{"id":"https://openalex.org/W1570187551","doi":"https://doi.org/10.1023/a:1018316919294","title":"The Capacitated Arc Routing Problem: Valid Inequalities and Facets","display_name":"The Capacitated Arc Routing Problem: Valid Inequalities and Facets","publication_year":1998,"publication_date":"1998-05-01","ids":{"openalex":"https://openalex.org/W1570187551","doi":"https://doi.org/10.1023/a:1018316919294","mag":"1570187551"},"language":"en","primary_location":{"id":"doi:10.1023/a:1018316919294","is_oa":false,"landing_page_url":"https://doi.org/10.1023/a:1018316919294","pdf_url":null,"source":{"id":"https://openalex.org/S39243548","display_name":"Computational Optimization and Applications","issn_l":"0926-6003","issn":["0926-6003","1573-2894"],"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":"Computational Optimization and Applications","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/A5034081349","display_name":"Jos\u00e9-Manuel Belenguer","orcid":"https://orcid.org/0000-0002-4604-2789"},"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":"J.M. Belenguer","raw_affiliation_strings":["Departamento de Estad\u00edstica e Investigaci\u00f3n Operativa, Universitat de Val\u00e8ncia, Dr. Moliner 50, 46100, Burjassot (Valencia), Spain","Departamento de Estad\u00edstica e Investigaci\u00f3n Operativa, Universitat de Val\u00e8ncia, Dr. Moliner 50, 46100 Burjassot, Valencia, Spain"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Departamento de Estad\u00edstica e Investigaci\u00f3n Operativa, Universitat de Val\u00e8ncia, Dr. Moliner 50, 46100, Burjassot (Valencia), Spain","institution_ids":["https://openalex.org/I16097986"]},{"raw_affiliation_string":"Departamento de Estad\u00edstica e Investigaci\u00f3n Operativa, Universitat de Val\u00e8ncia, Dr. Moliner 50, 46100 Burjassot, Valencia, Spain","institution_ids":["https://openalex.org/I16097986"]}]},{"author_position":"last","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":false,"raw_author_name":"E. Benavent","raw_affiliation_strings":["Departamento de Estad\u00edstica e Investigaci\u00f3n Operativa, Universitat de Val\u00e8ncia, Dr. Moliner 50, 46100, Burjassot (Valencia), Spain","Departamento de Estad\u00edstica e Investigaci\u00f3n Operativa, Universitat de Val\u00e8ncia, Dr. Moliner 50, 46100 Burjassot, Valencia, Spain"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Departamento de Estad\u00edstica e Investigaci\u00f3n Operativa, Universitat de Val\u00e8ncia, Dr. Moliner 50, 46100, Burjassot (Valencia), Spain","institution_ids":["https://openalex.org/I16097986"]},{"raw_affiliation_string":"Departamento de Estad\u00edstica e Investigaci\u00f3n Operativa, Universitat de Val\u00e8ncia, Dr. Moliner 50, 46100 Burjassot, Valencia, Spain","institution_ids":["https://openalex.org/I16097986"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":[],"corresponding_institution_ids":["https://openalex.org/I16097986"],"apc_list":{"value":3190,"currency":"USD","value_usd":3190},"apc_paid":null,"fwci":7.145,"has_fulltext":false,"cited_by_count":109,"citation_normalized_percentile":{"value":0.96125874,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":88,"max":99},"biblio":{"volume":"10","issue":"2","first_page":"165","last_page":"187"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10567","display_name":"Vehicle Routing Optimization Methods","score":0.9998000264167786,"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":0.9998000264167786,"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":0.9976999759674072,"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/T12306","display_name":"Urban and Freight Transport Logistics","score":0.9958000183105469,"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/polyhedron","display_name":"Polyhedron","score":0.9338705539703369},{"id":"https://openalex.org/keywords/arc-routing","display_name":"Arc routing","score":0.8702596426010132},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.7154498100280762},{"id":"https://openalex.org/keywords/facet","display_name":"Facet (psychology)","score":0.577648937702179},{"id":"https://openalex.org/keywords/upper-and-lower-bounds","display_name":"Upper and lower bounds","score":0.5478746891021729},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.5381029844284058},{"id":"https://openalex.org/keywords/routing","display_name":"Routing (electronic design automation)","score":0.53579181432724},{"id":"https://openalex.org/keywords/dual-polyhedron","display_name":"Dual polyhedron","score":0.5333281755447388},{"id":"https://openalex.org/keywords/set","display_name":"Set (abstract data type)","score":0.5196755528450012},{"id":"https://openalex.org/keywords/verifiable-secret-sharing","display_name":"Verifiable secret sharing","score":0.5189763903617859},{"id":"https://openalex.org/keywords/variety","display_name":"Variety (cybernetics)","score":0.5005700588226318},{"id":"https://openalex.org/keywords/class","display_name":"Class (philosophy)","score":0.4589783251285553},{"id":"https://openalex.org/keywords/arc","display_name":"Arc (geometry)","score":0.43666520714759827},{"id":"https://openalex.org/keywords/plane","display_name":"Plane (geometry)","score":0.4162313640117645},{"id":"https://openalex.org/keywords/unit","display_name":"Unit (ring theory)","score":0.4139939248561859},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.32883793115615845},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.21184739470481873},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.10878393054008484},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.07068395614624023},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.06177067756652832}],"concepts":[{"id":"https://openalex.org/C54829058","wikidata":"https://www.wikidata.org/wiki/Q172937","display_name":"Polyhedron","level":2,"score":0.9338705539703369},{"id":"https://openalex.org/C2778536092","wikidata":"https://www.wikidata.org/wiki/Q4785038","display_name":"Arc