{"id":"https://openalex.org/W2153243076","doi":"https://doi.org/10.1007/s10479-010-0767-1","title":"Mixed-integer programming techniques for decomposing IMRT fluence maps using rectangular apertures","display_name":"Mixed-integer programming techniques for decomposing IMRT fluence maps using rectangular apertures","publication_year":2010,"publication_date":"2010-06-21","ids":{"openalex":"https://openalex.org/W2153243076","doi":"https://doi.org/10.1007/s10479-010-0767-1","mag":"2153243076"},"language":"en","primary_location":{"id":"doi:10.1007/s10479-010-0767-1","is_oa":false,"landing_page_url":"https://doi.org/10.1007/s10479-010-0767-1","pdf_url":null,"source":{"id":"https://openalex.org/S57667410","display_name":"Annals of Operations Research","issn_l":"0254-5330","issn":["0254-5330","1572-9338"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Annals of Operations Research","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":false,"oa_status":"closed","oa_url":null,"any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5047632649","display_name":"Z. Caner Ta\u015fk\u0131n","orcid":"https://orcid.org/0000-0002-9904-4315"},"institutions":[{"id":"https://openalex.org/I4405392","display_name":"Bo\u011fazi\u00e7i University","ror":"https://ror.org/03z9tma90","country_code":"TR","type":"education","lineage":["https://openalex.org/I4405392"]}],"countries":["TR"],"is_corresponding":false,"raw_author_name":"Z. Caner Ta\u015fk\u0131n","raw_affiliation_strings":["Department of Industrial Engineering, Bo\u011fazi\u00e7i University, 34342, Bebek, \u0130stanbul, Turkey"],"affiliations":[{"raw_affiliation_string":"Department of Industrial Engineering, Bo\u011fazi\u00e7i University, 34342, Bebek, \u0130stanbul, Turkey","institution_ids":["https://openalex.org/I4405392"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5034706918","display_name":"J. Cole Smith","orcid":"https://orcid.org/0000-0001-5106-6964"},"institutions":[{"id":"https://openalex.org/I33213144","display_name":"University of Florida","ror":"https://ror.org/02y3ad647","country_code":"US","type":"education","lineage":["https://openalex.org/I33213144"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"J. Cole Smith","raw_affiliation_strings":["Department of Industrial and Systems Engineering, University of Florida, 303 Weil Hall, P.O. Box 116595, Gainesville, FL, 32611-6595, USA"],"affiliations":[{"raw_affiliation_string":"Department of Industrial and Systems Engineering, University of Florida, 303 Weil Hall, P.O. Box 116595, Gainesville, FL, 32611-6595, USA","institution_ids":["https://openalex.org/I33213144"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5004083650","display_name":"H. Edwin Romeijn","orcid":"https://orcid.org/0000-0003-0977-0274"},"institutions":[{"id":"https://openalex.org/I27837315","display_name":"University of Michigan\u2013Ann Arbor","ror":"https://ror.org/00jmfr291","country_code":"US","type":"education","lineage":["https://openalex.org/I27837315"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"H. Edwin Romeijn","raw_affiliation_strings":["Department of Industrial and Operations Engineering, University of Michigan, 1205 Beal Avenue, Ann Arbor, MI, 48109-2117, USA"],"affiliations":[{"raw_affiliation_string":"Department of Industrial and Operations Engineering, University of Michigan, 1205 Beal Avenue, Ann Arbor, MI, 48109-2117, USA","institution_ids":["https://openalex.org/I27837315"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5004083650"],"corresponding_institution_ids":["https://openalex.org/I27837315"],"apc_list":{"value":2390,"currency":"EUR","value_usd":2990},"apc_paid":null,"fwci":2.1872,"has_fulltext":false,"cited_by_count":11,"citation_normalized_percentile":{"value":0.88010462,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":96},"biblio":{"volume":"196","issue":"1","first_page":"799","last_page":"818"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10358","display_name":"Advanced Radiotherapy Techniques","score":0.9998000264167786,"subfield":{"id":"https://openalex.org/subfields/3108","display_name":"Radiation"},"field":{"id":"https://openalex.org/fields/31","display_name":"Physics and Astronomy"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T10358","display_name":"Advanced Radiotherapy Techniques","score":0.9998000264167786,"subfield":{"id":"https://openalex.org/subfields/3108","display_name":"Radiation"},"field":{"id":"https://openalex.org/fields/31","display_name":"Physics and Astronomy"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T10522","display_name":"Medical Imaging Techniques and Applications","score":0.9993000030517578,"subfield":{"id":"https://openalex.org/subfields/2741","display_name":"Radiology, Nuclear Medicine and Imaging"},"field":{"id":"https://openalex.org/fields/27","display_name":"Medicine"},"domain":{"id":"https://openalex.org/domains/4","display_name":"Health Sciences"}},{"id":"https://openalex.org/T10977","display_name":"Optical Imaging and Spectroscopy Techniques","score":0.9837999939918518,"subfield":{"id":"https://openalex.org/subfields/2741","display_name":"Radiology, Nuclear Medicine and Imaging"},"field":{"id":"https://openalex.org/fields/27","display_name":"Medicine"},"domain":{"id":"https://openalex.org/domains/4","display_name":"Health Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/integer-programming","display_name":"Integer programming","score":0.8195288777351379},{"id":"https://openalex.org/keywords/theory-of-computation","display_name":"Theory of computation","score":0.7132816314697266},{"id":"https://openalex.org/keywords/integer","display_name":"Integer (computer science)","score":0.5928816199302673},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.5786744356155396},{"id":"https://openalex.org/keywords/matrix","display_name":"Matrix (chemical analysis)","score":0.563774585723877},{"id":"https://openalex.org/keywords/integer-matrix","display_name":"Integer