{"id":"https://openalex.org/W3128903755","doi":"https://doi.org/10.1007/s00291-020-00615-8","title":"A machine learning-based branch and price algorithm for a sampled vehicle routing problem","display_name":"A machine learning-based branch and price algorithm for a sampled vehicle routing problem","publication_year":2021,"publication_date":"2021-01-30","ids":{"openalex":"https://openalex.org/W3128903755","doi":"https://doi.org/10.1007/s00291-020-00615-8","mag":"3128903755"},"language":"en","primary_location":{"id":"doi:10.1007/s00291-020-00615-8","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s00291-020-00615-8","pdf_url":"https://link.springer.com/content/pdf/10.1007/s00291-020-00615-8.pdf","source":{"id":"https://openalex.org/S2502551423","display_name":"OR Spectrum","issn_l":"0171-6468","issn":["0171-6468","1436-6304"],"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":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"OR Spectrum","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"hybrid","oa_url":"https://link.springer.com/content/pdf/10.1007/s00291-020-00615-8.pdf","any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5002998506","display_name":"Nikolaus Furian","orcid":"https://orcid.org/0000-0002-2137-1527"},"institutions":[{"id":"https://openalex.org/I4092182","display_name":"Graz University of Technology","ror":"https://ror.org/00d7xrm67","country_code":"AT","type":"education","lineage":["https://openalex.org/I4092182"]}],"countries":["AT"],"is_corresponding":true,"raw_author_name":"Nikolaus Furian","raw_affiliation_strings":["Department of Engineering and Business Informatics, Graz University of Technology, Graz, Austria"],"affiliations":[{"raw_affiliation_string":"Department of Engineering and Business Informatics, Graz University of Technology, Graz, Austria","institution_ids":["https://openalex.org/I4092182"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5114374504","display_name":"Michael O\u2019Sullivan","orcid":"https://orcid.org/0000-0002-5621-4206"},"institutions":[{"id":"https://openalex.org/I154130895","display_name":"University of Auckland","ror":"https://ror.org/03b94tp07","country_code":"NZ","type":"education","lineage":["https://openalex.org/I154130895"]}],"countries":["NZ"],"is_corresponding":false,"raw_author_name":"Michael O\u2019Sullivan","raw_affiliation_strings":["Department of Engineering Science, University of Auckland, 70 Symonds Street, Auckland, New Zealand"],"affiliations":[{"raw_affiliation_string":"Department of Engineering Science, University of Auckland, 70 Symonds Street, Auckland, New Zealand","institution_ids":["https://openalex.org/I154130895"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5001981346","display_name":"Cameron Walker","orcid":"https://orcid.org/0000-0003-3176-9341"},"institutions":[{"id":"https://openalex.org/I154130895","display_name":"University of Auckland","ror":"https://ror.org/03b94tp07","country_code":"NZ","type":"education","lineage":["https://openalex.org/I154130895"]}],"countries":["NZ"],"is_corresponding":false,"raw_author_name":"Cameron Walker","raw_affiliation_strings":["Department of Engineering Science, University of Auckland, 70 Symonds Street, Auckland, New Zealand"],"affiliations":[{"raw_affiliation_string":"Department of Engineering Science, University of Auckland, 70 Symonds Street, Auckland, New Zealand","institution_ids":["https://openalex.org/I154130895"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5056529887","display_name":"Eranda \u00c7ela","orcid":"https://orcid.org/0000-0002-5099-8804"},"institutions":[{"id":"https://openalex.org/I4092182","display_name":"Graz University of Technology","ror":"https://ror.org/00d7xrm67","country_code":"AT","type":"education","lineage":["https://openalex.org/I4092182"]}],"countries":["AT"],"is_corresponding":false,"raw_author_name":"Eranda \u00c7ela","raw_affiliation_strings":["Department of Discrete Mathematics, Graz University of Technology, Steyrergasse 30, 8010, Graz, Austria"],"affiliations":[{"raw_affiliation_string":"Department of Discrete Mathematics, Graz University of Technology, Steyrergasse 30, 