Mathematical Modeling and Optimal Blank Generation in Glass Manufacturing
This paper discusses the stock size selection problem (Chambers and Dyson, 1976), which is of relevance in the float glass industry. Given a fixed integer N, generally between 2 and 6 (but potentially larger), we find the N best sizes for intermediate stock from which to cut a roster of orders. An o...
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| Format: | Article |
| Language: | English |
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Wiley
2014-01-01
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| Series: | Journal of Applied Mathematics |
| Online Access: | http://dx.doi.org/10.1155/2014/959453 |
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| author | Raymond Phillips Matthew Woolway Dario Fanucchi M. Montaz Ali |
| author_facet | Raymond Phillips Matthew Woolway Dario Fanucchi M. Montaz Ali |
| author_sort | Raymond Phillips |
| collection | DOAJ |
| description | This paper discusses the stock size selection problem (Chambers and Dyson, 1976), which is of relevance in the float glass industry. Given a fixed integer N, generally between 2 and 6 (but potentially larger), we find the N best sizes for intermediate stock from which to cut a roster of orders. An objective function is formulated with the purpose of minimizing wastage, and the problem is phrased as a combinatorial optimization problem involving the selection of columns of a cost matrix. Some bounds and heuristics are developed, and two exact algorithms (depth-first search and branch-and-bound) are applied to the problem, as well as one approximate algorithm (NOMAD). It is found that wastage reduces dramatically as N increases, but this trend becomes less pronounced for larger values of N (beyond 6 or 7). For typical values of N, branch-and-bound is able to find the exact solution within a reasonable amount of time. |
| format | Article |
| id | doaj-art-e0235b6a79d64310906200f906b450f0 |
| institution | Kabale University |
| issn | 1110-757X 1687-0042 |
| language | English |
| publishDate | 2014-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Journal of Applied Mathematics |
| spelling | doaj-art-e0235b6a79d64310906200f906b450f02025-08-20T03:26:09ZengWileyJournal of Applied Mathematics1110-757X1687-00422014-01-01201410.1155/2014/959453959453Mathematical Modeling and Optimal Blank Generation in Glass ManufacturingRaymond Phillips0Matthew Woolway1Dario Fanucchi2M. Montaz Ali3School of Computational and Applied Mathematics, University of the Witwatersrand, 1 Jan Smuts Avenue, Private Bag 03, WITS 2050, Johannesburg, South AfricaSchool of Computational and Applied Mathematics, University of the Witwatersrand, 1 Jan Smuts Avenue, Private Bag 03, WITS 2050, Johannesburg, South AfricaSchool of Computational and Applied Mathematics, University of the Witwatersrand, 1 Jan Smuts Avenue, Private Bag 03, WITS 2050, Johannesburg, South AfricaSchool of Computational and Applied Mathematics, University of the Witwatersrand, 1 Jan Smuts Avenue, Private Bag 03, WITS 2050, Johannesburg, South AfricaThis paper discusses the stock size selection problem (Chambers and Dyson, 1976), which is of relevance in the float glass industry. Given a fixed integer N, generally between 2 and 6 (but potentially larger), we find the N best sizes for intermediate stock from which to cut a roster of orders. An objective function is formulated with the purpose of minimizing wastage, and the problem is phrased as a combinatorial optimization problem involving the selection of columns of a cost matrix. Some bounds and heuristics are developed, and two exact algorithms (depth-first search and branch-and-bound) are applied to the problem, as well as one approximate algorithm (NOMAD). It is found that wastage reduces dramatically as N increases, but this trend becomes less pronounced for larger values of N (beyond 6 or 7). For typical values of N, branch-and-bound is able to find the exact solution within a reasonable amount of time.http://dx.doi.org/10.1155/2014/959453 |
| spellingShingle | Raymond Phillips Matthew Woolway Dario Fanucchi M. Montaz Ali Mathematical Modeling and Optimal Blank Generation in Glass Manufacturing Journal of Applied Mathematics |
| title | Mathematical Modeling and Optimal Blank Generation in Glass Manufacturing |
| title_full | Mathematical Modeling and Optimal Blank Generation in Glass Manufacturing |
| title_fullStr | Mathematical Modeling and Optimal Blank Generation in Glass Manufacturing |
| title_full_unstemmed | Mathematical Modeling and Optimal Blank Generation in Glass Manufacturing |
| title_short | Mathematical Modeling and Optimal Blank Generation in Glass Manufacturing |
| title_sort | mathematical modeling and optimal blank generation in glass manufacturing |
| url | http://dx.doi.org/10.1155/2014/959453 |
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