{"id":"https://openalex.org/W4414183870","doi":"https://doi.org/10.1002/net.70005","title":"Vehicle Routing Problem With Time Windows\u2014New Valid Inequalities From Polar Duality","display_name":"Vehicle Routing Problem With Time Windows\u2014New Valid Inequalities From Polar Duality","publication_year":2025,"publication_date":"2025-09-15","ids":{"openalex":"https://openalex.org/W4414183870","doi":"https://doi.org/10.1002/net.70005"},"language":"en","primary_location":{"id":"doi:10.1002/net.70005","is_oa":false,"landing_page_url":"https://doi.org/10.1002/net.70005","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/A5071538660","display_name":"Yogesh K. Agarwal","orcid":"https://orcid.org/0000-0001-6189-0017"},"institutions":[{"id":"https://openalex.org/I26771391","display_name":"Jaipuria Institute of Management","ror":"https://ror.org/038dhfq97","country_code":"IN","type":"education","lineage":["https://openalex.org/I26771391"]},{"id":"https://openalex.org/I91699865","display_name":"Indian Institute of Management Lucknow","ror":"https://ror.org/05gfjrx96","country_code":"IN","type":"education","lineage":["https://openalex.org/I91699865"]}],"countries":["IN"],"is_corresponding":false,"raw_author_name":"Yogesh Kumar Agarwal","raw_affiliation_strings":["Indian Institute of Management  Lucknow India","Jaipuria Institute of Management  Lucknow India"],"affiliations":[{"raw_affiliation_string":"Indian Institute of Management  Lucknow India","institution_ids":["https://openalex.org/I91699865"]},{"raw_affiliation_string":"Jaipuria Institute of Management  Lucknow India","institution_ids":["https://openalex.org/I26771391"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5090849978","display_name":"Prahalad Venkateshan","orcid":"https://orcid.org/0000-0002-9566-7451"},"institutions":[{"id":"https://openalex.org/I150870154","display_name":"Indian Institute of Management Ahmedabad","ror":"https://ror.org/02egcpy68","country_code":"IN","type":"education","lineage":["https://openalex.org/I150870154"]}],"countries":["IN"],"is_corresponding":true,"raw_author_name":"Prahalad Venkateshan","raw_affiliation_strings":["Indian Institute of Management  Vastrapur Ahmedabad India"],"affiliations":[{"raw_affiliation_string":"Indian Institute of Management  Vastrapur Ahmedabad India","institution_ids":["https://openalex.org/I150870154"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5090849978"],"corresponding_institution_ids":["https://openalex.org/I150870154"],"apc_list":{"value":3400,"currency":"USD","value_usd":3400},"apc_paid":null,"fwci":0.0,"has_fulltext":false,"cited_by_count":0,"citation_normalized_percentile":{"value":0.3599787,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"87","issue":"1","first_page":"3","last_page":"22"},"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/T12176","display_name":"Optimization and Packing Problems","score":0.9918000102043152,"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/T12546","display_name":"Smart Parking Systems Research","score":0.9882000088691711,"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/benchmark","display_name":"Benchmark (surveying)","score":0.7131999731063843},{"id":"https://openalex.org/keywords/vehicle-routing-problem","display_name":"Vehicle routing problem","score":0.6820999979972839},{"id":"https://openalex.org/keywords/routing","display_name":"Routing (electronic design automation)","score":0.5598000288009644},{"id":"https://openalex.org/keywords/flow","display_name":"Flow (mathematics)","score":0.5579000115394592},{"id":"https://openalex.org/keywords/extant-taxon","display_name":"Extant taxon","score":0.5278000235557556},{"id":"https://openalex.org/keywords/duality","display_name":"Duality (order theory)","score":0.49410000443458557},{"id":"https://openalex.org/keywords/polar","display_name":"Polar","score":0.4885999858379364},{"id":"https://openalex.org/keywords/tree","display_name":"Tree (set theory)","score":0.4526999890804291},{"id":"https://openalex.org/keywords/upper-and-lower-bounds","display_name":"Upper and lower bounds","score":0.39489999413490295}],"concepts":[{"id":"https://openalex.org/C185798385","wikidata":"https://www.wikidata.org/wiki/Q1161707","display_name":"Benchmark (surveying)","level":2,"score":0.7131999731063843},{"id":"https://openalex.org/C123784306","wikidata":"https://www.wikidata.org/wiki/Q944041","display_name":"Vehicle routing problem","level":3,"score":0.6820999979972839},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5722000002861023},{"id":"https://openalex.org/C74172769","wikidata":"https://www.wikidata.org/wiki/Q1446839","display_name":"Routing (electronic design automation)","level":2,"score":0.5598000288009644},{"id":"https://openalex.org/C38349280","wikidata":"https://www.wikidata.org/wiki/Q1434290","display_name":"Flow (mathematics)","level":2,"score":0.5579000115394592},{"id":"https://openalex.org/C178300618","wikidata":"https://www.wikidata.org/wiki/Q1898509","display_name":"Extant taxon","level":2,"score":0.5278000235557556},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.4997999966144562},{"id":"https://openalex.org/C2778023678","wikidata":"https://www.wikidata.org/wiki/Q554403","display_name":"Duality (order theory)","level":2,"score":0.49410000443458557},{"id":"https://openalex.org/C29705727","wikidata":"https://www.wikidata.org/wiki/Q294562","display_name":"Polar","level":2,"score":0.4885999858379364},{"id":"https://openalex.org/C113174947","wikidata":"https://www.wikidata.org/wiki/Q2859736","display_name":"Tree (set theory)","level":2,"score":0.4526999890804291},{"id":"https://openalex.org/C77553402","wikidata":"https://www.wikidata.org/wiki/Q13222579","display_name":"Upper and lower bounds","level":2,"score":0.39489999413490295},{"id":"https://openalex.org/C114809511","wikidata":"https://www.wikidata.org/wiki/Q1412924","display_name":"Flow network","level":2,"score":0.3720000088214874},{"id":"https://openalex.org/C3017489831","wikidata":"https://www.wikidata.org/wiki/Q2393193","display_name":"Running time","level":2,"score":0.3691999912261963},{"id":"https://openalex.org/C40069579","wikidata":"https://www.wikidata.org/wiki/Q62494","display_name":"Polar coordinate system","level":2,"score":0.3483000099658966},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.3450999855995178},{"id":"https://openalex.org/C148764684","wikidata":"https://www.wikidata.org/wiki/Q621751","display_name":"Approximation algorithm","level":2,"score":0.34139999747276306},{"id":"https://openalex.org/C45555294","wikidata":"https://www.wikidata.org/wiki/Q28113351","display_name":"Inequality","level":2,"score":0.32839998602867126},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.3149999976158142},{"id":"https://openalex.org/C137836250","wikidata":"https://www.wikidata.org/wiki/Q984063","display_name":"Optimization problem","level":2,"score":0.31369999051094055},{"id":"https://openalex.org/C179799912","wikidata":"https://www.wikidata.org/wiki/Q205084","display_name":"Computational complexity theory","level":2,"score":0.3086000084877014},{"id":"https://openalex.org/C2164484","wikidata":"https://www.wikidata.org/wiki/Q5170150","display_name":"Core (optical fiber)","level":2,"score":0.3061000108718872},{"id":"https://openalex.org/C2985733770","wikidata":"https://www.wikidata.org/wiki/Q1233007","display_name":"Travel time","level":2,"score":0.30399999022483826},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.3019999861717224},{"id":"https://openalex.org/C311688","wikidata":"https://www.wikidata.org/wiki/Q2393193","display_name":"Time complexity","level":2,"score":0.29670000076293945},{"id":"https://openalex.org/C45374587","wikidata":"https://www.wikidata.org/wiki/Q12525525","display_name":"Computation","level":2,"score":0.27570000290870667},{"id":"https://openalex.org/C161999928","wikidata":"https://www.wikidata.org/wiki/Q4556320","display_name":"Variational inequality","level":2,"score":0.2694000005722046},{"id":"https://openalex.org/C193386753","wikidata":"https://www.wikidata.org/wiki/Q1130396","display_name":"Approximations