{"id":"https://openalex.org/W1561031615","doi":"https://doi.org/10.1145/2629653","title":"Minimum Makespan Multi-Vehicle Dial-a-Ride","display_name":"Minimum Makespan Multi-Vehicle Dial-a-Ride","publication_year":2015,"publication_date":"2015-01-13","ids":{"openalex":"https://openalex.org/W1561031615","doi":"https://doi.org/10.1145/2629653","mag":"1561031615"},"language":"en","primary_location":{"id":"doi:10.1145/2629653","is_oa":false,"landing_page_url":"https://doi.org/10.1145/2629653","pdf_url":null,"source":{"id":"https://openalex.org/S137348503","display_name":"ACM Transactions on Algorithms","issn_l":"1549-6325","issn":["1549-6325","1549-6333"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319798","host_organization_name":"Association for Computing Machinery","host_organization_lineage":["https://openalex.org/P4310319798"],"host_organization_lineage_names":["Association for Computing Machinery"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"ACM Transactions on Algorithms","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://orbit.dtu.dk/en/publications/1b9c0387-f02c-49cd-9281-82dd93fea47f","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5070148734","display_name":"Inge Li G\u00f8rtz","orcid":"https://orcid.org/0000-0002-8322-4952"},"institutions":[{"id":"https://openalex.org/I96673099","display_name":"Technical University of Denmark","ror":"https://ror.org/04qtj9h94","country_code":"DK","type":"education","lineage":["https://openalex.org/I96673099"]}],"countries":["DK"],"is_corresponding":true,"raw_author_name":"Inge Li G\u00f8rtz","raw_affiliation_strings":["Technical University of Denmark, Kongens Lyngby Denmark"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Technical University of Denmark, Kongens Lyngby Denmark","institution_ids":["https://openalex.org/I96673099"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5051270969","display_name":"Viswanath Nagarajan","orcid":"https://orcid.org/0000-0002-9514-5581"},"institutions":[{"id":"https://openalex.org/I27837315","display_name":"University of Michigan","ror":"https://ror.org/00jmfr291","country_code":"US","type":"education","lineage":["https://openalex.org/I27837315"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Viswanath Nagarajan","raw_affiliation_strings":["University of Michigan, USA","University of Michigan , USA"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"University of Michigan, USA","institution_ids":["https://openalex.org/I27837315"]},{"raw_affiliation_string":"University of Michigan , USA","institution_ids":["https://openalex.org/I27837315"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5087844619","display_name":"R. Ravi","orcid":"https://orcid.org/0000-0001-7603-1207"},"institutions":[{"id":"https://openalex.org/I74973139","display_name":"Carnegie Mellon University","ror":"https://ror.org/05x2bcf33","country_code":"US","type":"education","lineage":["https://openalex.org/I74973139"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"R. Ravi","raw_affiliation_strings":["Carnegie Mellon University, USA"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Carnegie Mellon University, USA","institution_ids":["https://openalex.org/I74973139"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5070148734"],"corresponding_institution_ids":["https://openalex.org/I96673099"],"apc_list":null,"apc_paid":null,"fwci":1.1514,"has_fulltext":false,"cited_by_count":10,"citation_normalized_percentile":{"value":0.80868768,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":98},"biblio":{"volume":"11","issue":"3","first_page":"1","last_page":"29"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11814","display_name":"Advanced Manufacturing and Logistics Optimization","score":0.9994999766349792,"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/T11814","display_name":"Advanced Manufacturing and Logistics Optimization","score":0.9994999766349792,"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/T12782","display_name":"Assembly Line Balancing