8010, Graz, Austria","institution_ids":["https://openalex.org/I4092182"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":4,"corresponding_author_ids":["https://openalex.org/A5002998506"],"corresponding_institution_ids":["https://openalex.org/I4092182"],"apc_list":{"value":2390,"currency":"EUR","value_usd":2990},"apc_paid":{"value":2390,"currency":"EUR","value_usd":2990},"fwci":4.2996,"has_fulltext":true,"cited_by_count":38,"citation_normalized_percentile":{"value":0.94593777,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":96,"max":100},"biblio":{"volume":"43","issue":"3","first_page":"693","last_page":"732"},"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":0.9961000084877014,"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/T10698","display_name":"Transportation Planning and Optimization","score":0.9860000014305115,"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/computer-science","display_name":"Computer science","score":0.6901696920394897},{"id":"https://openalex.org/keywords/vehicle-routing-problem","display_name":"Vehicle routing problem","score":0.6564764976501465},{"id":"https://openalex.org/keywords/benchmark","display_name":"Benchmark (surveying)","score":0.5943514704704285},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.5311101078987122},{"id":"https://openalex.org/keywords/binary-decision-diagram","display_name":"Binary decision diagram","score":0.5001914501190186},{"id":"https://openalex.org/keywords/branching","display_name":"Branching (polymer chemistry)","score":0.4742778241634369},{"id":"https://openalex.org/keywords/variable","display_name":"Variable (mathematics)","score":0.454424649477005},{"id":"https://openalex.org/keywords/context","display_name":"Context (archaeology)","score":0.43446409702301025},{"id":"https://openalex.org/keywords/routing","display_name":"Routing (electronic design automation)","score":0.41209572553634644},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.40187716484069824},{"id":"https://openalex.org/keywords/machine-learning","display_name":"Machine learning","score":0.3736039698123932},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.3325023651123047},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.23750099539756775}],"concepts":[{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.6901696920394897},{"id":"https://openalex.org/C123784306","wikidata":"https://www.wikidata.org/wiki/Q944041","display_name":"Vehicle routing problem","level":3,"score":0.6564764976501465},{"id":"https://openalex.org/C185798385","wikidata":"https://www.wikidata.org/wiki/Q1161707","display_name":"Benchmark (surveying)","level":2,"score":0.5943514704704285},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.5311101078987122},{"id":"https://openalex.org/C3309909","wikidata":"https://www.wikidata.org/wiki/Q864155","display_name":"Binary decision diagram","level":2,"score":0.5001914501190186},{"id":"https://openalex.org/C206175624","wikidata":"https://www.wikidata.org/wiki/Q595731","display_name":"Branching (polymer chemistry)","level":2,"score":0.4742778241634369},{"id":"https://openalex.org/C182365436","wikidata":"https://www.wikidata.org/wiki/Q50701","display_name":"Variable (mathematics)","level":2,"score":0.454424649477005},{"id":"https://openalex.org/C2779343474","wikidata":"https://www.wikidata.org/wiki/Q3109175","display_name":"Context (archaeology)","level":2,"score":0.43446409702301025},{"id":"https://openalex.org/C74172769","wikidata":"https://www.wikidata.org/wiki/Q1446839","display_name":"Routing (electronic design automation)","level":2,"score":0.41209572553634644},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.40187716484069824},{"id":"https://openalex.org/C119857082","wikidata":"https://www.wikidata.org/wiki/Q2539","display_name":"Machine learning","level":1,"score":0.3736039698123932},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.3325023651123047},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.23750099539756775},{"id":"https://openalex.org/C192562407","wikidata":"https://www.wikidata.org/wiki/Q228736","display_name":"Materials