{"id":"https://openalex.org/W2086761232","doi":"https://doi.org/10.1016/0305-0548(85)90042-5","title":"Lagrangean relaxation and decomposition in an uncapacitated 2-hierarchal location-allocation problem","display_name":"Lagrangean relaxation and decomposition in an uncapacitated 2-hierarchal location-allocation problem","publication_year":1985,"publication_date":"1985-01-01","ids":{"openalex":"https://openalex.org/W2086761232","doi":"https://doi.org/10.1016/0305-0548(85)90042-5","mag":"2086761232"},"language":"en","primary_location":{"id":"doi:10.1016/0305-0548(85)90042-5","is_oa":false,"landing_page_url":"https://doi.org/10.1016/0305-0548(85)90042-5","pdf_url":null,"source":{"id":"https://openalex.org/S173256270","display_name":"Computers & Operations Research","issn_l":"0305-0548","issn":["0305-0548","1873-765X"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320990","host_organization_name":"Elsevier BV","host_organization_lineage":["https://openalex.org/P4310320990"],"host_organization_lineage_names":["Elsevier BV"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Computers &amp; 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/A5110278773","display_name":"Subhash C. Narula","orcid":null},"institutions":[{"id":"https://openalex.org/I184840846","display_name":"Virginia Commonwealth University","ror":"https://ror.org/02nkdxk79","country_code":"US","type":"education","lineage":["https://openalex.org/I184840846"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Subhash C Narula","raw_affiliation_strings":["Virginia Commonwealth University, Richmond, VA 23284, U.S.A"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Virginia Commonwealth University, Richmond, VA 23284, U.S.A","institution_ids":["https://openalex.org/I184840846"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5024802922","display_name":"Ugonnaya I. Ogbu","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Ugonnaya I Ogbu","raw_affiliation_strings":["Ogobu International, Onitsha, Nigeria"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Ogobu International, Onitsha, Nigeria","institution_ids":[]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":{"value":3210,"currency":"USD","value_usd":3210},"apc_paid":null,"fwci":1.1814,"has_fulltext":false,"cited_by_count":23,"citation_normalized_percentile":{"value":0.81860756,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":97},"biblio":{"volume":"12","issue":"2","first_page":"169","last_page":"180"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11502","display_name":"Facility Location and Emergency Management","score":0.9994000196456909,"subfield":{"id":"https://openalex.org/subfields/1407","display_name":"Organizational Behavior and Human Resource Management"},"field":{"id":"https://openalex.org/fields/14","display_name":"Business, Management and Accounting"},"domain":{"id":"https://openalex.org/domains/2","display_name":"Social Sciences"}},"topics":[{"id":"https://openalex.org/T11502","display_name":"Facility Location and Emergency Management","score":0.9994000196456909,"subfield":{"id":"https://openalex.org/subfields/1407","display_name":"Organizational Behavior and Human Resource Management"},"field":{"id":"https://openalex.org/fields/14","display_name":"Business, Management and Accounting"},"domain":{"id":"https://openalex.org/domains/2","display_name":"Social Sciences"}},{"id":"https://openalex.org/T10567","display_name":"Vehicle Routing Optimization Methods","score":0.992900013923645,"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/T10698","display_name":"Transportation Planning and Optimization","score":0.9897000193595886,"subfield":{"id":"https://openalex.org/subfields/3313","display_name":"Transportation"},"field":{"id":"https://openalex.org/fields/33","display_name":"Social Sciences"},"domain":{"id":"https://openalex.org/domains/2","display_name":"Social Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/subgradient-method","display_name":"Subgradient method","score":0.8976083993911743},{"id":"https://openalex.org/keywords/facility-location-problem","display_name":"Facility location problem","score":0.8770039081573486},{"id":"https://openalex.org/keywords/1-center-problem","display_name":"1-center problem","score":0.6888749003410339},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.657658040523529},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.5775293111801147},{"id":"https://openalex.org/keywords/location-allocation","display_name":"Location-allocation","score":0.5534312725067139},{"id":"https://openalex.org/keywords/relaxation","display_name":"Relaxation (psychology)","score":0.5296145677566528},{"id":"https://openalex.org/keywords/benders-decomposition","display_name":"Benders' decomposition","score":0.5182549953460693},{"id":"https://openalex.org/keywords/decomposition","display_name":"Decomposition","score":0.5122730135917664},{"id":"https://openalex.org/keywords/lagrangian-relaxation","display_name":"Lagrangian relaxation","score":0.5000805854797363},{"id":"https://openalex.org/keywords/fraction","display_name":"Fraction (chemistry)","score":0.47760245203971863},{"id":"https://openalex.org/keywords/optimization-problem","display_name":"Optimization