Optimization","score":0.9973000288009644,"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/T10551","display_name":"Scheduling and Optimization Algorithms","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"}}],"keywords":[{"id":"https://openalex.org/keywords/job-shop-scheduling","display_name":"Job shop scheduling","score":0.6732772588729858},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.48719900846481323},{"id":"https://openalex.org/keywords/dial","display_name":"Dial","score":0.45145899057388306},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.4015679359436035},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.3320324420928955},{"id":"https://openalex.org/keywords/computer-network","display_name":"Computer network","score":0.22711309790611267},{"id":"https://openalex.org/keywords/engineering","display_name":"Engineering","score":0.12038382887840271},{"id":"https://openalex.org/keywords/electrical-engineering","display_name":"Electrical engineering","score":0.0759935975074768}],"concepts":[{"id":"https://openalex.org/C55416958","wikidata":"https://www.wikidata.org/wiki/Q6206757","display_name":"Job shop scheduling","level":3,"score":0.6732772588729858},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.48719900846481323},{"id":"https://openalex.org/C2779710594","wikidata":"https://www.wikidata.org/wiki/Q4151234","display_name":"Dial","level":2,"score":0.45145899057388306},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.4015679359436035},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.3320324420928955},{"id":"https://openalex.org/C31258907","wikidata":"https://www.wikidata.org/wiki/Q1301371","display_name":"Computer network","level":1,"score":0.22711309790611267},{"id":"https://openalex.org/C127413603","wikidata":"https://www.wikidata.org/wiki/Q11023","display_name":"Engineering","level":0,"score":0.12038382887840271},{"id":"https://openalex.org/C119599485","wikidata":"https://www.wikidata.org/wiki/Q43035","display_name":"Electrical engineering","level":1,"score":0.0759935975074768},{"id":"https://openalex.org/C74172769","wikidata":"https://www.wikidata.org/wiki/Q1446839","display_name":"Routing (electronic design automation)","level":2,"score":0.0}],"mesh":[],"locations_count":8,"locations":[{"id":"doi:10.1145/2629653","is_oa":false,"landing_page_url":"https://doi.org/10.1145/2629653","pdf_url":null,"source":{"id":"https://openalex.org/S137348503","display_name":"ACM Transactions on Algorithms","issn_l":"1549-6325","issn":["1549-6325","1549-6333"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319798","host_organization_name":"Association for Computing Machinery","host_organization_lineage":["https://openalex.org/P4310319798"],"host_organization_lineage_names":["Association for Computing Machinery"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"ACM Transactions on Algorithms","raw_type":"journal-article"},{"id":"pmh:doi:10.1184/r1/6706805","is_oa":false,"landing_page_url":null,"pdf_url":null,"source":{"id":"https://openalex.org/S4406922384","display_name":"Open MIND","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"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":"Journal contribution"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.157.4622","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.157.4622","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://www.andrew.cmu.edu/~viswanat/papers/mDR.pdf","raw_type":"text"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.218.9423","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.218.9423","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"text"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.369.7094","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.369.7094","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"text"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.575.6769","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.575.6769","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://www.imm.dtu.dk/~inge/esa2009.pdf","raw_type":"text"},{"id":"pmh:oai:pure.atira.dk:publications/1b9c0387-f02c-49cd-9281-82dd93fea47f","is_oa":true,"landing_page_url":"https://orbit.dtu.dk/en/publications/1b9c0387-f02c-49cd-9281-82dd93fea47f","pdf_url":null,"source":{"id":"https://openalex.org/S4306400705","display_name":"Technical