{"id":"https://openalex.org/W2065677521","doi":"https://doi.org/10.1155/2014/959453","title":"Mathematical Modeling and Optimal Blank Generation in Glass Manufacturing","display_name":"Mathematical Modeling and Optimal Blank Generation in Glass Manufacturing","publication_year":2014,"publication_date":"2014-01-01","ids":{"openalex":"https://openalex.org/W2065677521","doi":"https://doi.org/10.1155/2014/959453","mag":"2065677521"},"language":"en","primary_location":{"id":"doi:10.1155/2014/959453","is_oa":true,"landing_page_url":"https://doi.org/10.1155/2014/959453","pdf_url":"https://downloads.hindawi.com/journals/jam/2014/959453.pdf","source":{"id":"https://openalex.org/S190082376","display_name":"Journal of Applied Mathematics","issn_l":"1110-757X","issn":["1110-757X","1687-0042"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310319869","host_organization_name":"Hindawi Publishing Corporation","host_organization_lineage":["https://openalex.org/P4310319869"],"host_organization_lineage_names":["Hindawi Publishing Corporation"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Journal of Applied Mathematics","raw_type":"journal-article"},"type":"article","indexed_in":["crossref","doaj"],"open_access":{"is_oa":true,"oa_status":"gold","oa_url":"https://downloads.hindawi.com/journals/jam/2014/959453.pdf","any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5021798043","display_name":"Raymond E. Phillips","orcid":"https://orcid.org/0000-0001-6197-4333"},"institutions":[{"id":"https://openalex.org/I192619145","display_name":"University of the Witwatersrand","ror":"https://ror.org/03rp50x72","country_code":"ZA","type":"education","lineage":["https://openalex.org/I192619145"]}],"countries":["ZA"],"is_corresponding":false,"raw_author_name":"Raymond Phillips","raw_affiliation_strings":["School of Computational and Applied Mathematics, University of the Witwatersrand, 1 Jan Smuts Avenue, Private Bag 03, WITS 2050, Johannesburg, South Africa"],"raw_orcid":"https://orcid.org/0000-0001-6197-4333","affiliations":[{"raw_affiliation_string":"School of Computational and Applied Mathematics, University of the Witwatersrand, 1 Jan Smuts Avenue, Private Bag 03, WITS 2050, Johannesburg, South Africa","institution_ids":["https://openalex.org/I192619145"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5015475693","display_name":"Matthew Woolway","orcid":"https://orcid.org/0000-0002-4902-851X"},"institutions":[{"id":"https://openalex.org/I192619145","display_name":"University of the Witwatersrand","ror":"https://ror.org/03rp50x72","country_code":"ZA","type":"education","lineage":["https://openalex.org/I192619145"]}],"countries":["ZA"],"is_corresponding":false,"raw_author_name":"Matthew Woolway","raw_affiliation_strings":["School of Computational and Applied Mathematics, University of the Witwatersrand, 1 Jan Smuts Avenue, Private Bag 03, WITS 2050, Johannesburg, South Africa"],"raw_orcid":"https://orcid.org/0000-0002-4902-851X","affiliations":[{"raw_affiliation_string":"School of Computational and Applied Mathematics, University of the Witwatersrand, 1 Jan Smuts Avenue, Private Bag 03, WITS 2050, Johannesburg, South Africa","institution_ids":["https://openalex.org/I192619145"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5070128298","display_name":"D. Fanucchi","orcid":"https://orcid.org/0000-0001-9267-8879"},"institutions":[{"id":"https://openalex.org/I192619145","display_name":"University of the Witwatersrand","ror":"https://ror.org/03rp50x72","country_code":"ZA","type":"education","lineage":["https://openalex.org/I192619145"]}],"countries":["ZA"],"is_corresponding":false,"raw_author_name":"Dario Fanucchi","raw_affiliation_strings":["School of Computational and Applied Mathematics, University of the Witwatersrand, 1 Jan Smuts Avenue, Private Bag 03, WITS 2050, Johannesburg, South Africa"],"raw_orcid":"https://orcid.org/0000-0001-9267-8879","affiliations":[{"raw_affiliation_string":"School of Computational and Applied Mathematics, University of the Witwatersrand, 1 Jan Smuts Avenue, Private Bag 03, WITS 2050, Johannesburg, South Africa","institution_ids":["https://openalex.org/I192619145"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5008314297","display_name":"M. Montaz