{"id":"https://openalex.org/W2121888834","doi":"https://doi.org/10.1007/s10107-010-0382-6","title":"n-step mingling inequalities: new facets for the mixed-integer knapsack set","display_name":"n-step mingling inequalities: new facets for the mixed-integer knapsack set","publication_year":2010,"publication_date":"2010-05-24","ids":{"openalex":"https://openalex.org/W2121888834","doi":"https://doi.org/10.1007/s10107-010-0382-6","mag":"2121888834"},"language":"en","primary_location":{"id":"doi:10.1007/s10107-010-0382-6","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s10107-010-0382-6","pdf_url":"https://link.springer.com/content/pdf/10.1007/s10107-010-0382-6.pdf","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":"cc-by-nc","license_id":"https://openalex.org/licenses/cc-by-nc","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":true,"oa_status":"hybrid","oa_url":"https://link.springer.com/content/pdf/10.1007/s10107-010-0382-6.pdf","any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5008007328","display_name":"Alper Atamt\u00fcrk","orcid":"https://orcid.org/0000-0003-1220-808X"},"institutions":[{"id":"https://openalex.org/I95457486","display_name":"University of California, Berkeley","ror":"https://ror.org/01an7q238","country_code":"US","type":"education","lineage":["https://openalex.org/I95457486"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Alper Atamt\u00fcrk","raw_affiliation_strings":["Department of Industrial Engineering and Operations Research, University of California, Berkeley, CA, 94720-1777, USA","University of California, Department of Industrial Engineering and Operations Research, 94720-1777, Berkeley, CA, USA#TAB#"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Industrial Engineering and Operations Research, University of California, Berkeley, CA, 94720-1777, USA","institution_ids":["https://openalex.org/I95457486"]},{"raw_affiliation_string":"University of California, Department of Industrial Engineering and Operations Research, 94720-1777, Berkeley, CA, USA#TAB#","institution_ids":["https://openalex.org/I95457486"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5059653465","display_name":"Kiavash Kianfar","orcid":"https://orcid.org/0000-0002-7263-2571"},"institutions":[{"id":"https://openalex.org/I91045830","display_name":"Texas A&M University","ror":"https://ror.org/01f5ytq51","country_code":"US","type":"education","lineage":["https://openalex.org/I91045830"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Kiavash Kianfar","raw_affiliation_strings":["Department of Industrial and Systems Engineering, Texas A&M University, College Station, TX, 77843-3131, USA","Texas A&M University, Department of Industrial and Systems Engineering, 77843-3131, College Station, TX, USA#TAB#"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Industrial and Systems Engineering, Texas A&M University, College Station, TX, 77843-3131, USA","institution_ids":["https://openalex.org/I91045830"]},{"raw_affiliation_string":"Texas A&M University, Department of Industrial and Systems Engineering, 77843-3131, College Station, TX, USA#TAB#","institution_ids":["https://openalex.org/I91045830"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":{"value":2190,"currency":"EUR","value_usd":2890},"apc_paid":{"value":2190,"currency":"EUR","value_usd":2890},"fwci":2.4725,"has_fulltext":true,"cited_by_count":15,"citation_normalized_percentile":{"value":0.88413439,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":98},"biblio":{"volume":"132","issue":"1-2","first_page":"79","last_page":"98"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11830","display_name":"Point processes and geometric inequalities","score":0.9822999835014343,"subfield":{"id":"https://openalex.org/subfields/2604","display_name":"Applied Mathematics"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T11830","display_name":"Point processes and geometric inequalities","score":0.9822999835014343,"subfield":{"id":"https://openalex.org/subfields/2604","display_name":"Applied Mathematics"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T12176","display_name":"Optimization