{"id":"https://openalex.org/W1985873373","doi":"https://doi.org/10.1002/net.3230190403","title":"A continuous\u2010time network simplex algorithm","display_name":"A continuous\u2010time network simplex algorithm","publication_year":1989,"publication_date":"1989-07-01","ids":{"openalex":"https://openalex.org/W1985873373","doi":"https://doi.org/10.1002/net.3230190403","mag":"1985873373"},"language":"en","primary_location":{"id":"doi:10.1002/net.3230190403","is_oa":false,"landing_page_url":"https://doi.org/10.1002/net.3230190403","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/A5035254527","display_name":"Edward Anderson","orcid":"https://orcid.org/0000-0002-6375-4067"},"institutions":[{"id":"https://openalex.org/I241749","display_name":"University of Cambridge","ror":"https://ror.org/013meh722","country_code":"GB","type":"education","lineage":["https://openalex.org/I241749"]},{"id":"https://openalex.org/I4210096386","display_name":"Bridge University","ror":"https://ror.org/00cbm0437","country_code":"SS","type":"education","lineage":["https://openalex.org/I4210096386"]}],"countries":["GB","SS"],"is_corresponding":true,"raw_author_name":"E. J. Anderson","raw_affiliation_strings":["Cambridge University Engineering Department, Cambridge, England","Cambridge University Engineering Dept., Cambridge, England#TAB#"],"affiliations":[{"raw_affiliation_string":"Cambridge University Engineering Department, Cambridge, England","institution_ids":["https://openalex.org/I4210096386","https://openalex.org/I241749"]},{"raw_affiliation_string":"Cambridge University Engineering Dept., Cambridge, England#TAB#","institution_ids":["https://openalex.org/I241749"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5083158688","display_name":"Andy Philpott","orcid":"https://orcid.org/0000-0002-7094-3405"},"institutions":[{"id":"https://openalex.org/I241749","display_name":"University of Cambridge","ror":"https://ror.org/013meh722","country_code":"GB","type":"education","lineage":["https://openalex.org/I241749"]},{"id":"https://openalex.org/I4210096386","display_name":"Bridge University","ror":"https://ror.org/00cbm0437","country_code":"SS","type":"education","lineage":["https://openalex.org/I4210096386"]}],"countries":["GB","SS"],"is_corresponding":false,"raw_author_name":"A. B. Philpott","raw_affiliation_strings":["Cambridge University Engineering Department, Cambridge, England","Cambridge University Engineering Dept., Cambridge, England#TAB#"],"affiliations":[{"raw_affiliation_string":"Cambridge University Engineering Department, Cambridge, England","institution_ids":["https://openalex.org/I4210096386","https://openalex.org/I241749"]},{"raw_affiliation_string":"Cambridge University Engineering Dept., Cambridge, England#TAB#","institution_ids":["https://openalex.org/I241749"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5035254527"],"corresponding_institution_ids":["https://openalex.org/I241749","https://openalex.org/I4210096386"],"apc_list":{"value":3400,"currency":"USD","value_usd":3400},"apc_paid":null,"fwci":3.158,"has_fulltext":false,"cited_by_count":50,"citation_normalized_percentile":{"value":0.90128558,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":89,"max":98},"biblio":{"volume":"19","issue":"4","first_page":"395","last_page":"425"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10698","display_name":"Transportation Planning and Optimization","score":0.9940999746322632,"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":0.9940999746322632,"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/T10524","display_name":"Traffic control and management","score":0.9882000088691711,"subfield":{"id":"https://openalex.org/subfields/2207","display_name":"Control and Systems 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/T10374","display_name":"Advanced Graph Theory Research","score":0.9690999984741211,"subfield":{"id":"https://openalex.org/subfields/1703","display_name":"Computational Theory and Mathematics"},"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/minimum-cost-flow-problem","display_name":"Minimum-cost flow problem","score":0.8722267150878906},{"id":"https://openalex.org/keywords/flow-network","display_name":"Flow