science","level":0,"score":0.0},{"id":"https://openalex.org/C159985019","wikidata":"https://www.wikidata.org/wiki/Q181790","display_name":"Composite material","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},{"id":"https://openalex.org/C205649164","wikidata":"https://www.wikidata.org/wiki/Q1071","display_name":"Geography","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/C151730666","wikidata":"https://www.wikidata.org/wiki/Q7205","display_name":"Paleontology","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/C13280743","wikidata":"https://www.wikidata.org/wiki/Q131089","display_name":"Geodesy","level":1,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1007/s00291-020-00615-8","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s00291-020-00615-8","pdf_url":"https://link.springer.com/content/pdf/10.1007/s00291-020-00615-8.pdf","source":{"id":"https://openalex.org/S2502551423","display_name":"OR Spectrum","issn_l":"0171-6468","issn":["0171-6468","1436-6304"],"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":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"OR Spectrum","raw_type":"journal-article"},{"id":"pmh:oai:RePEc:spr:orspec:v:43:y:2021:i:3:d:10.1007_s00291-020-00615-8","is_oa":false,"landing_page_url":"http://link.springer.com/10.1007/s00291-020-00615-8","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":{"id":"doi:10.1007/s00291-020-00615-8","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s00291-020-00615-8","pdf_url":"https://link.springer.com/content/pdf/10.1007/s00291-020-00615-8.pdf","source":{"id":"https://openalex.org/S2502551423","display_name":"OR Spectrum","issn_l":"0171-6468","issn":["0171-6468","1436-6304"],"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":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"OR Spectrum","raw_type":"journal-article"},"sustainable_development_goals":[{"display_name":"Peace, Justice and strong institutions","id":"https://metadata.un.org/sdg/16","score":0.4399999976158142}],"awards":[],"funders":[{"id":"https://openalex.org/F4320310430","display_name":"TU Graz, Internationale Beziehungen und Mobilit\u00e4tsprogramme","ror":"https://ror.org/00d7xrm67"}],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W3128903755.pdf","grobid_xml":"https://content.openalex.org/works/W3128903755.grobid-xml"},"referenced_works_count":71,"referenced_works":["https://openalex.org/W9632173","https://openalex.org/W132403231","https://openalex.org/W1503398984","https://openalex.org/W1510850782","https://openalex.org/W1543377438","https://openalex.org/W1965032790","https://openalex.org/W1974709582","https://openalex.org/W1992769367","https://openalex.org/W2017070898","https://openalex.org/W2018743970","https://openalex.org/W2031236641","https://openalex.org/W2047612779","https://openalex.org/W2047664145","https://openalex.org/W2058490149","https://openalex.org/W2059816321","https://openalex.org/W2060514920","https://openalex.org/W2061082746","https://openalex.org/W2074473732","https://openalex.org/W2084602277","https://openalex.org/W2085952738","https://openalex.org/W2088672099","https://openalex.org/W2096305430","https://openalex.org/W2096796578","https://openalex.org/W2099391941","https://openalex.org/W2111658959","https://openalex.org/W2129360191","https://openalex.org/W2139148132","https://openalex.org/W2151159522","https://openalex.org/W2163352112","https://openalex.org/W2165085685","https://openalex.org/W2262276395","https://openalex.org/W2285723830","https://openalex.org/W2300024838","https://openalex.org/W2518529723","https://openalex.org/W2544711428","https://openalex.org/W2563592268","https://openalex.org/W2576311753","https://openalex.org/W2607264901","https://openalex.org/W2617704759","https://openalex.org/W2626188202","https://openalex.org/W2626674286","https://openalex.org/W2629084902","https://openalex.org/W2740635283","https://openalex.org/W2790488300","https://openalex.org/W2794874231","https://openalex.org/W2796614794","https://openalex.org/W2798768004","https://openalex.org/W2800222242","https://openalex.org/W2846823501","https://openalex.org/W2900896126","https://openalex.org/W2914109978","https://openalex.org/W2920821075","https://openalex.org/W2938157874","https://openalex.org/W2953793234","https://openalex.org/W2962979969","https://openalex.org/W2963867952","https://openalex.org/W2970019720","https://openalex.org/W2970731410","https://openalex.org/W2974149267","https://openalex.org/W2975306946","https://openalex.org/W2981937730","https://openalex.org/W2989868124","https://openalex.org/W3008081749","https://openalex.org/W3011810733","https://openalex.org/W3037819751","https://openalex.org/W3092319930","https://openalex.org/W3097495674","https://openalex.org/W4244421641","https://openalex.org/W6600192831","https://openalex.org/W6604381581","https://openalex.org/W6815235507"],"related_works":["https://openalex.org/W2378211422","https://openalex.org/W4321353415","https://openalex.org/W2745001401","https://openalex.org/W4312143452","https://openalex.org/W2018691209","https://openalex.org/W2130974462","https://openalex.org/W2028665553","https://openalex.org/W2086519370","https://openalex.org/W4247364272","https://openalex.org/W4246352526"],"abstract_inverted_index":{"Abstract":[0],"Planning":[1],"of":[2,7,31,76,135,159,216],"operations,":[3],"such":[4,32],"as":[5,59],"routing":[6],"vehicles,":[8],"is":[9,162,175,239],"often":[10],"performed":[11],"repetitively":[12],"in":[13,42,127,139,165,192,219,246],"rea-world":[14],"settings,":[15],"either":[16],"by":[17,207],"humans":[18,25],"or":[19],"algorithms":[20,48,228],"solving":[21],"mathematical":[22],"problems.":[23],"While":[24],"build":[26],"experience":[27],"over":[28],"multiple":[29],"executions":[30],"planning":[33],"tasks":[34],"and":[35,85,111,143,187,201],"are":[36,91,125,190],"able":[37],"to":[38,63,67,131,145,243],"recognize":[39,68],"common":[40,101],"patterns":[41,69],"different":[43],"problem":[44,97],"instances,":[45],"classical":[46,78],"optimization":[47],"solve":[49],"every":[50],"instance":[51,247],"independently.":[52],"Machine":[53],"learning":[54],"(ML)":[55],"can":[56],"be":[57],"seen":[58],"a":[60,108,166,171,178,193],"computational":[61],"counterpart":[62],"the":[64,77,94,122,133,140,214],"human":[65],"ability":[66],"based":[70,92,152],"on":[71,93,153],"experience.":[72],"We":[73],"consider":[74],"variants":[75],"Vehicle":[79,87],"Routing":[80,88],"Problem":[81],"with":[82,241],"Time":[83],"Windows":[84],"Capacitated":[86],"Problem,":[89],"which":[90,114],"assumption":[95],"that":[96,197,226,236],"instances":[98],"follow":[99],"specific":[100,217,221],"patterns.":[102,118],"For":[103],"this":[104,120],"problem,":[105],"we":[106,234],"propose":[107],"ML-based":[109,183],"branch":[110],"price":[112],"framework":[113],"explicitly":[115],"utilizes":[116],"those":[117],"In":[119],"context,":[121],"ML":[123,205],"models":[124],"used":[126,176],"two":[128],"ways:":[129],"(a)":[130],"predict":[132,146],"value":[134],"binary":[136],"decision":[137,160],"variables":[138,151,161,218],"optimal":[141],"solution":[142],"(b)":[144],"branching":[147,173,195,231],"scores":[148],"for":[149,185,203],"fractional":[150],"full":[154],"strong":[155],"branching.":[156],"The":[157],"prediction":[158],"then":[163],"integrated":[164,191],"node":[167,186],"selection":[168,180,189],"policy,":[169],"while":[170],"predicted":[172],"score":[174],"within":[177],"variable":[179,188],"policy.":[181],"These":[182],"approaches":[184,206,212],"reliability-based":[194],"algorithm":[196],"assesses":[198],"their":[199],"quality":[200],"allows":[202],"replacing":[204],"other":[208],"(classical)":[209],"better":[210],"performing":[211],"at":[213],"level":[215],"each":[220],"instance.":[222],"Computational":[223],"results":[224],"show":[225],"our":[227,237],"outperform":[229],"benchmark":[230],"strategies.":[232],"Further,":[233],"demonstrate":[235],"approach":[238],"robust":[240],"respect":[242],"small":[244],"changes":[245],"sizes.":[248]},"counts_by_year":[{"year":2026,"cited_by_count":2},{"year":2025,"cited_by_count":7},{"year":2024,"cited_by_count":14},{"year":2023,"cited_by_count":8},{"year":2022,"cited_by_count":3},{"year":2021,"cited_by_count":4}],"updated_date":"2026-02-25T08:12:03.925757","created_date":"2025-10-10T00:00:00"}