@article {10.3844/jmssp.2010.79.83, article_type = {journal}, title = {Solving One-Dimensional Cutting Stock Problem with Discrete Demands and Capacitated Planning Objective}, author = {Wongprakornkul, Sirirat and Charnsethikul, Peerayuth}, volume = {6}, year = {2010}, month = {Jun}, pages = {79-83}, doi = {10.3844/jmssp.2010.79.83}, url = {https://thescipub.com/abstract/jmssp.2010.79.83}, abstract = {Problem statement: One-dimensional cutting stock problem with discrete demands and capacitated planning objective is an NP hard problem. Approach: The mathematical model with column-generation technique by a branch-and-bound procedure and the heuristic based on the first fit decreasing method are proposed. Then, both approaches were compared and some characteristics were investigated such as upper-bound value, percentage above lower-bound value, computation time, and number of patterns. Results: The 24 instances were examined. The proposed heuristic provides the upper-bound value above the lower-bound around 0-16.78%. All upper-bound values from column-generation and integer programming are better than the proposed heuristic but all computation times are higher. Conclusion: The proposed heuristic has consistently high performance in computation times.}, journal = {Journal of Mathematics and Statistics}, publisher = {Science Publications} }