and Packing Problems","score":0.9704999923706055,"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/T10219","display_name":"Mechanical Behavior of Composites","score":0.9456999897956848,"subfield":{"id":"https://openalex.org/subfields/2211","display_name":"Mechanics of Materials"},"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/knapsack-problem","display_name":"Knapsack problem","score":0.9528976082801819},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.8622926473617554},{"id":"https://openalex.org/keywords/integer","display_name":"Integer (computer science)","score":0.7548125982284546},{"id":"https://openalex.org/keywords/integer-programming","display_name":"Integer programming","score":0.5575399398803711},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.5534199476242065},{"id":"https://openalex.org/keywords/set","display_name":"Set (abstract data type)","score":0.47198063135147095},{"id":"https://openalex.org/keywords/bounded-function","display_name":"Bounded function","score":0.4513784646987915},{"id":"https://openalex.org/keywords/cutting-plane-method","display_name":"Cutting-plane method","score":0.41161638498306274},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.39507198333740234},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.17233121395111084},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.06590846180915833},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.062125593423843384}],"concepts":[{"id":"https://openalex.org/C113138325","wikidata":"https://www.wikidata.org/wiki/Q864457","display_name":"Knapsack problem","level":2,"score":0.9528976082801819},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8622926473617554},{"id":"https://openalex.org/C97137487","wikidata":"https://www.wikidata.org/wiki/Q729138","display_name":"Integer (computer science)","level":2,"score":0.7548125982284546},{"id":"https://openalex.org/C56086750","wikidata":"https://www.wikidata.org/wiki/Q6042592","display_name":"Integer programming","level":2,"score":0.5575399398803711},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.5534199476242065},{"id":"https://openalex.org/C177264268","wikidata":"https://www.wikidata.org/wiki/Q1514741","display_name":"Set (abstract data type)","level":2,"score":0.47198063135147095},{"id":"https://openalex.org/C34388435","wikidata":"https://www.wikidata.org/wiki/Q2267362","display_name":"Bounded function","level":2,"score":0.4513784646987915},{"id":"https://openalex.org/C109839438","wikidata":"https://www.wikidata.org/wiki/Q1762039","display_name":"Cutting-plane method","level":3,"score":0.41161638498306274},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.39507198333740234},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.17233121395111084},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.06590846180915833},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.062125593423843384},{"id":"https://openalex.org/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","level":1,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1007/s10107-010-0382-6","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s10107-010-0382-6","pdf_url":"https://link.springer.com/content/pdf/10.1007/s10107-010-0382-6.pdf","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":"cc-by-nc","license_id":"https://openalex.org/licenses/cc-by-nc","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Mathematical Programming","raw_type":"journal-article"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.386.9568","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.386.9568","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://www.ieor.berkeley.edu/~atamturk/pubs/_published/mathprog132-2012.pdf","raw_type":"text"}],"best_oa_location":{"id":"doi:10.1007/s10107-010-0382-6","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s10107-010-0382-6","pdf_url":"https://link.springer.com/content/pdf/10.1007/s10107-010-0382-6.pdf","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":"cc-by-nc","license_id":"https://openalex.org/licenses/cc-by-nc","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Mathematical