{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,2,21]],"date-time":"2025-02-21T10:42:27Z","timestamp":1740134547798,"version":"3.37.3"},"reference-count":14,"publisher":"Wiley","license":[{"start":{"date-parts":[[2014,1,1]],"date-time":"2014-01-01T00:00:00Z","timestamp":1388534400000},"content-version":"unspecified","delay-in-days":0,"URL":"http:\/\/creativecommons.org\/licenses\/by\/3.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Journal of Applied Mathematics"],"published-print":{"date-parts":[[2014]]},"abstract":"<jats:p>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<jats:italic>N<\/jats:italic>, generally between 2 and 6 (but potentially larger), we find the<jats:italic>N<\/jats:italic>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<jats:italic>N<\/jats:italic>increases, but this trend becomes less pronounced for larger values of<jats:italic>N<\/jats:italic>(beyond 6 or 7). For typical values of<jats:italic>N<\/jats:italic>, branch-and-bound is able to find the exact solution within a reasonable amount of time.<\/jats:p>","DOI":"10.1155\/2014\/959453","type":"journal-article","created":{"date-parts":[[2014,4,27]],"date-time":"2014-04-27T17:04:57Z","timestamp":1398618297000},"page":"1-12","source":"Crossref","is-referenced-by-count":1,"title":["Mathematical Modeling and Optimal Blank Generation in Glass Manufacturing"],"prefix":"10.1155","volume":"2014","author":[{"ORCID":"https:\/\/orcid.org\/0000-0001-6197-4333","authenticated-orcid":true,"given":"Raymond","family":"Phillips","sequence":"first","affiliation":[{"name":"School of Computational and Applied Mathematics, University of the Witwatersrand, 1 Jan Smuts Avenue, Private Bag 03, WITS 2050, Johannesburg, South Africa"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-4902-851X","authenticated-orcid":true,"given":"Matthew","family":"Woolway","sequence":"additional","affiliation":[{"name":"School of Computational and Applied Mathematics, University of the Witwatersrand, 1 Jan Smuts Avenue, Private Bag 03, WITS 2050, Johannesburg, South Africa"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-9267-8879","authenticated-orcid":true,"given":"Dario","family":"Fanucchi","sequence":"additional","affiliation":[{"name":"School of Computational and Applied Mathematics, University of the Witwatersrand, 1 Jan Smuts Avenue, Private Bag 03, WITS 2050, Johannesburg, South Africa"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"M. 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