{"id":"https://openalex.org/W2036924136","doi":"https://doi.org/10.1002/net.3230220706","title":"The Capacitated Arc Routing Problem: Lower bounds","display_name":"The Capacitated Arc Routing Problem: Lower bounds","publication_year":1992,"publication_date":"1992-12-01","ids":{"openalex":"https://openalex.org/W2036924136","doi":"https://doi.org/10.1002/net.3230220706","mag":"2036924136"},"language":"en","primary_location":{"id":"doi:10.1002/net.3230220706","is_oa":false,"landing_page_url":"https://doi.org/10.1002/net.3230220706","pdf_url":null,"source":{"id":"https://openalex.org/S191798613","display_name":"Networks","issn_l":"0028-3045","issn":["0028-3045","1097-0037"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320595","host_organization_name":"Wiley","host_organization_lineage":["https://openalex.org/P4310320595"],"host_organization_lineage_names":["Wiley"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Networks","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/A5037766948","display_name":"Enrique Benavent","orcid":null},"institutions":[{"id":"https://openalex.org/I16097986","display_name":"Universitat de Val\u00e8ncia","ror":"https://ror.org/043nxc105","country_code":"ES","type":"education","lineage":["https://openalex.org/I16097986"]}],"countries":["ES"],"is_corresponding":true,"raw_author_name":"E. Benavent","raw_affiliation_strings":["Departamento De Estadistica e Investigacion Operativa Facultad de Matematicas Universidad de Valencia Dr. Moliner n. 50 46100 Burjassot-Valencia, Spain","Departamento De Estadistica e Investigacion Operativa Facultad de Matematicas Universidad de Valencia Dr. Moliner n. 50 46100 Burjassot\u2010Valencia, Spain"],"affiliations":[{"raw_affiliation_string":"Departamento De Estadistica e Investigacion Operativa Facultad de Matematicas Universidad de Valencia Dr. Moliner n. 50 46100 Burjassot-Valencia, Spain","institution_ids":["https://openalex.org/I16097986"]},{"raw_affiliation_string":"Departamento De Estadistica e Investigacion Operativa Facultad de Matematicas Universidad de Valencia Dr. Moliner n. 50 46100 Burjassot\u2010Valencia, Spain","institution_ids":["https://openalex.org/I16097986"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5056190675","display_name":"Vicente Campos","orcid":null},"institutions":[{"id":"https://openalex.org/I16097986","display_name":"Universitat de Val\u00e8ncia","ror":"https://ror.org/043nxc105","country_code":"ES","type":"education","lineage":["https://openalex.org/I16097986"]}],"countries":["ES"],"is_corresponding":false,"raw_author_name":"V. Campos","raw_affiliation_strings":["Departamento De Estadistica e Investigacion Operativa Facultad de Matematicas Universidad de Valencia Dr. Moliner n. 50 46100 Burjassot-Valencia, Spain","Departamento De Estadistica e Investigacion Operativa Facultad de Matematicas Universidad de Valencia Dr. Moliner n. 50 46100 Burjassot\u2010Valencia, Spain"],"affiliations":[{"raw_affiliation_string":"Departamento De Estadistica e Investigacion Operativa Facultad de Matematicas Universidad de Valencia Dr. Moliner n. 50 46100 Burjassot-Valencia, Spain","institution_ids":["https://openalex.org/I16097986"]},{"raw_affiliation_string":"Departamento De Estadistica e Investigacion Operativa Facultad de Matematicas Universidad de Valencia Dr. Moliner n. 50 46100 Burjassot\u2010Valencia, Spain","institution_ids":["https://openalex.org/I16097986"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5013452668","display_name":"\u00c1ngel Corber\u00e1n","orcid":"https://orcid.org/0000-0002-0664-4232"},"institutions":[{"id":"https://openalex.org/I16097986","display_name":"Universitat de Val\u00e8ncia","ror":"https://ror.org/043nxc105","country_code":"ES","type":"education","lineage":["https://openalex.org/I16097986"]}],"countries":["ES"],"is_corresponding":false,"raw_author_name":"A. Corberan","raw_affiliation_strings":["Departamento De Estadistica e Investigacion Operativa Facultad de Matematicas Universidad de Valencia Dr. Moliner n. 50 46100 Burjassot-Valencia, Spain","Departamento De Estadistica e Investigacion Operativa Facultad de Matematicas Universidad de Valencia Dr. Moliner n. 50 46100 Burjassot\u2010Valencia, Spain"],"affiliations":[{"raw_affiliation_string":"Departamento De Estadistica e Investigacion Operativa Facultad de Matematicas Universidad de Valencia Dr. Moliner n. 50 46100 Burjassot-Valencia, Spain","institution_ids":["https://openalex.org/I16097986"]},{"raw_affiliation_string":"Departamento De Estadistica e Investigacion Operativa Facultad