演算法求得最佳解，於問題較大時，可以最高利用決定法在短時間內取得品質不錯的切割編排樣式。

This study investigates the two-dimensional cutting problem with angle restriction (AR2DCP), in which each product has to be cut with a specific angle. The cutting problem has been extensively studied in the TFT-LCD industry. There are two cutting processes, single-stage process and multi-stage process, in the TFT-LCD industry. We develop the angle restricted cutting (ARC) algorithm based on column generation for the single-stage cutting process. Additionally, we develop the maximal utilization (MU) and angle restricted guillotine cutting (ARGC) algorithms for the multi-stage cutting process. The use of the ARC and ARGC algorithms can obtain the optimal solution for a small-sized problem. For large-sized problems, the feasible solutions can be obtained from the MU algorithm, which would cause less trim loss.

中文部分：
王祥安，2011年，利用線性規劃法求解LCD光學膜切割問題，國立成功大學工業與資訊管理學系碩士在職專班碩士論文。
吳東儒，2012年，偏光板裁切計畫之編排研究，國立成功大學工程科學系碩士在職專班碩士論文。
鄒筱薇，2010年，數量受限制之多尺寸材料切割問題，國立成功大學工業與資訊管理學系碩士論文。
劉育青，2010年，利用數學規劃與啟發式演算法求解角度限制產品的裁切問題，國立成功大學工業與資訊管理學系碩士在職專班碩士論文。
謝秉倫，2006年，平面原料切割問題之最佳化演算法，國立台北科技大學商業自動化與管理學系碩士論文。

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