{"id":"https://openalex.org/W2130679277","doi":"https://doi.org/10.1002/net.3230190402","title":"An algorithm for the resource constrained shortest path problem","display_name":"An algorithm for the resource constrained shortest path problem","publication_year":1989,"publication_date":"1989-07-01","ids":{"openalex":"https://openalex.org/W2130679277","doi":"https://doi.org/10.1002/net.3230190402","mag":"2130679277"},"language":"en","primary_location":{"id":"doi:10.1002/net.3230190402","is_oa":false,"landing_page_url":"https://doi.org/10.1002/net.3230190402","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/A5079112547","display_name":"J. E. Beasley","orcid":"https://orcid.org/0000-0002-4758-9970"},"institutions":[{"id":"https://openalex.org/I47508984","display_name":"Imperial College London","ror":"https://ror.org/041kmwe10","country_code":"GB","type":"education","lineage":["https://openalex.org/I47508984"]}],"countries":["GB"],"is_corresponding":false,"raw_author_name":"J. E. Beasley","raw_affiliation_strings":["School of Management, Imperial College, London SW7 2AZ, England"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"School of Management, Imperial College, London SW7 2AZ, England","institution_ids":["https://openalex.org/I47508984"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5111446110","display_name":"N.D. Christofides","orcid":null},"institutions":[{"id":"https://openalex.org/I47508984","display_name":"Imperial College London","ror":"https://ror.org/041kmwe10","country_code":"GB","type":"education","lineage":["https://openalex.org/I47508984"]}],"countries":["GB"],"is_corresponding":false,"raw_author_name":"N. Christofides","raw_affiliation_strings":["School of Management, Imperial College, London SW7 2AZ, England"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"School of Management, Imperial College, London SW7 2AZ, England","institution_ids":["https://openalex.org/I47508984"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":[],"corresponding_institution_ids":["https://openalex.org/I47508984"],"apc_list":{"value":3400,"currency":"USD","value_usd":3400},"apc_paid":null,"fwci":11.2483,"has_fulltext":false,"cited_by_count":320,"citation_normalized_percentile":{"value":0.97903373,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":98,"max":100},"biblio":{"volume":"19","issue":"4","first_page":"379","last_page":"394"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10698","display_name":"Transportation Planning and Optimization","score":0.9965999722480774,"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"}},"topics":[{"id":"https://openalex.org/T10698","display_name":"Transportation Planning and Optimization","score":0.9965999722480774,"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"}},{"id":"https://openalex.org/T10567","display_name":"Vehicle Routing Optimization Methods","score":0.9962000250816345,"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/T11106","display_name":"Data Management and Algorithms","score":0.9879000186920166,"subfield":{"id":"https://openalex.org/subfields/1711","display_name":"Signal Processing"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/shortest-path-problem","display_name":"Shortest path problem","score":0.8057050704956055},{"id":"https://openalex.org/keywords/integer-programming","display_name":"Integer programming","score":0.7019627094268799},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.6931884288787842},{"id":"https://openalex.org/keywords/relaxation","display_name":"Relaxation (psychology)","score":0.6051456928253174},{"id":"https://openalex.org/keywords/path","display_name":"Path (computing)","score":0.5996902585029602},{"id":"https://openalex.org/keywords/linear-programming-relaxation","display_name":"Linear programming relaxation","score":0.5173339247703552},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.4891069531440735},{"id":"https://openalex.org/keywords/branch-and-cut","display_name":"Branch and cut","score":0.4753125309944153},{"id":"https://openalex.org/keywords/reduction","display_name":"Reduction (mathematics)","score":0.4742155075073242},{"id":"https://openalex.org/keywords/integer","display_name":"Integer (computer science)","score":0.4597085118293762},{"id":"https://openalex.org/keywords/tree","display_name":"Tree (set