A method for demand-accurate one-dimensional cutting problems with pattern reduction
The main objective in the one-dimensional cutting stock problem (1D-CSP) is to minimize material costs. In practice, it is useful to focus on auxiliary objectives, one of which is to reduce the number of different cutting patterns. This paper discusses the classical integer IDCSP, where only one typ...
| Main Authors: | , , , , |
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| Format: | Article |
| Language: | English |
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AIMS Press
2023-02-01
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| Series: | Mathematical Biosciences and Engineering |
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| Online Access: | https://www.aimspress.com/article/doi/10.3934/mbe.2023323?viewType=HTML |
| _version_ | 1811159671857217536 |
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| author | Haihua Xiao Qiaokang Liang Dan Zhang Suhua Xiao Gangzhuo Nie |
| author_facet | Haihua Xiao Qiaokang Liang Dan Zhang Suhua Xiao Gangzhuo Nie |
| author_sort | Haihua Xiao |
| collection | DOAJ |
| description | The main objective in the one-dimensional cutting stock problem (1D-CSP) is to minimize material costs. In practice, it is useful to focus on auxiliary objectives, one of which is to reduce the number of different cutting patterns. This paper discusses the classical integer IDCSP, where only one type of stock object is included. Meanwhile, the demands of various items must be precisely satisfied in the constraints. In other words, no overproduction or underproduction is allowed. Therefore, to solve this issue, a variable-to-constant method based on a new mathematical model is proposed. In addition, we integrate the approach with two other representative methods to demonstrate its effectiveness. Both benchmark instances and real instances are used in the experiments, and the results show that the methodology is effective in reducing patterns. In particular, in terms of the solutions to the real-life instances, the proposed approach presents a 31.93 to 37.6% pattern reduction compared to other similar methods (including commercial software). |
| first_indexed | 2024-04-10T05:46:14Z |
| format | Article |
| id | doaj.art-38ec195f7aac4942ac79c37a6a359c79 |
| institution | Directory Open Access Journal |
| issn | 1551-0018 |
| language | English |
| last_indexed | 2024-04-10T05:46:14Z |
| publishDate | 2023-02-01 |
| publisher | AIMS Press |
| record_format | Article |
| series | Mathematical Biosciences and Engineering |
| spelling | doaj.art-38ec195f7aac4942ac79c37a6a359c792023-03-06T01:11:50ZengAIMS PressMathematical Biosciences and Engineering1551-00182023-02-012047453748610.3934/mbe.2023323A method for demand-accurate one-dimensional cutting problems with pattern reductionHaihua Xiao0Qiaokang Liang 1Dan Zhang2Suhua Xiao3Gangzhuo Nie41. College of Electrical and Information Engineering, Hunan University, Changsha 410082, China 2. National Engineering Laboratory for Robot Vision Perception and Control, Changsha 410082, China1. College of Electrical and Information Engineering, Hunan University, Changsha 410082, China 2. National Engineering Laboratory for Robot Vision Perception and Control, Changsha 410082, China3. Department of Mechanical Engineering, York University, Toronto ONM3J1P3, Canada4. College of Electromechanical Engineering, Guangdong Polytechnic Normal University, Guangzhou 510635, China5. Aluminum Corporation of China, Beijing 100000, ChinaThe main objective in the one-dimensional cutting stock problem (1D-CSP) is to minimize material costs. In practice, it is useful to focus on auxiliary objectives, one of which is to reduce the number of different cutting patterns. This paper discusses the classical integer IDCSP, where only one type of stock object is included. Meanwhile, the demands of various items must be precisely satisfied in the constraints. In other words, no overproduction or underproduction is allowed. Therefore, to solve this issue, a variable-to-constant method based on a new mathematical model is proposed. In addition, we integrate the approach with two other representative methods to demonstrate its effectiveness. Both benchmark instances and real instances are used in the experiments, and the results show that the methodology is effective in reducing patterns. In particular, in terms of the solutions to the real-life instances, the proposed approach presents a 31.93 to 37.6% pattern reduction compared to other similar methods (including commercial software).https://www.aimspress.com/article/doi/10.3934/mbe.2023323?viewType=HTMLcuttingcutting stockcutting patterncolumn generationoptimization algorithms |
| spellingShingle | Haihua Xiao Qiaokang Liang Dan Zhang Suhua Xiao Gangzhuo Nie A method for demand-accurate one-dimensional cutting problems with pattern reduction Mathematical Biosciences and Engineering cutting cutting stock cutting pattern column generation optimization algorithms |
| title | A method for demand-accurate one-dimensional cutting problems with pattern reduction |
| title_full | A method for demand-accurate one-dimensional cutting problems with pattern reduction |
| title_fullStr | A method for demand-accurate one-dimensional cutting problems with pattern reduction |
| title_full_unstemmed | A method for demand-accurate one-dimensional cutting problems with pattern reduction |
| title_short | A method for demand-accurate one-dimensional cutting problems with pattern reduction |
| title_sort | method for demand accurate one dimensional cutting problems with pattern reduction |
| topic | cutting cutting stock cutting pattern column generation optimization algorithms |
| url | https://www.aimspress.com/article/doi/10.3934/mbe.2023323?viewType=HTML |
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