{"id":"https://openalex.org/W2069344303","doi":"https://doi.org/10.4018/ijeoe.2012010104","title":"Lagrangian Bounds and a Heuristic for the Two-Stage Capacitated Facility Location Problem","display_name":"Lagrangian Bounds and a Heuristic for the Two-Stage Capacitated Facility Location Problem","publication_year":2012,"publication_date":"2012-01-01","ids":{"openalex":"https://openalex.org/W2069344303","doi":"https://doi.org/10.4018/ijeoe.2012010104","mag":"2069344303"},"language":"en","primary_location":{"id":"doi:10.4018/ijeoe.2012010104","is_oa":false,"landing_page_url":"https://doi.org/10.4018/ijeoe.2012010104","pdf_url":null,"source":{"id":"https://openalex.org/S4210172736","display_name":"International Journal of Energy Optimization and Engineering","issn_l":"2160-9500","issn":["2160-9500","2160-9543"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320424","host_organization_name":"IGI Global","host_organization_lineage":["https://openalex.org/P4310320424"],"host_organization_lineage_names":["IGI Global"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"International Journal of Energy Optimization and Engineering","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/A5088187330","display_name":"Igor Litvinchev","orcid":"https://orcid.org/0000-0002-1850-4755"},"institutions":[{"id":"https://openalex.org/I169046204","display_name":"Universidad Aut\u00f3noma de Nuevo Le\u00f3n","ror":"https://ror.org/01fh86n78","country_code":"MX","type":"education","lineage":["https://openalex.org/I169046204"]}],"countries":["MX"],"is_corresponding":false,"raw_author_name":"Igor Litvinchev","raw_affiliation_strings":["Nuevo Leon State University, Mexico"],"raw_orcid":"https://orcid.org/0000-0002-1850-4755","affiliations":[{"raw_affiliation_string":"Nuevo Leon State University, Mexico","institution_ids":["https://openalex.org/I169046204"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5080304089","display_name":"Edith Lucero Ozuna","orcid":null},"institutions":[{"id":"https://openalex.org/I169046204","display_name":"Universidad Aut\u00f3noma de Nuevo Le\u00f3n","ror":"https://ror.org/01fh86n78","country_code":"MX","type":"education","lineage":["https://openalex.org/I169046204"]}],"countries":["MX"],"is_corresponding":false,"raw_author_name":"Edith L. Ozuna","raw_affiliation_strings":["Nuevo Leon State University, Mexico"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Nuevo Leon State University, Mexico","institution_ids":["https://openalex.org/I169046204"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":2.696,"has_fulltext":false,"cited_by_count":28,"citation_normalized_percentile":{"value":0.9063649,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":90,"max":98},"biblio":{"volume":"1","issue":"1","first_page":"59","last_page":"71"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11502","display_name":"Facility Location and Emergency Management","score":0.9998999834060669,"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":0.9998999834060669,"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":0.9973000288009644,"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/T12306","display_name":"Urban and Freight Transport Logistics","score":0.9934999942779541,"subfield":{"id":"https://openalex.org/subfields/2215","display_name":"Building and Construction"},"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/mathematical-optimization","display_name":"Mathematical optimization","score":0.7261910438537598},{"id":"https://openalex.org/keywords/heuristic","display_name":"Heuristic","score":0.6980012655258179},{"id":"https://openalex.org/keywords/lagrangian-relaxation","display_name":"Lagrangian relaxation","score":0.6915292739868164},{"id":"https://openalex.org/keywords/integer-programming","display_name":"Integer programming","score":0.6628909111022949},{"id":"https://openalex.org/keywords/lagrangian","display_name":"Lagrangian","score":0.6557490229606628},{"id":"https://openalex.org/keywords/fixed-cost","display_name":"Fixed cost","score":0.6293706893920898},{"id":"https://openalex.org/keywords/facility-location-problem","display_name":"Facility location problem","score":0.6168810129165649},{"id":"https://openalex.org/keywords/set","display_name":"Set (abstract