University of Denmark, DTU Orbit (Technical University of Denmark, DTU)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I96673099","host_organization_name":"Technical University of Denmark","host_organization_lineage":["https://openalex.org/I96673099"],"host_organization_lineage_names":[],"type":"repository"},"license":"other-oa","license_id":"https://openalex.org/licenses/other-oa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"G\u00f8rtz , I L , Nagarajan , V &amp; Ravi , R 2009 , Minimum Makespan Multi-vehicle Dial-a-Ride . in Algorithms - ESA 2009 . Springer , Lecture Notes in Computer Science , no. Volume 5757/2009 , pp. 540-552 , 17th European Symposium on Algorithms , K\u00f8benhavn , Denmark , 07/09/2009 . https://doi.org/10.1007/978-3-642-04128-0_48","raw_type":"contributionToPeriodical"},{"id":"pmh:oai:pure.atira.dk:publications/48d13879-f520-4a54-93a0-0c36fa44a06b","is_oa":false,"landing_page_url":"https://orbit.dtu.dk/en/publications/48d13879-f520-4a54-93a0-0c36fa44a06b","pdf_url":null,"source":{"id":"https://openalex.org/S4306400705","display_name":"Technical University of Denmark, DTU Orbit (Technical University of Denmark, DTU)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I96673099","host_organization_name":"Technical University of Denmark","host_organization_lineage":["https://openalex.org/I96673099"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"G\u00f8rtz , I L , Nagarajan , V &amp; Ravi , R 2015 , ' Minimum Makespan Multi-Vehicle Dial-a-Ride ' , A C M Transactions on Algorithms , vol. 11 , no. 3 , 23 . https://doi.org/10.1145/2629653","raw_type":"article"}],"best_oa_location":{"id":"pmh:oai:pure.atira.dk:publications/1b9c0387-f02c-49cd-9281-82dd93fea47f","is_oa":true,"landing_page_url":"https://orbit.dtu.dk/en/publications/1b9c0387-f02c-49cd-9281-82dd93fea47f","pdf_url":null,"source":{"id":"https://openalex.org/S4306400705","display_name":"Technical University of Denmark, DTU Orbit (Technical University of Denmark, DTU)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I96673099","host_organization_name":"Technical University of Denmark","host_organization_lineage":["https://openalex.org/I96673099"],"host_organization_lineage_names":[],"type":"repository"},"license":"other-oa","license_id":"https://openalex.org/licenses/other-oa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"G\u00f8rtz , I L , Nagarajan , V &amp; Ravi , R 2009 , Minimum Makespan Multi-vehicle Dial-a-Ride . in Algorithms - ESA 2009 . Springer , Lecture Notes in Computer Science , no. Volume 5757/2009 , pp. 540-552 , 17th European Symposium on Algorithms , K\u00f8benhavn , Denmark , 07/09/2009 . https://doi.org/10.1007/978-3-642-04128-0_48","raw_type":"contributionToPeriodical"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":37,"referenced_works":["https://openalex.org/W1506243241","https://openalex.org/W1974713906","https://openalex.org/W1983649454","https://openalex.org/W2002041206","https://openalex.org/W2002356593","https://openalex.org/W2006527299","https://openalex.org/W2010587722","https://openalex.org/W2017383000","https://openalex.org/W2020400310","https://openalex.org/W2042899161","https://openalex.org/W2059149798","https://openalex.org/W2063659595","https://openalex.org/W2066590823","https://openalex.org/W2077626805","https://openalex.org/W2082353536","https://openalex.org/W2085325317","https://openalex.org/W2087806988","https://openalex.org/W2091569826","https://openalex.org/W2100961486","https://openalex.org/W2109721451","https://openalex.org/W2117226423","https://openalex.org/W2117324637","https://openalex.org/W2119483402","https://openalex.org/W2133156969","https://openalex.org/W2137716917","https://openalex.org/W2141105412","https://openalex.org/W2143987816","https://openalex.org/W2149929647","https://openalex.org/W2151534739","https://openalex.org/W2155735286","https://openalex.org/W2156