Ali","orcid":"https://orcid.org/0000-0003-0864-8146"},"institutions":[{"id":"https://openalex.org/I192619145","display_name":"University of the Witwatersrand","ror":"https://ror.org/03rp50x72","country_code":"ZA","type":"education","lineage":["https://openalex.org/I192619145"]}],"countries":["ZA"],"is_corresponding":true,"raw_author_name":"M. Montaz Ali","raw_affiliation_strings":["School of Computational and Applied Mathematics, University of the Witwatersrand, 1 Jan Smuts Avenue, Private Bag 03, WITS 2050, Johannesburg, South Africa","TCSE, Faculty of Engineering and the Build Environment, University of the Witwatersrand, 1 Jan Smuts Avenue, Private Bag 03, WITS 2050, Johannesburg, South Africa"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"School of Computational and Applied Mathematics, University of the Witwatersrand, 1 Jan Smuts Avenue, Private Bag 03, WITS 2050, Johannesburg, South Africa","institution_ids":["https://openalex.org/I192619145"]},{"raw_affiliation_string":"TCSE, Faculty of Engineering and the Build Environment, University of the Witwatersrand, 1 Jan Smuts Avenue, Private Bag 03, WITS 2050, Johannesburg, South Africa","institution_ids":["https://openalex.org/I192619145"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5008314297"],"corresponding_institution_ids":["https://openalex.org/I192619145"],"apc_list":{"value":1050,"currency":"USD","value_usd":1050},"apc_paid":{"value":1050,"currency":"USD","value_usd":1050},"fwci":0.0,"has_fulltext":true,"cited_by_count":1,"citation_normalized_percentile":{"value":0.18498253,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":94},"biblio":{"volume":"2014","issue":null,"first_page":"1","last_page":"12"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T12176","display_name":"Optimization and Packing Problems","score":0.9997000098228455,"subfield":{"id":"https://openalex.org/subfields/2209","display_name":"Industrial and Manufacturing Engineering"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T12176","display_name":"Optimization and Packing Problems","score":0.9997000098228455,"subfield":{"id":"https://openalex.org/subfields/2209","display_name":"Industrial and Manufacturing Engineering"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T11159","display_name":"Manufacturing Process and Optimization","score":0.9537000060081482,"subfield":{"id":"https://openalex.org/subfields/2209","display_name":"Industrial and Manufacturing Engineering"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T10996","display_name":"Computational Geometry and Mesh Generation","score":0.9502999782562256,"subfield":{"id":"https://openalex.org/subfields/1704","display_name":"Computer Graphics and Computer-Aided Design"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/heuristics","display_name":"Heuristics","score":0.6738870143890381},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.5789968967437744},{"id":"https://openalex.org/keywords/blank","display_name":"Blank","score":0.5581632852554321},{"id":"https://openalex.org/keywords/upper-and-lower-bounds","display_name":"Upper and lower bounds","score":0.5575380921363831},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.5559974908828735},{"id":"https://openalex.org/keywords/branch-and-bound","display_name":"Branch and bound","score":0.5555529594421387},{"id":"https://openalex.org/keywords/selection","display_name":"Selection (genetic algorithm)","score":0.5218983292579651},{"id":"https://openalex.org/keywords/integer","display_name":"Integer (computer science)","score":0.4965537190437317},{"id":"https://openalex.org/keywords/combinatorial-optimization","display_name":"Combinatorial optimization","score":0.4797269403934479},{"id":"https://openalex.org/keywords/matrix","display_name":"Matrix (chemical analysis)","score":0.44272708892822266},{"id":"https://openalex.org/keywords/function","display_name":"Function (biology)","score":0.41070297360420227},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.39070966839790344},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.33267107605934143}],"concepts":[{"id":"https://openalex.org/C127705205","wikidata":"https://www.wikidata.org/wiki/Q5748245","display_name":"Heuristics","level":2,"score":0.6738870143890381},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.5789968967437744},{"id":"https://openalex.org/C2778089247","wikidata":"https://www.wikidata.org/wiki/Q368951","display_name":"Blank","level":2,"score":0.5581632852554321},{"id":"https://openalex.org/C77553402","wikidata":"https://www.wikidata.org/wiki/Q13222579","display_name":"Upper