data type)","score":0.547965407371521},{"id":"https://openalex.org/keywords/product","display_name":"Product (mathematics)","score":0.5450873374938965},{"id":"https://openalex.org/keywords/integer","display_name":"Integer (computer science)","score":0.5050395131111145},{"id":"https://openalex.org/keywords/variable","display_name":"Variable (mathematics)","score":0.46026402711868286},{"id":"https://openalex.org/keywords/total-cost","display_name":"Total cost","score":0.4359186291694641},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.4236612915992737},{"id":"https://openalex.org/keywords/variable-cost","display_name":"Variable cost","score":0.412354052066803},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.3826178014278412},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.07188087701797485}],"concepts":[{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.7261910438537598},{"id":"https://openalex.org/C173801870","wikidata":"https://www.wikidata.org/wiki/Q201413","display_name":"Heuristic","level":2,"score":0.6980012655258179},{"id":"https://openalex.org/C91765299","wikidata":"https://www.wikidata.org/wiki/Q3424292","display_name":"Lagrangian relaxation","level":2,"score":0.6915292739868164},{"id":"https://openalex.org/C56086750","wikidata":"https://www.wikidata.org/wiki/Q6042592","display_name":"Integer programming","level":2,"score":0.6628909111022949},{"id":"https://openalex.org/C53469067","wikidata":"https://www.wikidata.org/wiki/Q505735","display_name":"Lagrangian","level":2,"score":0.6557490229606628},{"id":"https://openalex.org/C42866809","wikidata":"https://www.wikidata.org/wiki/Q466764","display_name":"Fixed cost","level":2,"score":0.6293706893920898},{"id":"https://openalex.org/C108005400","wikidata":"https://www.wikidata.org/wiki/Q1305598","display_name":"Facility location problem","level":2,"score":0.6168810129165649},{"id":"https://openalex.org/C177264268","wikidata":"https://www.wikidata.org/wiki/Q1514741","display_name":"Set (abstract data type)","level":2,"score":0.547965407371521},{"id":"https://openalex.org/C90673727","wikidata":"https://www.wikidata.org/wiki/Q901718","display_name":"Product (mathematics)","level":2,"score":0.5450873374938965},{"id":"https://openalex.org/C97137487","wikidata":"https://www.wikidata.org/wiki/Q729138","display_name":"Integer (computer science)","level":2,"score":0.5050395131111145},{"id":"https://openalex.org/C182365436","wikidata":"https://www.wikidata.org/wiki/Q50701","display_name":"Variable (mathematics)","level":2,"score":0.46026402711868286},{"id":"https://openalex.org/C182299520","wikidata":"https://www.wikidata.org/wiki/Q1289588","display_name":"Total cost","level":2,"score":0.4359186291694641},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.4236612915992737},{"id":"https://openalex.org/C145760622","wikidata":"https://www.wikidata.org/wiki/Q174915","display_name":"Variable cost","level":2,"score":0.412354052066803},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.3826178014278412},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.07188087701797485},{"id":"https://openalex.org/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","level":0,"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/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.0},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.0},{"id":"https://openalex.org/C121955636","wikidata":"https://www.wikidata.org/wiki/Q4116214","display_name":"Accounting","level":1,"score":0.0},{"id":"https://openalex.org/C175444787","wikidata":"https://www.wikidata.org/wiki/Q39072","display_name":"Microeconomics","level":1,"score":0.0},{"id":"https://openalex.org/C144133560","wikidata":"https://www.wikidata.org/wiki/Q4830453","display_name":"Business","level":0,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.4018/ijeoe.2012010104","is_oa":false,"landing_page_url":"https://doi.org/10.4018/ijeoe.2012010104","pdf_url":null,"source":{"id":"https://openalex.org/S4210172736","display_name":"International Journal of Energy Optimization and Engineering","issn_l":"2160-9500","issn":["2160-9500","2160-9543"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320424","host_organization_name":"IGI