Programming","raw_type":"journal-article"},"sustainable_development_goals":[{"id":"https://metadata.un.org/sdg/10","display_name":"Reduced inequalities","score":0.47999998927116394}],"awards":[],"funders":[],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W2121888834.pdf","grobid_xml":"https://content.openalex.org/works/W2121888834.grobid-xml"},"referenced_works_count":18,"referenced_works":["https://openalex.org/W36169824","https://openalex.org/W1549174816","https://openalex.org/W1965681691","https://openalex.org/W1965761939","https://openalex.org/W1968143987","https://openalex.org/W1981753748","https://openalex.org/W1990585107","https://openalex.org/W2020159749","https://openalex.org/W2021043398","https://openalex.org/W2065803772","https://openalex.org/W2074134927","https://openalex.org/W2139797076","https://openalex.org/W2148159997","https://openalex.org/W2158515702","https://openalex.org/W2336259629","https://openalex.org/W2505968561","https://openalex.org/W3124498598","https://openalex.org/W4236743999"],"related_works":["https://openalex.org/W2048233275","https://openalex.org/W2110818895","https://openalex.org/W2045076853","https://openalex.org/W1973064890","https://openalex.org/W2002159391","https://openalex.org/W2065369945","https://openalex.org/W3126345618","https://openalex.org/W2038141985","https://openalex.org/W1991394924","https://openalex.org/W3006617646"],"abstract_inverted_index":{"The":[0,38],"n-step":[1,29,113,129,137,155,214,230],"mixed":[2,78,163,199,221,249],"integer":[3,65,79,108,118,126,164,200,222,250],"rounding":[4],"(MIR)":[5],"inequalities":[6,17,43,73,100,115,121,216,239],"of":[7,44,98,136,145,178,185],"Kianfar":[8],"and":[9,32,40,46,58,85,139,180,240,245],"Fathi":[10],"(Math":[11,48],"Program":[12,49],"120(2):313\u2013346,":[13],"2009)":[14],"are":[15,24,52,74],"valid":[16,89,99,238],"for":[18,35,76,101,151,161,197,219,248],"the":[19,64,77,102,134,154,162,176,198,213,220],"mixed-integer":[20,103],"knapsack":[21,80,104,165,201,223,251],"set":[22,81,105,166],"that":[23,71,150,229],"derived":[25,54],"by":[26],"using":[27],"periodic":[28],"MIR":[30,57,130,138,215],"functions":[31],"define":[33,217],"facets":[34,196,218,241],"group":[36],"problems.":[37],"mingling":[39,42,114,140,156,187,231],"2-step":[41,186],"Atamt\u00fcrk":[45,179],"G\u00fcnl\u00fck":[47,181],"123(2):315\u2013338,":[50],"2010)":[51],"also":[53,208],"based":[55,242],"on":[56,63,125,182,243],"they":[59],"incorporate":[60,122],"upper":[61,123],"bounds":[62,124],"variables.":[66],"It":[67],"has":[68],"been":[69],"shown":[70],"these":[72],"facet-defining":[75,183],"under":[82,167,211],"certain":[83,168],"conditions":[84,210],"generalize":[86],"several":[87],"well-known":[88],"inequalities.":[90,146,188],"In":[91,225],"this":[92],"paper,":[93],"we":[94,111,148,174,193,207,227],"introduce":[95],"new":[96,195,237],"classes":[97],"with":[106],"bounded":[107],"variables,":[109],"which":[110,212],"call":[112],"(for":[116],"positive":[117],"n).":[119],"These":[120],"variables":[127],"into":[128],"and,":[131],"therefore,":[132],"unify":[133],"concepts":[135],"in":[141],"a":[142,159,204],"single":[143],"class":[144],"Furthermore,":[147],"show":[149,228],"each":[152],"n,":[153],"inequality":[157],"defines":[158],"facet":[160],"conditions.":[169],"For":[170,189],"n":[171,190],"=":[172],"2,":[173],"extend":[175],"results":[177],"properties":[184],"\u2265":[191],"3,":[192],"present":[194],"set.":[202,224],"As":[203],"special":[205],"case":[206],"derive":[209],"addition,":[226],"can":[232],"be":[233],"used":[234],"to":[235],"generate":[236],"covers":[244],"packs":[246],"defined":[247],"sets.":[252]},"counts_by_year":[{"year":2022,"cited_by_count":2},{"year":2020,"cited_by_count":1},{"year":2018,"cited_by_count":1},{"year":2017,"cited_by_count":1},{"year":2015,"cited_by_count":2},{"year":2014,"cited_by_count":2},{"year":2013,"cited_by_count":1},{"year":2012,"cited_by_count":4}],"updated_date":"2026-06-11T09:08:48.828518","created_date":"2025-10-10T00:00:00"}