760067","https://openalex.org/W2167397341","https://openalex.org/W2168563161","https://openalex.org/W2398231527","https://openalex.org/W2714858040","https://openalex.org/W2951475756","https://openalex.org/W3030774092"],"related_works":["https://openalex.org/W2899084033","https://openalex.org/W2748952813","https://openalex.org/W4391375266","https://openalex.org/W2002530021","https://openalex.org/W1541183083","https://openalex.org/W2377291837","https://openalex.org/W1610756803","https://openalex.org/W1566343967","https://openalex.org/W340370915","https://openalex.org/W4253901018"],"abstract_inverted_index":{"Dial-a-Ride":[0,55,205,251],"problems":[1],"consist":[2],"of":[3,7,22,87,133,139,156,164,231,243,287,306],"a":[4,11,20,88,121],"set":[5,21],"V":[6,81],"n":[8,199,227,240,310],"vertices":[9,176],"in":[10,167,269],"metric":[12],"space":[13],"(denoting":[14],"travel":[15],"time":[16,129,138,144],"between":[17],"vertices)":[18],"and":[19,65,98,177,207,316],"m":[23,35],"objects":[24,110],"represented":[25],"as":[26],"source-destination":[27],"pairs":[28],"{(":[29],"s":[30],"i":[31,33,36],",t":[32],")}":[34],"=1":[37],",":[38,206],"where":[39,66,135],"each":[40,61,67,92],"object":[41,170],"requires":[42],"to":[43,49,114,119,148,189],"be":[44,172],"moved":[45,186],"from":[46,111,187,278],"its":[47,75,101,149,157,215],"source":[48,188],"destination":[50],"vertex.":[51],"In":[52,299],"the":[53,126,136,143,154,161,229,279,284,320],"multi-vehicle":[54,165,204,256,314],"problem,":[56],"there":[57,219,261],"are":[58,194,262,272],"q":[59,72],"vehicles,":[60,134],"having":[62],"capacity":[63,222],"k":[64],"vehicle":[68,93,95,140,249],"j":[69,79,96,104,141,152],"\u2208":[70,80],"[":[71],"]":[73],"has":[74],"own":[76],"depot-vertex":[77],"r":[78,103,151],".":[82],"A":[83],"feasible":[84,122],"schedule":[85,123],"consists":[86],"capacitated":[89,250,313],"route":[90],"for":[91,202,214,247,312,319],"(where":[94],"originates":[97],"ends":[99],"at":[100,153,174],"depot":[102,150],")":[105,132,241,275,311],"that":[106,124,260],"together":[107],"move":[108],"all":[109],"their":[112],"sources":[113],"destinations.":[115],"The":[116],"objective":[117],"is":[118,142,220,228,235],"find":[120],"minimizes":[125],"maximum":[127],"completion":[128,137],"(i.e.,":[130],"makespan":[131],"when":[145,218,264],"it":[146],"returns":[147],"end":[155],"route.":[158],"We":[159,281],"study":[160],"preemptive":[162,203],"version":[163],"Dial-a-Ride,":[166,257,315],"which":[168],"an":[169,195,208,236],"may":[171],"left":[173],"intermediate":[175],"transported":[178],"by":[179,290],"more":[180],"than":[181],"one":[182],"vehicle,":[183],"while":[184],"being":[185],"destination.":[190],"Our":[191],"main":[192],"results":[193],"O":[196,210,307,317],"(log":[197,211,238,308],"3":[198],")-approximation":[200,213],"algorithm":[201],"improved":[209,304],"t":[212,225,274],"special":[216,285],"case":[217],"no":[221],"constraint":[223],"(here":[224],"\u2264":[226],"number":[230],"distinct":[232],"depot-vertices).":[233],"There":[234],"\u03a9":[237],"1/4-\u03f5":[239],"hardness":[242],"approximation":[244],"known":[245],"even":[246],"single":[248],"[G\u00f8rtz":[252],"2006].":[253],"For":[254],"uncapacitated":[255,321],"we":[258,302],"show":[259],"instances":[263],"natural":[265],"lower":[266],"bounds":[267],"(used":[268],"our":[270],"algorithm)":[271],"\u02dc\u03a9(log":[273],"factor":[276],"away":[277],"optimum.":[280],"also":[282],"consider":[283],"class":[286],"metrics":[288],"induced":[289],"graphs":[291],"excluding":[292],"any":[293],"fixed":[294],"minor":[295],"(e.g.,":[296],"planar":[297],"metrics).":[298],"this":[300],"case,":[301],"obtain":[303],"guarantees":[305],"2":[309],"(1)":[318],"problem.":[322]},"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2024,"cited_by_count":1},{"year":2022,"cited_by_count":2},{"year":2021,"cited_by_count":1},{"year":2019,"cited_by_count":2},{"year":2018,"cited_by_count":1},{"year":2017,"cited_by_count":1},{"year":2013,"cited_by_count":1}],"updated_date":"2026-04-28T14:05:53.105641","created_date":"2025-10-10T00:00:00"}
