{"id":"https://openalex.org/W2155708792","doi":"https://doi.org/10.1007/s10107-008-0225-x","title":"MIR closures of polyhedral sets","display_name":"MIR closures of polyhedral sets","publication_year":2008,"publication_date":"2008-05-16","ids":{"openalex":"https://openalex.org/W2155708792","doi":"https://doi.org/10.1007/s10107-008-0225-x","mag":"2155708792"},"language":"en","primary_location":{"id":"doi:10.1007/s10107-008-0225-x","is_oa":false,"landing_page_url":"https://doi.org/10.1007/s10107-008-0225-x","pdf_url":null,"source":{"id":"https://openalex.org/S193920097","display_name":"Mathematical Programming","issn_l":"0025-5610","issn":["0025-5610","1436-4646"],"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":"Mathematical Programming","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/A5115590938","display_name":"Sanjeeb Dash","orcid":null},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Sanjeeb Dash","raw_affiliation_strings":["IBM, T.J. Watson Research Center, P.O. Box 218, Yorktown Heights, NY, 10598, USA"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"IBM, T.J. Watson Research Center, P.O. Box 218, Yorktown Heights, NY, 10598, USA","institution_ids":[]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5034471689","display_name":"Oktay G\u00fcnl\u00fck","orcid":"https://orcid.org/0000-0002-9272-377X"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Oktay G\u00fcnl\u00fck","raw_affiliation_strings":["IBM, T.J. Watson Research Center, P.O. Box 218, Yorktown Heights, NY, 10598, USA"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"IBM, T.J. Watson Research Center, P.O. Box 218, Yorktown Heights, NY, 10598, USA","institution_ids":[]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5083656325","display_name":"Andrea Lodi","orcid":"https://orcid.org/0000-0001-9269-633X"},"institutions":[{"id":"https://openalex.org/I9360294","display_name":"University of Bologna","ror":"https://ror.org/01111rn36","country_code":"IT","type":"education","lineage":["https://openalex.org/I9360294"]}],"countries":["IT"],"is_corresponding":false,"raw_author_name":"Andrea Lodi","raw_affiliation_strings":["DEIS, University of Bologna, viale Risorgimento 2, 40136, Bologna, Italy"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"DEIS, University of Bologna, viale Risorgimento 2, 40136, Bologna, Italy","institution_ids":["https://openalex.org/I9360294"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5115590938"],"corresponding_institution_ids":[],"apc_list":{"value":2890,"currency":"USD","value_usd":2890},"apc_paid":null,"fwci":9.4477,"has_fulltext":false,"cited_by_count":62,"citation_normalized_percentile":{"value":0.98347176,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":89,"max":98},"biblio":{"volume":"121","issue":"1","first_page":"33","last_page":"60"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10374","display_name":"Advanced Graph Theory Research","score":0.9980000257492065,"subfield":{"id":"https://openalex.org/subfields/1703","display_name":"Computational Theory and Mathematics"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T10374","display_name":"Advanced Graph Theory Research","score":0.9980000257492065,"subfield":{"id":"https://openalex.org/subfields/1703","display_name":"Computational Theory and Mathematics"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T10567","display_name":"Vehicle Routing Optimization Methods","score":0.9980000257492065,"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/T12176","display_name":"Optimization and Packing Problems","score":0.9966999888420105,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.8403549790382385},{"id":"https://openalex.org/keywords/polyhedron","display_name":"Polyhedron","score":0.8278952836990356},{"id":"https://openalex.org/keywords/closure","display_name":"Closure (psychology)","score":0.8035876154899597},{"id":"https://openalex.org/keywords/rounding","display_name":"Rounding","score":0.7929136753082275},{"id":"https://openalex.org/keywords/integer-programming","display_name":"Integer programming","score":0.7002180218696594},{"id":"https://openalex.org/keywords/integer","display_name":"Integer (computer science)","score":0.591715395450592},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.5829963088035583},{"id":"https://openalex.org/keywords/linear-programming","display_name":"Linear programming","score":0.5387483835220337},{"id":"https://openalex.org/keywords/set","display_name":"Set (abstract data type)","score":0.5271422863006592},{"id":"https://openalex.org/keywords/heuristic","display_name":"Heuristic","score":0.5066326260566711},{"id":"https://openalex.org/keywords/set-packing","display_name":"Set packing","score":0.45833805203437805},{"id":"https://openalex.org/keywords/separation","display_name":"Separation (statistics)","score":0.4323713779449463},{"id":"https://openalex.org/keywords/interior-point-method","display_name":"Interior point method","score":0.4127194583415985},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.3907262086868286},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.3552517890930176},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.08880376815795898}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8403549790382385},{"id":"https://openalex.org/C54829058","wikidata":"https://www.wikidata.org/wiki/Q172937","display_name":"Polyhedron","level":2,"score":0.8278952836990356},{"id":"https://openalex.org/C146834321","wikidata":"https://www.wikidata.org/wiki/Q2979672","display_name":"Closure (psychology)","level":2,"score":0.8035876154899597},{"id":"https://openalex.org/C136625980","wikidata":"https://www.wikidata.org/wiki/Q663208","display_name":"Rounding","level":2,"score":0.7929136753082275},{"id":"https://openalex.org/C56086750","wikidata":"https://www.wikidata.org/wiki/Q6042592","display_name":"Integer