routing","level":3,"score":0.8702596426010132},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7154498100280762},{"id":"https://openalex.org/C43122875","wikidata":"https://www.wikidata.org/wiki/Q5428522","display_name":"Facet (psychology)","level":4,"score":0.577648937702179},{"id":"https://openalex.org/C77553402","wikidata":"https://www.wikidata.org/wiki/Q13222579","display_name":"Upper and lower bounds","level":2,"score":0.5478746891021729},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.5381029844284058},{"id":"https://openalex.org/C74172769","wikidata":"https://www.wikidata.org/wiki/Q1446839","display_name":"Routing (electronic design automation)","level":2,"score":0.53579181432724},{"id":"https://openalex.org/C105313907","wikidata":"https://www.wikidata.org/wiki/Q1053857","display_name":"Dual polyhedron","level":2,"score":0.5333281755447388},{"id":"https://openalex.org/C177264268","wikidata":"https://www.wikidata.org/wiki/Q1514741","display_name":"Set (abstract data type)","level":2,"score":0.5196755528450012},{"id":"https://openalex.org/C85847156","wikidata":"https://www.wikidata.org/wiki/Q59015987","display_name":"Verifiable secret sharing","level":3,"score":0.5189763903617859},{"id":"https://openalex.org/C136197465","wikidata":"https://www.wikidata.org/wiki/Q1729295","display_name":"Variety (cybernetics)","level":2,"score":0.5005700588226318},{"id":"https://openalex.org/C2777212361","wikidata":"https://www.wikidata.org/wiki/Q5127848","display_name":"Class (philosophy)","level":2,"score":0.4589783251285553},{"id":"https://openalex.org/C83415579","wikidata":"https://www.wikidata.org/wiki/Q161973","display_name":"Arc (geometry)","level":2,"score":0.43666520714759827},{"id":"https://openalex.org/C17825722","wikidata":"https://www.wikidata.org/wiki/Q17285","display_name":"Plane (geometry)","level":2,"score":0.4162313640117645},{"id":"https://openalex.org/C122637931","wikidata":"https://www.wikidata.org/wiki/Q118084","display_name":"Unit (ring theory)","level":2,"score":0.4139939248561859},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.32883793115615845},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.21184739470481873},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.10878393054008484},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.07068395614624023},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.06177067756652832},{"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/C145420912","wikidata":"https://www.wikidata.org/wiki/Q853077","display_name":"Mathematics education","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/C31258907","wikidata":"https://www.wikidata.org/wiki/Q1301371","display_name":"Computer network","level":1,"score":0.0},{"id":"https://openalex.org/C187288502","wikidata":"https://www.wikidata.org/wiki/Q641118","display_name":"Personality","level":2,"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/C2865642","wikidata":"https://www.wikidata.org/wiki/Q378132","display_name":"Big Five personality traits","level":3,"score":0.0},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1023/a:1018316919294","is_oa":false,"landing_page_url":"https://doi.org/10.1023/a:1018316919294","pdf_url":null,"source":{"id":"https://openalex.org/S39243548","display_name":"Computational Optimization and Applications","issn_l":"0926-6003","issn":["0926-6003","1573-2894"],"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":"Computational Optimization and Applications","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[{"id":"https://metadata.un.org/sdg/10","score":0.5899999737739563,"display_name":"Reduced inequalities"}],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":29,"referenced_works":["https://openalex.org/W94346702","https://openalex.org/W1531233258","https://openalex.org/W1602262247","https://openalex.org/W1968143987","https://openalex.org/W1983945124","https://openalex.org/W1998205685","https://openalex.org/W2011039300","https://openalex.org/W2017695941","https://openalex.org/W2019001024","https://openalex.org/W2021646400","https://openalex.org/W2035083284","https://openalex.org/W2036924136","https://openalex.org/W2039011874","https://openalex.org/W2041989601","https://openalex.org/W2044807391","https://openalex.org/W2047773548","https://openalex.org/W2048033806","https://openalex.org/W2056839836","https://openalex.org/W2071463225","https://openalex.org/W2074271250","https://openalex.org/W2081814459","https://openalex.org/W2091502736","https://openalex.org/W2093737100","https://openalex.org/W2123789618","https://openalex.org/W2123805664","https://openalex.org/W2126141749","https://openalex.org/W2505968561","https://openalex.org/W3139666781","https://openalex.org/W7018068752"],"related_works":["https://openalex.org/W2008231869","https://openalex.org/W2090263210","https://openalex.org/W2949692952","https://openalex.org/W2197678707","https://openalex.org/W1995855104","https://openalex.org/W2900515541","https://openalex.org/W2254121517","https://openalex.org/W2090864852","https://openalex.org/W280563082","https://openalex.org/W1990071052"],"abstract_inverted_index":null,"counts_by_year":[{"year":2026,"cited_by_count":2},{"year":2023,"cited_by_count":2},{"year":2022,"cited_by_count":1},{"year":2021,"cited_by_count":1},{"year":2020,"cited_by_count":3},{"year":2019,"cited_by_count":5},{"year":2018,"cited_by_count":2},{"year":2017,"cited_by_count":4},{"year":2016,"cited_by_count":5},{"year":2015,"cited_by_count":7},{"year":2014,"cited_by_count":8},{"year":2013,"cited_by_count":4},{"year":2012,"cited_by_count":7}],"updated_date":"2026-08-25T07:29:55.448023","created_date":"2016-06-24T00:00:00"}