problem","score":0.44049912691116333},{"id":"https://openalex.org/keywords/integer-programming","display_name":"Integer programming","score":0.428437739610672},{"id":"https://openalex.org/keywords/linear-programming-relaxation","display_name":"Linear programming relaxation","score":0.4172784686088562},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.3214527368545532}],"concepts":[{"id":"https://openalex.org/C158968445","wikidata":"https://www.wikidata.org/wiki/Q7631150","display_name":"Subgradient method","level":2,"score":0.8976083993911743},{"id":"https://openalex.org/C108005400","wikidata":"https://www.wikidata.org/wiki/Q1305598","display_name":"Facility location problem","level":2,"score":0.8770039081573486},{"id":"https://openalex.org/C50524431","wikidata":"https://www.wikidata.org/wiki/Q4545814","display_name":"1-center problem","level":3,"score":0.6888749003410339},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.657658040523529},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.5775293111801147},{"id":"https://openalex.org/C2778212267","wikidata":"https://www.wikidata.org/wiki/Q6664764","display_name":"Location-allocation","level":2,"score":0.5534312725067139},{"id":"https://openalex.org/C2776029896","wikidata":"https://www.wikidata.org/wiki/Q3935810","display_name":"Relaxation (psychology)","level":2,"score":0.5296145677566528},{"id":"https://openalex.org/C27665512","wikidata":"https://www.wikidata.org/wiki/Q3042795","display_name":"Benders' decomposition","level":2,"score":0.5182549953460693},{"id":"https://openalex.org/C124681953","wikidata":"https://www.wikidata.org/wiki/Q339062","display_name":"Decomposition","level":2,"score":0.5122730135917664},{"id":"https://openalex.org/C91765299","wikidata":"https://www.wikidata.org/wiki/Q3424292","display_name":"Lagrangian relaxation","level":2,"score":0.5000805854797363},{"id":"https://openalex.org/C149629883","wikidata":"https://www.wikidata.org/wiki/Q660926","display_name":"Fraction (chemistry)","level":2,"score":0.47760245203971863},{"id":"https://openalex.org/C137836250","wikidata":"https://www.wikidata.org/wiki/Q984063","display_name":"Optimization problem","level":2,"score":0.44049912691116333},{"id":"https://openalex.org/C56086750","wikidata":"https://www.wikidata.org/wiki/Q6042592","display_name":"Integer programming","level":2,"score":0.428437739610672},{"id":"https://openalex.org/C25360446","wikidata":"https://www.wikidata.org/wiki/Q1512771","display_name":"Linear programming relaxation","level":3,"score":0.4172784686088562},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.3214527368545532},{"id":"https://openalex.org/C178790620","wikidata":"https://www.wikidata.org/wiki/Q11351","display_name":"Organic chemistry","level":1,"score":0.0},{"id":"https://openalex.org/C77805123","wikidata":"https://www.wikidata.org/wiki/Q161272","display_name":"Social psychology","level":1,"score":0.0},{"id":"https://openalex.org/C15744967","wikidata":"https://www.wikidata.org/wiki/Q9418","display_name":"Psychology","level":0,"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/C185592680","wikidata":"https://www.wikidata.org/wiki/Q2329","display_name":"Chemistry","level":0,"score":0.0},{"id":"https://openalex.org/C18903297","wikidata":"https://www.wikidata.org/wiki/Q7150","display_name":"Ecology","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1016/0305-0548(85)90042-5","is_oa":false,"landing_page_url":"https://doi.org/10.1016/0305-0548(85)90042-5","pdf_url":null,"source":{"id":"https://openalex.org/S173256270","display_name":"Computers & Operations Research","issn_l":"0305-0548","issn":["0305-0548","1873-765X"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320990","host_organization_name":"Elsevier BV","host_organization_lineage":["https://openalex.org/P4310320990"],"host_organization_lineage_names":["Elsevier BV"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Computers &amp; Operations Research","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":16,"referenced_works":["https://openalex.org/W1576264907","https://openalex.org/W1975579958","https://openalex.org/W1996693553","https://openalex.org/W2007325778","https://openalex.org/W2009841227","https://openalex.org/W2017697298","https://openalex.org/W2026517383","https://openalex.org/W2072741634","https://openalex.org/W2086153488","https://openalex.org/W2092680662","https://openalex.org/W2093497970","https://openalex.org/W2139211712","https://openalex.org/W2333137125","https://openalex.org/W2565484686","https://openalex.org/W4232055611","https://openalex.org/W4242130683"],"related_works":["https://openalex.org/W3464401","https://openalex.org/W2012703063","https://openalex.org/W2087641500","https://openalex.org/W3143387519","https://openalex.org/W2023136715","https://openalex.org/W2012229304","https://openalex.org/W2117722264","https://openalex.org/W2074804239","https://openalex.org/W276709744","https://openalex.org/W1978117135"],"abstract_inverted_index":null,"counts_by_year":[{"year":2021,"cited_by_count":1},{"year":2019,"cited_by_count":1},{"year":2016,"cited_by_count":2},{"year":2013,"cited_by_count":3}],"updated_date":"2026-06-20T20:08:15.867695","created_date":"2025-10-10T00:00:00"}