theory)","score":0.45841145515441895},{"id":"https://openalex.org/keywords/flow-network","display_name":"Flow network","score":0.44525110721588135},{"id":"https://openalex.org/keywords/minimum-cost-flow-problem","display_name":"Minimum-cost flow problem","score":0.44111737608909607},{"id":"https://openalex.org/keywords/resource","display_name":"Resource (disambiguation)","score":0.43813759088516235},{"id":"https://openalex.org/keywords/k-shortest-path-routing","display_name":"K shortest path routing","score":0.4321567714214325},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.4163539409637451},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.3603591322898865},{"id":"https://openalex.org/keywords/theoretical-computer-science","display_name":"Theoretical computer science","score":0.11999762058258057},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.10120970010757446},{"id":"https://openalex.org/keywords/graph","display_name":"Graph","score":0.09405010938644409}],"concepts":[{"id":"https://openalex.org/C22590252","wikidata":"https://www.wikidata.org/wiki/Q1058754","display_name":"Shortest path problem","level":3,"score":0.8057050704956055},{"id":"https://openalex.org/C56086750","wikidata":"https://www.wikidata.org/wiki/Q6042592","display_name":"Integer programming","level":2,"score":0.7019627094268799},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.6931884288787842},{"id":"https://openalex.org/C2776029896","wikidata":"https://www.wikidata.org/wiki/Q3935810","display_name":"Relaxation (psychology)","level":2,"score":0.6051456928253174},{"id":"https://openalex.org/C2777735758","wikidata":"https://www.wikidata.org/wiki/Q817765","display_name":"Path (computing)","level":2,"score":0.5996902585029602},{"id":"https://openalex.org/C25360446","wikidata":"https://www.wikidata.org/wiki/Q1512771","display_name":"Linear programming relaxation","level":3,"score":0.5173339247703552},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.4891069531440735},{"id":"https://openalex.org/C50797617","wikidata":"https://www.wikidata.org/wiki/Q498566","display_name":"Branch and cut","level":3,"score":0.4753125309944153},{"id":"https://openalex.org/C111335779","wikidata":"https://www.wikidata.org/wiki/Q3454686","display_name":"Reduction (mathematics)","level":2,"score":0.4742155075073242},{"id":"https://openalex.org/C97137487","wikidata":"https://www.wikidata.org/wiki/Q729138","display_name":"Integer (computer science)","level":2,"score":0.4597085118293762},{"id":"https://openalex.org/C113174947","wikidata":"https://www.wikidata.org/wiki/Q2859736","display_name":"Tree (set theory)","level":2,"score":0.45841145515441895},{"id":"https://openalex.org/C114809511","wikidata":"https://www.wikidata.org/wiki/Q1412924","display_name":"Flow network","level":2,"score":0.44525110721588135},{"id":"https://openalex.org/C99545648","wikidata":"https://www.wikidata.org/wiki/Q2897180","display_name":"Minimum-cost flow problem","level":3,"score":0.44111737608909607},{"id":"https://openalex.org/C206345919","wikidata":"https://www.wikidata.org/wiki/Q20380951","display_name":"Resource (disambiguation)","level":2,"score":0.43813759088516235},{"id":"https://openalex.org/C70266271","wikidata":"https://www.wikidata.org/wiki/Q6343044","display_name":"K shortest path routing","level":4,"score":0.4321567714214325},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.4163539409637451},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.3603591322898865},{"id":"https://openalex.org/C80444323","wikidata":"https://www.wikidata.org/wiki/Q2878974","display_name":"Theoretical computer science","level":1,"score":0.11999762058258057},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.10120970010757446},{"id":"https://openalex.org/C132525143","wikidata":"https://www.wikidata.org/wiki/Q141488","display_name":"Graph","level":2,"score":0.09405010938644409},{"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/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"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/C77805123","wikidata":"https://www.wikidata.org/wiki/Q161272","display_name":"Social psychology","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1002/net.3230190402","is_oa":false,"landing_page_url":"https://doi.org/10.1002/net.3230190402","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":[{"id":"https://metadata.un.org/sdg/8","display_name":"Decent