{"id":"https://openalex.org/W2002520482","doi":"https://doi.org/10.1109/tits.2011.2169961","title":"Robust Train Timetabling Problem: Mathematical Model and Branch and Bound Algorithm","display_name":"Robust Train Timetabling Problem: Mathematical Model and Branch and Bound Algorithm","publication_year":2011,"publication_date":"2011-10-26","ids":{"openalex":"https://openalex.org/W2002520482","doi":"https://doi.org/10.1109/tits.2011.2169961","mag":"2002520482"},"language":"en","primary_location":{"id":"doi:10.1109/tits.2011.2169961","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tits.2011.2169961","pdf_url":null,"source":{"id":"https://openalex.org/S144771191","display_name":"IEEE Transactions on Intelligent Transportation Systems","issn_l":"1524-9050","issn":["1524-9050","1558-0016"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319808","host_organization_name":"Institute of Electrical and Electronics Engineers","host_organization_lineage":["https://openalex.org/P4310319808"],"host_organization_lineage_names":["Institute of Electrical and Electronics Engineers"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"IEEE Transactions on Intelligent Transportation Systems","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/A5041851258","display_name":"Mohammad Ali Shafia","orcid":"https://orcid.org/0000-0001-7674-4338"},"institutions":[{"id":"https://openalex.org/I67009956","display_name":"Iran University of Science and Technology","ror":"https://ror.org/01jw2p796","country_code":"IR","type":"education","lineage":["https://openalex.org/I67009956"]}],"countries":["IR"],"is_corresponding":true,"raw_author_name":"Mohammad Ali Shafia","raw_affiliation_strings":["Industrial Technology Division, Industrial Engineering Department, Iran University of Science and Technology, Tehran, Iran","Ind. Eng. Dept., Iran Univ. of Sci. & Technol., Tehran, Iran"],"affiliations":[{"raw_affiliation_string":"Industrial Technology Division, Industrial Engineering Department, Iran University of Science and Technology, Tehran, Iran","institution_ids":["https://openalex.org/I67009956"]},{"raw_affiliation_string":"Ind. Eng. Dept., Iran Univ. of Sci. & Technol., Tehran, Iran","institution_ids":["https://openalex.org/I67009956"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5049190893","display_name":"Mohsen Pourseyed Aghaee","orcid":"https://orcid.org/0000-0003-4290-3841"},"institutions":[{"id":"https://openalex.org/I67009956","display_name":"Iran University of Science and Technology","ror":"https://ror.org/01jw2p796","country_code":"IR","type":"education","lineage":["https://openalex.org/I67009956"]}],"countries":["IR"],"is_corresponding":false,"raw_author_name":"Mohsen Pourseyed Aghaee","raw_affiliation_strings":["Railway Department, Iran University of Science and Technology, Tehran, Iran"],"affiliations":[{"raw_affiliation_string":"Railway Department, Iran University of Science and Technology, Tehran, Iran","institution_ids":["https://openalex.org/I67009956"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5054891554","display_name":"Seyed Jafar Sadjadi","orcid":"https://orcid.org/0000-0002-9069-5453"},"institutions":[{"id":"https://openalex.org/I67009956","display_name":"Iran University of Science and Technology","ror":"https://ror.org/01jw2p796","country_code":"IR","type":"education","lineage":["https://openalex.org/I67009956"]}],"countries":["IR"],"is_corresponding":false,"raw_author_name":"Seyed Jafar Sadjadi","raw_affiliation_strings":["Industrial Department, Iran University of Science and Technology, Tehran, Iran","Ind. Dept., Iran Univ. of Sci. & Technol., Tehran, Iran"],"affiliations":[{"raw_affiliation_string":"Industrial Department, Iran University of Science and Technology, Tehran, Iran","institution_ids":["https://openalex.org/I67009956"]},{"raw_affiliation_string":"Ind. Dept., Iran Univ. of Sci. & Technol., Tehran, Iran","institution_ids":["https://openalex.org/I67009956"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5112898320","display_name":"Amin Jamili","orcid":null},"institutions":[{"id":"https://openalex.org/I67009956","display_name":"Iran University of Science and Technology","ror":"https://ror.org/01jw2p796","country_code":"IR","type":"education","lineage":["https://openalex.org/I67009956"]}],"countries":["IR"],"is_corresponding":false,"raw_author_name":"Amin Jamili","raw_affiliation_strings":["Industrial Department, Iran University of Science and Technology, Tehran, Iran","Ind. Dept., Iran Univ. of Sci. & Technol., Tehran, Iran"],"affiliations":[{"raw_affiliation_string":"Industrial Department, Iran University of Science and