matrix","score":0.5173096656799316},{"id":"https://openalex.org/keywords/decomposition","display_name":"Decomposition","score":0.5086315870285034},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.4916432499885559},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.4781726002693176},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.43374863266944885},{"id":"https://openalex.org/keywords/linear-programming","display_name":"Linear programming","score":0.43081045150756836},{"id":"https://openalex.org/keywords/benders-decomposition","display_name":"Benders' decomposition","score":0.4200061559677124},{"id":"https://openalex.org/keywords/symmetric-matrix","display_name":"Symmetric matrix","score":0.1250891387462616},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.11388245224952698},{"id":"https://openalex.org/keywords/eigenvalues-and-eigenvectors","display_name":"Eigenvalues and eigenvectors","score":0.06561011075973511}],"concepts":[{"id":"https://openalex.org/C56086750","wikidata":"https://www.wikidata.org/wiki/Q6042592","display_name":"Integer programming","level":2,"score":0.8195288777351379},{"id":"https://openalex.org/C24858836","wikidata":"https://www.wikidata.org/wiki/Q844718","display_name":"Theory of computation","level":2,"score":0.7132816314697266},{"id":"https://openalex.org/C97137487","wikidata":"https://www.wikidata.org/wiki/Q729138","display_name":"Integer (computer science)","level":2,"score":0.5928816199302673},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.5786744356155396},{"id":"https://openalex.org/C106487976","wikidata":"https://www.wikidata.org/wiki/Q685816","display_name":"Matrix (chemical analysis)","level":2,"score":0.563774585723877},{"id":"https://openalex.org/C62555958","wikidata":"https://www.wikidata.org/wiki/Q6042601","display_name":"Integer matrix","level":5,"score":0.5173096656799316},{"id":"https://openalex.org/C124681953","wikidata":"https://www.wikidata.org/wiki/Q339062","display_name":"Decomposition","level":2,"score":0.5086315870285034},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.4916432499885559},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.4781726002693176},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.43374863266944885},{"id":"https://openalex.org/C41045048","wikidata":"https://www.wikidata.org/wiki/Q202843","display_name":"Linear programming","level":2,"score":0.43081045150756836},{"id":"https://openalex.org/C27665512","wikidata":"https://www.wikidata.org/wiki/Q3042795","display_name":"Benders' decomposition","level":2,"score":0.4200061559677124},{"id":"https://openalex.org/C54848796","wikidata":"https://www.wikidata.org/wiki/Q339011","display_name":"Symmetric matrix","level":3,"score":0.1250891387462616},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.11388245224952698},{"id":"https://openalex.org/C158693339","wikidata":"https://www.wikidata.org/wiki/Q190524","display_name":"Eigenvalues and eigenvectors","level":2,"score":0.06561011075973511},{"id":"https://openalex.org/C18903297","wikidata":"https://www.wikidata.org/wiki/Q7150","display_name":"Ecology","level":1,"score":0.0},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","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/C192562407","wikidata":"https://www.wikidata.org/wiki/Q228736","display_name":"Materials science","level":0,"score":0.0},{"id":"https://openalex.org/C139018669","wikidata":"https://www.wikidata.org/wiki/Q6961560","display_name":"Nonnegative matrix","level":4,"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}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1007/s10479-010-0767-1","is_oa":false,"landing_page_url":"https://doi.org/10.1007/s10479-010-0767-1","pdf_url":null,"source":{"id":"https://openalex.org/S57667410","display_name":"Annals of Operations Research","issn_l":"0254-5330","issn":["0254-5330","1572-9338"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Annals of Operations Research","raw_type":"journal-article"},{"id":"pmh:oai:RePEc:spr:annopr:v:196:y:2012:i:1:p:799-818:10.1007/s10479-010-0767-1","is_oa":false,"landing_page_url":"http://hdl.handle.net/10.1007/s10479-010-0767-1","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"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":26,"referenced_works":["https://openalex.org/W26314658","https://openalex.org/W337408891","https://openalex.org/W1966876292","https://openalex.org/W1968143413","https://openalex.org/W1968143987","https://openalex.org/W1972562189","https://openalex.org/W1973619523","https://openalex.org/W1975598755","https://openalex.org/W1984280574","https://openalex.org/W2017244914","https://openalex.org/W2024644980","https://openalex.org/W2030993720","https://openalex.org/W2042443501","https://openalex.org/W2049181072","https://openalex.org/W2066474750","https://openalex.org/W2084991719","https://openalex.org/W2087205557","https://openalex.org/W2117801253","https://openalex.org/W2155417411","https://openalex.org/W2157771622","https://openalex.org/W2163241124","https://openalex.org/W2169315729","https://openalex.org/W2183888585","https://openalex.org/W2798566347","https://openalex.org/W4254913749","https://openalex.org/W6724904386"],"related_works":["https://openalex.org/W3024185138","https://openalex.org/W4285278887","https://openalex.org/W2995925505","https://openalex.org/W2365237642","https://openalex.org/W1993356786","https://openalex.org/W3116484972","https://openalex.org/W2941986668","https://openalex.org/W4232431455","https://openalex.org/W2064698314","https://openalex.org/W2089185195"],"abstract_inverted_index":null,"counts_by_year":[{"year":2021,"cited_by_count":1},{"year":2019,"cited_by_count":1},{"year":2018,"cited_by_count":1},{"year":2015,"cited_by_count":2},{"year":2013,"cited_by_count":1},{"year":2012,"cited_by_count":1}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}