de Matematicas Universidad de Valencia Dr. Moliner n. 50 46100 Burjassot\u2010Valencia, Spain","institution_ids":["https://openalex.org/I16097986"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5067820788","display_name":"Enrique Mota","orcid":"https://orcid.org/0000-0003-4105-1835"},"institutions":[{"id":"https://openalex.org/I16097986","display_name":"Universitat de Val\u00e8ncia","ror":"https://ror.org/043nxc105","country_code":"ES","type":"education","lineage":["https://openalex.org/I16097986"]}],"countries":["ES"],"is_corresponding":false,"raw_author_name":"E. Mota","raw_affiliation_strings":["Departamento De Estadistica e Investigacion Operativa Facultad de Matematicas Universidad de Valencia Dr. Moliner n. 50 46100 Burjassot-Valencia, Spain","Departamento De Estadistica e Investigacion Operativa Facultad de Matematicas Universidad de Valencia Dr. Moliner n. 50 46100 Burjassot\u2010Valencia, Spain"],"affiliations":[{"raw_affiliation_string":"Departamento De Estadistica e Investigacion Operativa Facultad de Matematicas Universidad de Valencia Dr. Moliner n. 50 46100 Burjassot-Valencia, Spain","institution_ids":["https://openalex.org/I16097986"]},{"raw_affiliation_string":"Departamento De Estadistica e Investigacion Operativa Facultad de Matematicas Universidad de Valencia Dr. Moliner n. 50 46100 Burjassot\u2010Valencia, Spain","institution_ids":["https://openalex.org/I16097986"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":4,"corresponding_author_ids":["https://openalex.org/A5037766948"],"corresponding_institution_ids":["https://openalex.org/I16097986"],"apc_list":{"value":3400,"currency":"USD","value_usd":3400},"apc_paid":null,"fwci":3.0577,"has_fulltext":false,"cited_by_count":158,"citation_normalized_percentile":{"value":0.91093243,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":97,"max":99},"biblio":{"volume":"22","issue":"7","first_page":"669","last_page":"690"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10567","display_name":"Vehicle Routing Optimization Methods","score":0.9998999834060669,"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"}},"topics":[{"id":"https://openalex.org/T10567","display_name":"Vehicle Routing Optimization Methods","score":0.9998999834060669,"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/T11942","display_name":"Transportation and Mobility Innovations","score":0.9957000017166138,"subfield":{"id":"https://openalex.org/subfields/2203","display_name":"Automotive 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/T11502","display_name":"Facility Location and Emergency Management","score":0.9907000064849854,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/arc-routing","display_name":"Arc routing","score":0.8676584959030151},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.6219584941864014},{"id":"https://openalex.org/keywords/vertex","display_name":"Vertex (graph theory)","score":0.5312803983688354},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.5199905037879944},{"id":"https://openalex.org/keywords/vehicle-routing-problem","display_name":"Vehicle routing problem","score":0.4684619605541229},{"id":"https://openalex.org/keywords/upper-and-lower-bounds","display_name":"Upper and lower bounds","score":0.4576493799686432},{"id":"https://openalex.org/keywords/graph","display_name":"Graph","score":0.42220380902290344},{"id":"https://openalex.org/keywords/arc","display_name":"Arc (geometry)","score":0.4165256917476654},{"id":"https://openalex.org/keywords/routing","display_name":"Routing (electronic design automation)","score":0.40873903036117554},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.3716972768306732},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.23486772179603577}],"concepts":[{"id":"https://openalex.org/C2778536092","wikidata":"https://www.wikidata.org/wiki/Q4785038","display_name":"Arc routing","level":3,"score":0.8676584959030151},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.6219584941864014},{"id":"https://openalex.org/C80899671","wikidata":"https://www.wikidata.org/wiki/Q1304193","display_name":"Vertex (graph theory)","level":3,"score":0.5312803983688354},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.5199905037879944},{"id":"https://openalex.org/C123784306","wikidata":"https://www.wikidata.org/wiki/Q944041","display_name":"Vehicle routing problem","level":3,"score":0.4684619605541229},{"id":"https://openalex.org/C77553402","wikidata":"https://www.wikidata.org/wiki/Q13222579","display_name":"Upper and lower