Technology, Tehran, Iran","institution_ids":["https://openalex.org/I67009956"]},{"raw_affiliation_string":"Ind. Dept., Iran Univ. of Sci. & Technol., Tehran, Iran","institution_ids":["https://openalex.org/I67009956"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":4,"corresponding_author_ids":["https://openalex.org/A5041851258"],"corresponding_institution_ids":["https://openalex.org/I67009956"],"apc_list":null,"apc_paid":null,"fwci":9.8225,"has_fulltext":false,"cited_by_count":77,"citation_normalized_percentile":{"value":0.9762419,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":94,"max":99},"biblio":{"volume":"13","issue":"1","first_page":"307","last_page":"317"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11568","display_name":"Railway Systems and Energy Efficiency","score":0.9997000098228455,"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/T11568","display_name":"Railway Systems and Energy Efficiency","score":0.9997000098228455,"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/T10698","display_name":"Transportation Planning and Optimization","score":0.9972000122070312,"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":0.9904999732971191,"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/branch-and-bound","display_name":"Branch and bound","score":0.6325597167015076},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.5958350300788879},{"id":"https://openalex.org/keywords/heuristic","display_name":"Heuristic","score":0.5880898237228394},{"id":"https://openalex.org/keywords/upper-and-lower-bounds","display_name":"Upper and lower bounds","score":0.5458739399909973},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.5420156717300415},{"id":"https://openalex.org/keywords/integer","display_name":"Integer (computer science)","score":0.5367532968521118},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.5196493864059448},{"id":"https://openalex.org/keywords/measure","display_name":"Measure (data warehouse)","score":0.5103163123130798},{"id":"https://openalex.org/keywords/software","display_name":"Software","score":0.4745693504810333},{"id":"https://openalex.org/keywords/stability","display_name":"Stability (learning theory)","score":0.4272746443748474},{"id":"https://openalex.org/keywords/scale","display_name":"Scale (ratio)","score":0.4171184301376343},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.27687227725982666},{"id":"https://openalex.org/keywords/data-mining","display_name":"Data mining","score":0.1081981360912323}],"concepts":[{"id":"https://openalex.org/C93693863","wikidata":"https://www.wikidata.org/wiki/Q897659","display_name":"Branch and bound","level":2,"score":0.6325597167015076},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.5958350300788879},{"id":"https://openalex.org/C173801870","wikidata":"https://www.wikidata.org/wiki/Q201413","display_name":"Heuristic","level":2,"score":0.5880898237228394},{"id":"https://openalex.org/C77553402","wikidata":"https://www.wikidata.org/wiki/Q13222579","display_name":"Upper and lower bounds","level":2,"score":0.5458739399909973},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.5420156717300415},{"id":"https://openalex.org/C97137487","wikidata":"https://www.wikidata.org/wiki/Q729138","display_name":"Integer (computer science)","level":2,"score":0.5367532968521118},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.5196493864059448},{"id":"https://openalex.org/C2780009758","wikidata":"https://www.wikidata.org/wiki/Q6804172","display_name":"Measure (data warehouse)","level":2,"score":0.5103163123130798},{"id":"https://openalex.org/C2777904410","wikidata":"https://www.wikidata.org/wiki/Q7397","display_name":"Software","level":2,"score":0.4745693504810333},{"id":"https://openalex.org/C112972136","wikidata":"https://www.wikidata.org/wiki/Q7595718","display_name":"Stability (learning theory)","level":2,"score":0.4272746443748474},{"id":"https://openalex.org/C2778755073","wikidata":"https://www.wikidata.org/wiki/Q10858537","display_name":"Scale (ratio)","level":2,"score":0.4171184301376343},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.27687227725982666},{"id":"https://openalex.org/C124101348","wikidata":"https://www.wikidata.org/wiki/Q172491","display_name":"Data mining","level":1,"score":0.1081981360912323},{"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/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.0},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"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/C119857082","wikidata":"https://www.wikidata.org/wiki/Q2539","display_name":"Machine learning","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1109/tits.2011.2169961","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tits.2011.2169961","pdf_url":null,"source":{"id":"https://openalex.org/S144771191","display_name":"IEEE