work and economic growth","score":0.44999998807907104}],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":50,"referenced_works":["https://openalex.org/W10162269","https://openalex.org/W119169328","https://openalex.org/W197883060","https://openalex.org/W575490387","https://openalex.org/W1931114878","https://openalex.org/W1964443412","https://openalex.org/W1965039153","https://openalex.org/W1973745435","https://openalex.org/W1973804680","https://openalex.org/W1986652726","https://openalex.org/W1998132337","https://openalex.org/W2001912652","https://openalex.org/W2007572995","https://openalex.org/W2009927490","https://openalex.org/W2010160212","https://openalex.org/W2011039300","https://openalex.org/W2011282943","https://openalex.org/W2015092026","https://openalex.org/W2016049811","https://openalex.org/W2017697298","https://openalex.org/W2023132252","https://openalex.org/W2033097611","https://openalex.org/W2035231387","https://openalex.org/W2051956023","https://openalex.org/W2058479406","https://openalex.org/W2062266989","https://openalex.org/W2063317962","https://openalex.org/W2066047491","https://openalex.org/W2066732937","https://openalex.org/W2070409008","https://openalex.org/W2071852134","https://openalex.org/W2072765922","https://openalex.org/W2073471848","https://openalex.org/W2078948975","https://openalex.org/W2079537248","https://openalex.org/W2086778464","https://openalex.org/W2089845007","https://openalex.org/W2089957823","https://openalex.org/W2093952957","https://openalex.org/W2098074159","https://openalex.org/W2125690626","https://openalex.org/W2127456145","https://openalex.org/W2144050074","https://openalex.org/W2151842399","https://openalex.org/W2169528473","https://openalex.org/W2330056579","https://openalex.org/W2525478591","https://openalex.org/W2566091043","https://openalex.org/W4236384091","https://openalex.org/W6995914840"],"related_works":["https://openalex.org/W2009796757","https://openalex.org/W3141113327","https://openalex.org/W2080904092","https://openalex.org/W3035974271","https://openalex.org/W3161514703","https://openalex.org/W3207627914","https://openalex.org/W2270959725","https://openalex.org/W4252122881","https://openalex.org/W2151525839","https://openalex.org/W648253840"],"abstract_inverted_index":{"Abstract":[0],"In":[1],"this":[2,102],"paper":[3],"we":[4],"examine":[5],"an":[6,73],"integer":[7,54],"programming":[8,55],"formulation":[9,56],"of":[10,21,27,52,57,114],"the":[11,19,42,53,58,98,112],"resource":[12,43],"constrained":[13],"shortest":[14,75],"path":[15,76],"problem.":[16],"This":[17],"is":[18,78],"problem":[20,59,66,100],"a":[22,25,34,61,82,88],"traveller":[23],"with":[24],"budget":[26],"various":[28],"resources":[29],"who":[30],"has":[31],"to":[32,72,118],"reach":[33],"given":[35],"destination":[36],"as":[37,39],"quickly":[38],"possible":[40],"within":[41],"constraints":[44],"imposed":[45],"by":[46],"his":[47],"budget.":[48],"A":[49],"lagrangean":[50,103],"relaxation":[51,104],"into":[60],"minimum":[62],"cost":[63],"network":[64],"flow":[65],"(which":[67],"in":[68,87],"certain":[69],"circumstances":[70],"reduces":[71],"unconstrained":[74],"problem)":[77],"developed":[79],"which":[80],"provides":[81],"lower":[83],"bound":[84],"for":[85,111],"use":[86],"tree":[89],"search":[90],"procedure.":[91],"Problem":[92],"reduction":[93],"tests":[94],"based":[95],"on":[96],"both":[97],"original":[99],"and":[101,123],"are":[105,109],"given.":[106],"Computational":[107],"results":[108],"presented":[110],"solution":[113],"problems":[115],"involving":[116],"up":[117],"500":[119],"vertices,":[120],"5000":[121],"arcs,":[122],"10":[124],"resources.":[125]},"counts_by_year":[{"year":2026,"cited_by_count":5},{"year":2025,"cited_by_count":5},{"year":2024,"cited_by_count":9},{"year":2023,"cited_by_count":11},{"year":2022,"cited_by_count":6},{"year":2021,"cited_by_count":12},{"year":2020,"cited_by_count":11},{"year":2019,"cited_by_count":19},{"year":2018,"cited_by_count":11},{"year":2017,"cited_by_count":9},{"year":2016,"cited_by_count":20},{"year":2015,"cited_by_count":13},{"year":2014,"cited_by_count":16},{"year":2013,"cited_by_count":13},{"year":2012,"cited_by_count":21}],"updated_date":"2026-07-15T18:14:33.161393","created_date":"2025-10-10T00:00:00"}