在過去的多尺寸平面切割問題中，皆假設平面材料的數量是無限制，而實際的生產情形，則是需考慮材料成本，因此並非所有材料是無限制供應，因此本研究將在考量材料數量受限制的情況下，以節省材料成本為目標，討論平面切割問題。
本研究依據切割問題特性發展啟發式演算法，為解決過多的變數（切割樣式），使用變數產生法去產生可行且可降低材料成本的切割樣式，透過變數產生法為主架構將本研究中的三個數學模式，單一材料切割模式、產生切割樣式以及構件排列模式巧妙的串連起來，建立一套演算法。透過各種問題類型測試演算法，觀察其求解績效。
經數量受限制切割演算法實際建構後，其演算法可處理至二十五種不同的產品種類，且其最長求解時間也在四十分鐘內完成，因此使用變數產生法做為數量受限制切割演算法的架構著實能大大縮短找尋切割樣式的時間，且找到的切割樣式能有效降低材料使用成本。此外，在考量實際的生產情況，材料數量有限制的情形，數量受限制切割演算法能有效幫工廠找出合適的生產方式，進而達到節省材料成本的目標。

In the past multi-dimensional cutting stock problem assumed that the amount of material is unconstrained. In fact, material costs should be considered at the actual production situation, and not all materials have unlimited amount. Based on that the amount of material is limited, this research discussed the cutting stock problem, and minimize the total stock cost.
Because of too many variables (cutting patterns) of the cutting stock problem, we developed a heuristic algorithm based on column generation method to generate feasible cutting patterns. Column generation is the core construction of the heuristic algorithm. This research uses three sub-models which are the cutting stock, the cutting patterns and the arrangement of items to construct the algorithm. Through a variety of instances the algorithm is tested, and its solution performance is observed.
The cutting algorithm can handle 25 different products, and the maximum solving time is 40 minutes. So using a column generation method as algorithm schema can greatly reduce the time of finding cutting pattern, and the cutting pattern found can effectively reduce material cost. Moreover, the algorithm can help facility effectively to find a good way of production with limited materials.

中文部分：
謝秉倫，「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研究所碩士論文，中華民國九十四年六月。
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