bounds","level":2,"score":0.4576493799686432},{"id":"https://openalex.org/C132525143","wikidata":"https://www.wikidata.org/wiki/Q141488","display_name":"Graph","level":2,"score":0.42220380902290344},{"id":"https://openalex.org/C83415579","wikidata":"https://www.wikidata.org/wiki/Q161973","display_name":"Arc (geometry)","level":2,"score":0.4165256917476654},{"id":"https://openalex.org/C74172769","wikidata":"https://www.wikidata.org/wiki/Q1446839","display_name":"Routing (electronic design automation)","level":2,"score":0.40873903036117554},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.3716972768306732},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.23486772179603577},{"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/C31258907","wikidata":"https://www.wikidata.org/wiki/Q1301371","display_name":"Computer network","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1002/net.3230220706","is_oa":false,"landing_page_url":"https://doi.org/10.1002/net.3230220706","pdf_url":null,"source":{"id":"https://openalex.org/S191798613","display_name":"Networks","issn_l":"0028-3045","issn":["0028-3045","1097-0037"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320595","host_organization_name":"Wiley","host_organization_lineage":["https://openalex.org/P4310320595"],"host_organization_lineage_names":["Wiley"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Networks","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":21,"referenced_works":["https://openalex.org/W15274158","https://openalex.org/W252777739","https://openalex.org/W1531233258","https://openalex.org/W1578430290","https://openalex.org/W1584880296","https://openalex.org/W1983945124","https://openalex.org/W2007214900","https://openalex.org/W2021646400","https://openalex.org/W2035231387","https://openalex.org/W2039011874","https://openalex.org/W2044807391","https://openalex.org/W2048033806","https://openalex.org/W2056839836","https://openalex.org/W2058494699","https://openalex.org/W2063961786","https://openalex.org/W2069530841","https://openalex.org/W2070561727","https://openalex.org/W2074271250","https://openalex.org/W2146870367","https://openalex.org/W2163873159","https://openalex.org/W7052089110"],"related_works":["https://openalex.org/W1822681810","https://openalex.org/W2737096452","https://openalex.org/W2473635752","https://openalex.org/W2355014420","https://openalex.org/W1563136009","https://openalex.org/W2059958986","https://openalex.org/W3215808204","https://openalex.org/W4243384718","https://openalex.org/W3019964836","https://openalex.org/W2075582476"],"abstract_inverted_index":{"Abstract":[0],"In":[1],"this":[2,66],"paper,":[3],"we":[4],"consider":[5],"the":[6,37,49,75,81,88,103],"Capacitated":[7],"Arc":[8],"Routing":[9],"Problem":[10],"(CARP),":[11],"in":[12,116],"which":[13,117],"a":[14,20,27,34,40,91,110,123],"fleet":[15],"of":[16,36,39,80,90,125],"vehicles,":[17],"based":[18],"on":[19,122],"specified":[21],"vertex":[22],"(the":[23],"depot)":[24],"and":[25,46,106],"with":[26,42],"known":[28],"capacity":[29,105],"Q":[30],",":[31],"must":[32],"service":[33],"subset":[35],"edges":[38],"graph,":[41],"minimum":[43,92],"total":[44],"cost":[45,93],"such":[47],"that":[48],"load":[50],"assigned":[51],"to":[52],"each":[53],"vehicle":[54,104],"does":[55],"not":[56],"exceed":[57],"its":[58],"capacity.":[59],"New":[60],"lower":[61,83],"bounds":[62,84,119],"are":[63,85,120,128],"developed":[64],"for":[65],"problem,":[67],"producing":[68],"at":[69],"least":[70],"as":[71,74],"good":[72],"results":[73],"already":[76],"existing":[77],"ones.":[78],"Three":[79],"proposed":[82],"obtained":[86],"from":[87],"resolution":[89],"perfect":[94],"matching":[95],"problem.":[96],"The":[97],"fourth":[98],"one":[99],"takes":[100],"into":[101],"account":[102],"is":[107],"computed":[108],"using":[109],"dynamic":[111],"programming":[112],"algorithm.":[113],"Computational":[114],"results,":[115],"these":[118],"compared":[121],"set":[124],"test":[126],"problems,":[127],"included.":[129]},"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2025,"cited_by_count":4},{"year":2024,"cited_by_count":6},{"year":2023,"cited_by_count":4},{"year":2022,"cited_by_count":5},{"year":2021,"cited_by_count":5},{"year":2020,"cited_by_count":7},{"year":2019,"cited_by_count":4},{"year":2018,"cited_by_count":6},{"year":2017,"cited_by_count":5},{"year":2016,"cited_by_count":11},{"year":2015,"cited_by_count":5},{"year":2014,"cited_by_count":12},{"year":2013,"cited_by_count":7},{"year":2012,"cited_by_count":8}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}
