裁切問題(Cutting Stock Problem; CSP) 是屬於NP-hard的問題，以往學者們都是利用數學模式合併啟發式演算法，針對矩型產品進行空間分割與規劃。而在薄膜液晶顯示器(TFT-LCD)產業中，光學膜內的高分子排列角度是重要的規格之一，因此為符合產品角度限制，生產過程中需依客戶角度進行裁切，而利用率也因此降低。本文針對角度限制產品(Bias Product)的裁切問題特性進行探討，並以數學模式合併啟發式演算法，來有效提昇原料的利用率。
本研究為有效提昇原料的利用率，首先需要依客戶尺寸與角度的限制，建構裁斷作業(Guillotine)的數學模式，然後以數學規劃模式求得其基本配置與利用率。接著以基本配置為基礎，分別以4種循序啟發式演算法(Sequential Heuristic Procedures; SHP) 演算後提出配置建議，並比較4種循序啟發式演算法的優劣。
為驗證所提出手法的實用性，本文實際運用某偏光板廠的生產訂單，利用數學規劃模式合併啟發式演算法進行求解與手法驗證。結果本文所提手法均較該廠實際利用率為佳，而其中以基礎配置結合循序啟發式演算法中的以最少空間決定法 (Best Fit; BF)表現最好，可以達到最高的利用率。最後並對原料寬幅寬度、寬幅種類與使用方式，提供管理上的建議。

The cutting stock problem (CSP) was classified to NP-Hard problem. Most scholars used the mathematical with heuristic methods to solve rectangle space cutting problem. In TFT-LCD industrial, some high polymer film need be used with angle in inlayer. To achieve the customer request, the material need be cut with angle and that will cause some useless triangle part. We not found any paper discuss about the bias product cutting problem as our searching. This paper will use mathematical with heuristic methods to solve bias product cutting problem.
We will show the mathematical model of the bias product cutting process by guillotine, before to construct mathematical programming model. After the mathematical model constructed, the basic yield and basic pattern will defined. In order to get higher yield, we try to use four kinds of heuristic methods to fill the available product in useless space and to verify the best one.
In this paper, we used real order data that got from a polarizer maker to verify our model. We suggested using Best Fit (BF) heuristic methods to solve the problem and approved our methods could help to get more usage part than the original polarizer maker. By the research result, also suggest controlling material width、material width quantity and calculating volume of orders to get more benefit.

Carvalho, J. M. & Rodrigues, A. J., An LP-based approach to a two-stage cutting stock problem, European Journal of Operational Research, 84, 580-589, 1995.

Carvalho, J. M., LP models for bin packing and cutting stock problems, European Journal of Operational Research, 141, 253-273, 2002.

Chauhan, S. S., Martal, A. & Amour, S. D., Roll assortment optimization in a paper mill:An integer programming approach, Computers & Operations Research, 35,614-617, 2008.

Cherri, A. C., Arenales, M. N. & Yanasse, H. H., The one-dimensional cutting stock problem with usable leftover – A heuristic approach, European Journal of Operational Research, 196, 897-908, 2009.

Cintra, G. F., Miyazawa, F. K., Wakabayashi, Y. & Xavier, E. C., A note on the approimability of cutting stock problems, European Journal of Operational Research, 183, 1328-1332, 2007.

Cintra, G. F., Miyazawa, F. K., Wakabayashi, Y. & Xavier, E. C., Algorithms for two-dimensional cutting stock and strip packing problems using dynamic programming and column generation, European Journal of Operational Research, 191, 61-85, 2008.

Dyckhoff, H., A typology of cutting and packing problems, European Journal of Operational Research, 44, 145-159, 1990.

Erjavec, J., Gradisar, M. & Trkman, P., Renovation of the cutting stock process, International Journal of Production Research, 47, 3979-3996, 2009.

Gilmore, P. C. & Gomory, R. E., A linear programming approach to the cutting stock problem - Part II., Operational Research, 9, 848-859, 1963.

Gilmore, P. C. & Gomory, R. E., A linear programming approach to the cutting stock problem., Operational Research, 9, 848-859, 1961.

Gilmore, P. C. & Gomory, R. E., Multi-stage cutting stock problems of two and more dimensions, Operational Research, 13, 94-120, 1965.

Glannelos, N. F. & Georgiadis, M. C., Scheduling of cutting-stock process on multiple parallel machines, Institution of Chemical Engineers, 79, 747-753, 2001.

Hinxmzn, A., The trimloss and assortment problems: a survey, European Journal of Operational Research, 5, 8-18, 1980.

Lodi, A., Martello, S. & Monaci, M., Two-dimensional packing problems: A survey, European Journal of Operational Research, 141, 241-252, 2002.

Lodi, A., Martello, S. & Vigo, D., Recent advances on two-dimensional bin packing problems, Discrete Applied Mathematics, 123, 379-396, 2002.

Poldi, K. C. & Arenales, M. N., Heuristics for the one-dimensional cutting stock problem with limite dmultiple stock lengths, Computers & Operations Research, 36,2074-2081, 2009.

Schilling, G. & Georgiadis, M. C., An algorithm for the determination of optimal cutting patterns, Computers & Operations Research, 29, 1041-1058, 2002.

Trkman, P. & Gradisar, M., One-dimensional cutting stock optimization in consecutive time periods, European Journal of Operational Research, 179, 291-301, 2007.

Umetani, S., Yagiura, M. & Ibaraki, T., One-dimensional cutting stock problem to minimize the number of different patterns, European Journal of Operational Research, 146, 388-402, 2003.

Washer, G., Haubner, H. & Schumann, H., An improved typology of cutting and packing problems, European Journal of Operational Research, 183, 1109-1130, 2007.

Yanasse, H. H. & Lamosa, M. J. P., An integrated cutting stock and sequencing problem, European Journal of Operational Research, 183, 1353-1370, 2007.

Zak, E. J., Modeling multistage cutting stock problems, European Journal of Operational Research, 141, 313-327, 2002.

Zak, E. J., Row and column generation technique for a multistage cutting stock problem, Computers & Operations Research, 29, 1143-1156, 2002.

晶威光電股份有限公司，「偏光板的結構」，http://www.skypola.com/

友達光電股份有限公司，「TFT-LCD製程介紹」，http://www.auo.com.tw/

奇美電子股份有限公司 ，「技術介紹」，http://www.chimei-innolux.com/