and lower bounds","level":2,"score":0.5575380921363831},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5559974908828735},{"id":"https://openalex.org/C93693863","wikidata":"https://www.wikidata.org/wiki/Q897659","display_name":"Branch and bound","level":2,"score":0.5555529594421387},{"id":"https://openalex.org/C81917197","wikidata":"https://www.wikidata.org/wiki/Q628760","display_name":"Selection (genetic algorithm)","level":2,"score":0.5218983292579651},{"id":"https://openalex.org/C97137487","wikidata":"https://www.wikidata.org/wiki/Q729138","display_name":"Integer (computer science)","level":2,"score":0.4965537190437317},{"id":"https://openalex.org/C52692508","wikidata":"https://www.wikidata.org/wiki/Q1333872","display_name":"Combinatorial optimization","level":2,"score":0.4797269403934479},{"id":"https://openalex.org/C106487976","wikidata":"https://www.wikidata.org/wiki/Q685816","display_name":"Matrix (chemical analysis)","level":2,"score":0.44272708892822266},{"id":"https://openalex.org/C14036430","wikidata":"https://www.wikidata.org/wiki/Q3736076","display_name":"Function (biology)","level":2,"score":0.41070297360420227},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.39070966839790344},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.33267107605934143},{"id":"https://openalex.org/C127413603","wikidata":"https://www.wikidata.org/wiki/Q11023","display_name":"Engineering","level":0,"score":0.0},{"id":"https://openalex.org/C192562407","wikidata":"https://www.wikidata.org/wiki/Q228736","display_name":"Materials science","level":0,"score":0.0},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.0},{"id":"https://openalex.org/C78519656","wikidata":"https://www.wikidata.org/wiki/Q101333","display_name":"Mechanical engineering","level":1,"score":0.0},{"id":"https://openalex.org/C86803240","wikidata":"https://www.wikidata.org/wiki/Q420","display_name":"Biology","level":0,"score":0.0},{"id":"https://openalex.org/C78458016","wikidata":"https://www.wikidata.org/wiki/Q840400","display_name":"Evolutionary biology","level":1,"score":0.0},{"id":"https://openalex.org/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","level":1,"score":0.0},{"id":"https://openalex.org/C159985019","wikidata":"https://www.wikidata.org/wiki/Q181790","display_name":"Composite material","level":1,"score":0.0},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.0}],"mesh":[],"locations_count":4,"locations":[{"id":"doi:10.1155/2014/959453","is_oa":true,"landing_page_url":"https://doi.org/10.1155/2014/959453","pdf_url":"https://downloads.hindawi.com/journals/jam/2014/959453.pdf","source":{"id":"https://openalex.org/S190082376","display_name":"Journal of Applied Mathematics","issn_l":"1110-757X","issn":["1110-757X","1687-0042"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310319869","host_organization_name":"Hindawi Publishing Corporation","host_organization_lineage":["https://openalex.org/P4310319869"],"host_organization_lineage_names":["Hindawi Publishing Corporation"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Journal of Applied Mathematics","raw_type":"journal-article"},{"id":"pmh:oai:CULeuclid:euclid.jam/1425305708","is_oa":false,"landing_page_url":"https://projecteuclid.org/euclid.jam/1425305708","pdf_url":null,"source":{"id":"https://openalex.org/S4306400787","display_name":"Project Euclid (Cornell University)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"Text"},{"id":"pmh:oai:RePEc:hin:jnljam:959453","is_oa":false,"landing_page_url":"http://downloads.hindawi.com/journals/JAM/2014/959453.xml","pdf_url":null,"source":{"id":"https://openalex.org/S4306401271","display_name":"RePEc: Research Papers in Economics","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I77793887","host_organization_name":"Federal Reserve Bank of St. Louis","host_organization_lineage":["https://openalex.org/I77793887"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"article"},{"id":"pmh:oai:doaj.org/article:e0235b6a79d64310906200f906b450f0","is_oa":false,"landing_page_url":"https://doaj.org/article/e0235b6a79d64310906200f906b450f0","pdf_url":null,"source":{"id":"https://openalex.org/S4306401280","display_name":"DOAJ (DOAJ: Directory of Open Access Journals)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Journal of Applied Mathematics, Vol 2014 (2014)","raw_type":"article"}],"best_oa_location":{"id":"doi:10.1155/2014/959453","is_oa":true,"landing_page_url":"https://doi.org/10.1155/2014/959453","pdf_url":"https://downloads.hindawi.com/journals/jam/2014/959453.pdf","source":{"id":"https://openalex.org/S190082376","display_name":"Journal of Applied Mathematics","issn_l":"1110-757X","issn":["1110-757X","1687-0042"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310319869","host_organization_name":"Hindawi Publishing Corporation","host_organization_lineage":["https://openalex.org/P4310319869"],"host_organization_lineage_names":["Hindawi Publishing Corporation"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Journal of Applied Mathematics","raw_type":"journal-article"},"sustainable_development_goals":[{"id":"https://metadata.un.org/sdg/9","display_name":"Industry, innovation and infrastructure","score":0.6399999856948853}],"awards":[],"funders":[{"id":"https://openalex.org/F4320332268","display_name":"Michigan Sea Grant, University of Michigan","ror":"https://ror.org/015tnsz82"}],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W2065677521.pdf","grobid_xml":"https://content.openalex.org/works/W2065677521.grobid-xml"},"referenced_works_count":16,"referenced_works":["https://openalex.org/W1998855065","https://openalex.org/W2011690685","https://openalex.org/W2024948279","https://openalex.org/W2033555577","https://openalex.org/W2085774108","https://openalex.org/W2088352008","https://openalex.org/W2091364465","https://openalex.org/W2092801126","https://openalex.org/W2094132822","https://openalex.org/W2094268929","https://openalex.org/W2144946856","https://openalex.org/W2153171506","https://openalex.org/W2153774705","https://openalex.org/W3145128584","https://openalex.org/W4240374930","https://openalex.org/W4243557394"],"related_works":["https://openalex.org/W2361638505","https://openalex.org/W2370352440","https://openalex.org/W2009954581","https://openalex.org/W4296141694","https://openalex.org/W2379220204","https://openalex.org/W4249926107","https://openalex.org/W2005071119","https://openalex.org/W3158546193","https://openalex.org/W2742225279","https://openalex.org/W2337361920"],"abstract_inverted_index":{"This":[0],"paper":[1],"discusses":[2],"the":[3,17,37,58,64,74,99,144],"stock":[4,43],"size":[5],"selection":[6,75],"problem":[7,65,72],"(Chambers":[8],"and":[9,30,63,84,88,94],"Dyson,":[10],"1976),":[11],"which":[12,45],"is":[13,55,66,109,140],"of":[14,50,60,76,78,127,136,151],"relevance":[15],"in":[16],"float":[18],"glass":[19],"industry.":[20],"Given":[21],"a":[22,48,69,79,148],"fixed":[23],"integer":[24],"N":[25,38,116,128,137],",":[26,138],"generally":[27],"between":[28],"2":[29],"6":[31,130],"(but":[32],"potentially":[33],"larger),":[34],"we":[35],"find":[36,143],"best":[39],"sizes":[40],"for":[41,124],"intermediate":[42],"from":[44],"to":[46,98,142],"cut":[47],"roster":[49],"orders.":[51],"An":[52],"objective":[53],"function":[54],"formulated":[56],"with":[57],"purpose":[59],"minimizing":[61],"wastage,":[62],"phrased":[67],"as":[68,101,103,115],"combinatorial":[70],"optimization":[71],"involving":[73],"columns":[77],"cost":[80],"matrix.":[81],"Some":[82],"bounds":[83],"heuristics":[85],"are":[86,96],"developed,":[87],"two":[89],"exact":[90,145],"algorithms":[91],"(depth-first":[92],"search":[93],"branch-and-bound)":[95],"applied":[97],"problem,":[100],"well":[102],"one":[104],"approximate":[105],"algorithm":[106],"(NOMAD).":[107],"It":[108],"found":[110],"that":[111],"wastage":[112],"reduces":[113],"dramatically":[114],"increases,":[117],"but":[118],"this":[119],"trend":[120],"becomes":[121],"less":[122],"pronounced":[123],"larger":[125],"values":[126,135],"(beyond":[129],"or":[131],"7).":[132],"For":[133],"typical":[134],"branch-and-bound":[139],"able":[141],"solution":[146],"within":[147],"reasonable":[149],"amount":[150],"time.":[152]},"counts_by_year":[{"year":2020,"cited_by_count":1}],"updated_date":"2026-07-23T08:03:31.855105","created_date":"2025-10-10T00:00:00"}