programming","level":2,"score":0.7002180218696594},{"id":"https://openalex.org/C97137487","wikidata":"https://www.wikidata.org/wiki/Q729138","display_name":"Integer (computer science)","level":2,"score":0.591715395450592},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.5829963088035583},{"id":"https://openalex.org/C41045048","wikidata":"https://www.wikidata.org/wiki/Q202843","display_name":"Linear programming","level":2,"score":0.5387483835220337},{"id":"https://openalex.org/C177264268","wikidata":"https://www.wikidata.org/wiki/Q1514741","display_name":"Set (abstract data type)","level":2,"score":0.5271422863006592},{"id":"https://openalex.org/C173801870","wikidata":"https://www.wikidata.org/wiki/Q201413","display_name":"Heuristic","level":2,"score":0.5066326260566711},{"id":"https://openalex.org/C134516590","wikidata":"https://www.wikidata.org/wiki/Q475603","display_name":"Set packing","level":3,"score":0.45833805203437805},{"id":"https://openalex.org/C2776061190","wikidata":"https://www.wikidata.org/wiki/Q7451805","display_name":"Separation (statistics)","level":2,"score":0.4323713779449463},{"id":"https://openalex.org/C155253501","wikidata":"https://www.wikidata.org/wiki/Q461992","display_name":"Interior point method","level":2,"score":0.4127194583415985},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.3907262086868286},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.3552517890930176},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.08880376815795898},{"id":"https://openalex.org/C34447519","wikidata":"https://www.wikidata.org/wiki/Q179522","display_name":"Market economy","level":1,"score":0.0},{"id":"https://openalex.org/C111919701","wikidata":"https://www.wikidata.org/wiki/Q9135","display_name":"Operating system","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/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.0},{"id":"https://openalex.org/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","level":0,"score":0.0}],"mesh":[],"locations_count":4,"locations":[{"id":"doi:10.1007/s10107-008-0225-x","is_oa":false,"landing_page_url":"https://doi.org/10.1007/s10107-008-0225-x","pdf_url":null,"source":{"id":"https://openalex.org/S193920097","display_name":"Mathematical Programming","issn_l":"0025-5610","issn":["0025-5610","1436-4646"],"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":"Mathematical Programming","raw_type":"journal-article"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.555.300","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.555.300","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://www.optimization-online.org/DB_FILE/2007/03/1604.pdf","raw_type":"text"},{"id":"pmh:oai:cris.unibo.it:11585/74176","is_oa":false,"landing_page_url":"http://hdl.handle.net/11585/74176","pdf_url":null,"source":{"id":"https://openalex.org/S4306402579","display_name":"Archivio istituzionale della ricerca (Alma Mater Studiorum Universit\u00e0 di Bologna)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I4210117483","host_organization_name":"Istituto di Ematologia di Bologna","host_organization_lineage":["https://openalex.org/I4210117483"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"info:eu-repo/semantics/article"},{"id":"pmh:oai:publications.polymtl.ca:18435","is_oa":false,"landing_page_url":"https://publications.polymtl.ca/18435/","pdf_url":null,"source":{"id":"https://openalex.org/S4306401013","display_name":"PolyPublie (\u00c9cole Polytechnique de Montr\u00e9al)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I45683168","host_organization_name":"Polytechnique Montr\u00e9al","host_organization_lineage":["https://openalex.org/I45683168"],"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 de revue"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":31,"referenced_works":["https://openalex.org/W180443138","https://openalex.org/W1497481553","https://openalex.org/W1968143987","https://openalex.org/W1975254220","https://openalex.org/W2004489140","https://openalex.org/W2010730730","https://openalex.org/W2017095313","https://openalex.org/W2021043398","https://openalex.org/W2034266713","https://openalex.org/W2037426997","https://openalex.org/W2039648193","https://openalex.org/W2052281387","https://openalex.org/W2066961446","https://openalex.org/W2083016760","https://openalex.org/W2083625505","https://openalex.org/W2084285121","https://openalex.org/W2101620967","https://openalex.org/W2103254960","https://openalex.org/W2106068249","https://openalex.org/W2111574881","https://openalex.org/W2134946135","https://openalex.org/W2145243417","https://openalex.org/W2148159997","https://openalex.org/W2152088446","https://openalex.org/W2163013568","https://openalex.org/W2336259629","https://openalex.org/W2505968561","https://openalex.org/W3124498598","https://openalex.org/W4253741566","https://openalex.org/W6652873848","https://openalex.org/W6823566691"],"related_works":["https://openalex.org/W1523191918","https://openalex.org/W2228244008","https://openalex.org/W2486684489","https://openalex.org/W2613884615","https://openalex.org/W1881614784","https://openalex.org/W1982719520","https://openalex.org/W134055995","https://openalex.org/W2016815536","https://openalex.org/W2061101246","https://openalex.org/W2155708792"],"abstract_inverted_index":null,"counts_by_year":[{"year":2023,"cited_by_count":1},{"year":2022,"cited_by_count":1},{"year":2021,"cited_by_count":3},{"year":2020,"cited_by_count":2},{"year":2019,"cited_by_count":3},{"year":2018,"cited_by_count":4},{"year":2017,"cited_by_count":3},{"year":2016,"cited_by_count":3},{"year":2015,"cited_by_count":5},{"year":2014,"cited_by_count":4},{"year":2013,"cited_by_count":4},{"year":2012,"cited_by_count":3}],"updated_date":"2026-07-29T09:40:50.615796","created_date":"2025-10-10T00:00:00"}