Transactions on Intelligent Transportation Systems","issn_l":"1524-9050","issn":["1524-9050","1558-0016"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319808","host_organization_name":"Institute of Electrical and Electronics Engineers","host_organization_lineage":["https://openalex.org/P4310319808"],"host_organization_lineage_names":["Institute of Electrical and Electronics Engineers"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"IEEE Transactions on Intelligent Transportation Systems","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[{"score":0.5,"id":"https://metadata.un.org/sdg/9","display_name":"Industry, innovation and infrastructure"}],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":35,"referenced_works":["https://openalex.org/W1484713270","https://openalex.org/W1663385755","https://openalex.org/W1827600673","https://openalex.org/W1977010611","https://openalex.org/W1983181479","https://openalex.org/W1983597930","https://openalex.org/W1990275757","https://openalex.org/W1995285162","https://openalex.org/W2002916127","https://openalex.org/W2003777645","https://openalex.org/W2031545009","https://openalex.org/W2033525034","https://openalex.org/W2033916191","https://openalex.org/W2048679451","https://openalex.org/W2051402648","https://openalex.org/W2057022383","https://openalex.org/W2057411721","https://openalex.org/W2084575717","https://openalex.org/W2088260265","https://openalex.org/W2089105401","https://openalex.org/W2094138214","https://openalex.org/W2099701496","https://openalex.org/W2101331319","https://openalex.org/W2113245304","https://openalex.org/W2113725413","https://openalex.org/W2116009168","https://openalex.org/W2118578357","https://openalex.org/W2133392222","https://openalex.org/W2144382499","https://openalex.org/W2153835920","https://openalex.org/W2155162516","https://openalex.org/W2157204667","https://openalex.org/W2164521075","https://openalex.org/W2604096579","https://openalex.org/W2913566234"],"related_works":["https://openalex.org/W4255837520","https://openalex.org/W2387011115","https://openalex.org/W4234808182","https://openalex.org/W4255628145","https://openalex.org/W2382043075","https://openalex.org/W2389899617","https://openalex.org/W1591098987","https://openalex.org/W1931020284","https://openalex.org/W4319942994","https://openalex.org/W2182290077"],"abstract_inverted_index":{"This":[0],"paper":[1],"illustrates":[2],"the":[3,30,51,67,72,89,92,101,119,141],"results":[4,102,116],"of":[5,29,74,80,91,130,154],"an":[6],"investigation":[7],"into":[8],"developing":[9],"a":[10,16,26,40,110,127,147,151],"new":[11,41,111],"robust":[12,27],"train-timetabling":[13],"problem":[14],"in":[15,56,126,150],"single-track":[17],"railway":[18],"line.":[19],"The":[20,115],"proposed":[21],"model":[22,52],"is":[23,47],"formulated":[24],"as":[25,107,109,138],"form":[28],"mixed":[31],"integer":[32],"approach.":[33],"A":[34],"branch-and-bound":[35],"(B&B)":[36],"algorithm,":[37,46],"along":[38],"with":[39,103,133],"heuristic":[42],"beam":[43],"search":[44],"(BS)":[45],"presented":[48],"to":[49,65],"solve":[50],"for":[53],"large-scale":[54],"problems":[55],"reasonable":[57],"time.":[58,155],"We":[59,82],"also":[60],"propose":[61],"two":[62],"different":[63],"methods":[64],"measure":[66],"required":[68],"buffer":[69],"times":[70],"under":[71],"assumption":[73],"unknown":[75],"and":[76,88,94],"known":[77],"distribution":[78],"functions":[79],"disturbances.":[81],"have":[83],"generated":[84],"some":[85],"random":[86],"instances,":[87],"efficiency":[90],"B&B":[93,120],"BS":[95,142],"algorithms":[96],"are":[97],"demonstrated":[98],"by":[99],"comparing":[100],"common":[104,134],"software":[105,135],"packages":[106,136],"well":[108],"lower":[112],"bound":[113],"method.":[114],"demonstrate":[117],"that":[118],"algorithm":[121,143],"can":[122,144],"find":[123,146],"optimum":[124],"solutions":[125],"shorter":[128],"amount":[129,153],"time":[131],"compared":[132],"such":[137],"Lingo.":[139],"Moreover,":[140],"effectively":[145],"near-optimum":[148],"solution":[149],"rational":[152]},"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2024,"cited_by_count":5},{"year":2023,"cited_by_count":3},{"year":2022,"cited_by_count":6},{"year":2021,"cited_by_count":5},{"year":2020,"cited_by_count":5},{"year":2019,"cited_by_count":4},{"year":2018,"cited_by_count":6},{"year":2017,"cited_by_count":7},{"year":2016,"cited_by_count":12},{"year":2015,"cited_by_count":9},{"year":2014,"cited_by_count":3},{"year":2013,"cited_by_count":7},{"year":2012,"cited_by_count":2}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}