of \u03c0","level":2,"score":0.2687000036239624},{"id":"https://openalex.org/C182964748","wikidata":"https://www.wikidata.org/wiki/Q208216","display_name":"Triangle inequality","level":2,"score":0.2621000111103058}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1002/net.70005","is_oa":false,"landing_page_url":"https://doi.org/10.1002/net.70005","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":36,"referenced_works":["https://openalex.org/W1492984840","https://openalex.org/W1586016561","https://openalex.org/W1965032790","https://openalex.org/W1973565128","https://openalex.org/W1973658994","https://openalex.org/W1977129671","https://openalex.org/W1984727134","https://openalex.org/W1994184140","https://openalex.org/W2001944236","https://openalex.org/W2003264207","https://openalex.org/W2017070898","https://openalex.org/W2021033250","https://openalex.org/W2026220041","https://openalex.org/W2031722814","https://openalex.org/W2039766013","https://openalex.org/W2040678783","https://openalex.org/W2049287714","https://openalex.org/W2053375152","https://openalex.org/W2056958455","https://openalex.org/W2059816321","https://openalex.org/W2088310799","https://openalex.org/W2089158966","https://openalex.org/W2096305430","https://openalex.org/W2110818895","https://openalex.org/W2111658959","https://openalex.org/W2119949770","https://openalex.org/W2135680984","https://openalex.org/W2138131169","https://openalex.org/W2150176315","https://openalex.org/W2505968561","https://openalex.org/W2629084902","https://openalex.org/W3122956505","https://openalex.org/W3175586709","https://openalex.org/W3199547674","https://openalex.org/W4245026044","https://openalex.org/W4408320441"],"related_works":[],"abstract_inverted_index":{"ABSTRACT":[0],"The":[1],"vehicle":[2],"routing":[3],"problem":[4,11,22,65],"with":[5,73,83],"time":[6,75,85,177],"windows":[7],"is":[8,48,89],"a":[9,25,129,152],"well\u2010researched":[10],"in":[12,123,155,175,180,185],"literature.":[13,125],"We":[14,126],"study":[15],"the":[16,21,40,60,103,114,124,133,181,186,196,200],"2\u2010index":[17],"flow":[18,197],"formulation":[19,198],"for":[20,39,161,199],"and":[23,52,66,158,178],"propose":[24],"relatively":[26],"little\u2010used":[27],"approach":[28,88],"of":[29,44,58,91,102,132,164,183],"polar":[30,46],"duality/local":[31],"cuts":[32],"to":[33,54,63,100,141,151,191],"compute":[34,142],"new":[35,130],"general":[36],"valid":[37],"inequalities":[38,137,148],"problem.":[41,201],"Our":[42],"method":[43],"applying":[45,59],"duality":[47],"quite":[49],"distinct":[50],"from":[51],"complimentary":[53],"an":[55],"earlier":[56],"attempt":[57],"same":[61],"idea":[62],"this":[64],"produces":[67],"significantly":[68,118],"better":[69,119],"results":[70],"on":[71,169],"instances":[72,82,112,171],"tight":[74,84],"windows.":[76],"On":[77,110],"almost":[78],"all":[79],"25\u2010customer":[80],"Solomon":[81],"windows,":[86],"our":[87],"capable":[90],"producing":[92],"very":[93],"strong":[94],"lower":[95,115,156],"bounds":[96,116,157],"that":[97,138,194],"are":[98,117,139],"close":[99],"100%":[101],"optimal":[104],"solution":[105,159],"within":[106],"reasonable":[107],"computing":[108,176],"time.":[109],"larger":[111],"too":[113],"than":[120],"those":[121],"reported":[122],"also":[127,149],"present":[128],"version":[131],"previously":[134],"proposed":[135],"\u2010path":[136],"easy":[140],"as":[143,145,189],"well":[144],"effective.":[146],"These":[147],"lead":[150],"substantial":[153],"improvement":[154,174],"times":[160],"some":[162],"classes":[163],"instances.":[165],"Computational":[166],"tests":[167],"performed":[168],"benchmark":[170],"indicate":[172],"significant":[173],"decrease":[179],"number":[182],"nodes":[184],"branch\u2010and\u2010bound":[187],"tree":[188],"compared":[190],"extant":[192],"methods":[193],"employ":[195]},"counts_by_year":[],"updated_date":"2026-03-07T16:01:11.037858","created_date":"2025-10-10T00:00:00"}