Global","host_organization_lineage":["https://openalex.org/P4310320424"],"host_organization_lineage_names":["IGI Global"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"International Journal of Energy Optimization and Engineering","raw_type":"journal-article"},{"id":"pmh:oai:RePEc:igg:jeoe00:v:1:y:2012:i:1:p:59-71","is_oa":false,"landing_page_url":"http://services.igi-global.com/resolvedoi/resolve.aspx?doi=10.4018/ijeoe.2012010104","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":[{"score":0.5199999809265137,"display_name":"Industry, innovation and infrastructure","id":"https://metadata.un.org/sdg/9"}],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":40,"referenced_works":["https://openalex.org/W197064018","https://openalex.org/W619430382","https://openalex.org/W632834909","https://openalex.org/W642949223","https://openalex.org/W1566753057","https://openalex.org/W1593849271","https://openalex.org/W1936976612","https://openalex.org/W1973658994","https://openalex.org/W1993074566","https://openalex.org/W1997231674","https://openalex.org/W1999269508","https://openalex.org/W2001912652","https://openalex.org/W2010136497","https://openalex.org/W2017019823","https://openalex.org/W2019270865","https://openalex.org/W2019468200","https://openalex.org/W2028274662","https://openalex.org/W2028282210","https://openalex.org/W2036802487","https://openalex.org/W2049302102","https://openalex.org/W2060828289","https://openalex.org/W2062545539","https://openalex.org/W2067320236","https://openalex.org/W2075035506","https://openalex.org/W2078286011","https://openalex.org/W2079204917","https://openalex.org/W2088626788","https://openalex.org/W2091790699","https://openalex.org/W2100844228","https://openalex.org/W2101446817","https://openalex.org/W2116725038","https://openalex.org/W2117977366","https://openalex.org/W2142912132","https://openalex.org/W2152381971","https://openalex.org/W2167430432","https://openalex.org/W2914183180","https://openalex.org/W3125560213","https://openalex.org/W4210576321","https://openalex.org/W4234997161","https://openalex.org/W4256046638"],"related_works":["https://openalex.org/W2783359165","https://openalex.org/W1998320212","https://openalex.org/W4281955670","https://openalex.org/W2288827760","https://openalex.org/W2285639748","https://openalex.org/W3163636510","https://openalex.org/W1529622016","https://openalex.org/W4206831742","https://openalex.org/W3037930571","https://openalex.org/W4292200574"],"abstract_inverted_index":{"In":[0,80],"the":[1,34,39,93],"two-stage":[2],"capacitated":[3],"facility":[4],"location":[5],"problem,":[6],"a":[7,54,103,114],"single":[8],"product":[9,22],"is":[10,23,47,109],"produced":[11],"at":[12],"some":[13,29],"plants":[14,27,40,58,69],"in":[15],"order":[16],"to":[17,28,33,48],"satisfy":[18],"customer":[19],"demands.":[20],"The":[21,36,45,111],"transported":[24],"from":[25,53],"these":[26],"depots":[30,42],"and":[31,41,59,70,72,100,102],"then":[32],"customers.":[35],"capacities":[37],"of":[38,56,113],"are":[43,90,98,117],"limited.":[44],"aim":[46],"select":[49],"cost":[50,62,65,74],"minimizing":[51],"locations":[52],"set":[55],"potential":[57],"depots.":[60],"This":[61],"includes":[63],"fixed":[64],"associated":[66,75],"with":[67,76],"opening":[68],"depots,":[71],"variable":[73],"both":[77],"transportation":[78],"stages.":[79],"this":[81],"work,":[82],"two":[83],"different":[84],"mixed":[85],"integer":[86],"linear":[87],"programming":[88],"formulations":[89],"considered":[91],"for":[92],"problem.":[94],"Several":[95],"Lagrangian":[96,104],"relaxations":[97],"analyzed":[99],"compared,":[101],"heuristic":[105],"producing":[106],"feasible":[107],"solutions":[108],"presented.":[110],"results":[112],"computational":[115],"study":[116],"reported.":[118]},"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2025,"cited_by_count":3},{"year":2024,"cited_by_count":4},{"year":2023,"cited_by_count":1},{"year":2022,"cited_by_count":2},{"year":2021,"cited_by_count":3},{"year":2020,"cited_by_count":4},{"year":2019,"cited_by_count":1},{"year":2018,"cited_by_count":3},{"year":2016,"cited_by_count":1},{"year":2014,"cited_by_count":1},{"year":2013,"cited_by_count":2},{"year":2012,"cited_by_count":2}],"updated_date":"2026-06-17T08:01:34.144755","created_date":"2025-10-10T00:00:00"}