network","score":0.7329208850860596},{"id":"https://openalex.org/keywords/simplex-algorithm","display_name":"Simplex algorithm","score":0.6658501625061035},{"id":"https://openalex.org/keywords/maximum-flow-problem","display_name":"Maximum flow problem","score":0.6491944789886475},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.6415302753448486},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.5874476432800293},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.5637990236282349},{"id":"https://openalex.org/keywords/out-of-kilter-algorithm","display_name":"Out-of-kilter algorithm","score":0.5575987696647644},{"id":"https://openalex.org/keywords/simplex","display_name":"Simplex","score":0.550885796546936},{"id":"https://openalex.org/keywords/node","display_name":"Node (physics)","score":0.5262911915779114},{"id":"https://openalex.org/keywords/linear-programming","display_name":"Linear programming","score":0.5175982713699341},{"id":"https://openalex.org/keywords/multi-commodity-flow-problem","display_name":"Multi-commodity flow problem","score":0.5065773725509644},{"id":"https://openalex.org/keywords/time-complexity","display_name":"Time complexity","score":0.48164406418800354},{"id":"https://openalex.org/keywords/flow","display_name":"Flow (mathematics)","score":0.47594332695007324},{"id":"https://openalex.org/keywords/constraint","display_name":"Constraint (computer-aided design)","score":0.450281023979187},{"id":"https://openalex.org/keywords/upper-and-lower-bounds","display_name":"Upper and lower bounds","score":0.4215674102306366},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.29834622144699097},{"id":"https://openalex.org/keywords/theoretical-computer-science","display_name":"Theoretical computer science","score":0.14447268843650818},{"id":"https://openalex.org/keywords/graph","display_name":"Graph","score":0.12641167640686035},{"id":"https://openalex.org/keywords/dijkstras-algorithm","display_name":"Dijkstra's algorithm","score":0.09013459086418152},{"id":"https://openalex.org/keywords/shortest-path-problem","display_name":"Shortest path problem","score":0.0810914933681488},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.06326594948768616}],"concepts":[{"id":"https://openalex.org/C99545648","wikidata":"https://www.wikidata.org/wiki/Q2897180","display_name":"Minimum-cost flow problem","level":3,"score":0.8722267150878906},{"id":"https://openalex.org/C114809511","wikidata":"https://www.wikidata.org/wiki/Q1412924","display_name":"Flow network","level":2,"score":0.7329208850860596},{"id":"https://openalex.org/C144521790","wikidata":"https://www.wikidata.org/wiki/Q134164","display_name":"Simplex algorithm","level":3,"score":0.6658501625061035},{"id":"https://openalex.org/C157469704","wikidata":"https://www.wikidata.org/wiki/Q2585642","display_name":"Maximum flow problem","level":2,"score":0.6491944789886475},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.6415302753448486},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.5874476432800293},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.5637990236282349},{"id":"https://openalex.org/C133824558","wikidata":"https://www.wikidata.org/wiki/Q16893660","display_name":"Out-of-kilter algorithm","level":5,"score":0.5575987696647644},{"id":"https://openalex.org/C62438384","wikidata":"https://www.wikidata.org/wiki/Q331350","display_name":"Simplex","level":2,"score":0.550885796546936},{"id":"https://openalex.org/C62611344","wikidata":"https://www.wikidata.org/wiki/Q1062658","display_name":"Node (physics)","level":2,"score":0.5262911915779114},{"id":"https://openalex.org/C41045048","wikidata":"https://www.wikidata.org/wiki/Q202843","display_name":"Linear programming","level":2,"score":0.5175982713699341},{"id":"https://openalex.org/C170334043","wikidata":"https://www.wikidata.org/wiki/Q6934437","display_name":"Multi-commodity flow problem","level":3,"score":0.5065773725509644},{"id":"https://openalex.org/C311688","wikidata":"https://www.wikidata.org/wiki/Q2393193","display_name":"Time complexity","level":2,"score":0.48164406418800354},{"id":"https://openalex.org/C38349280","wikidata":"https://www.wikidata.org/wiki/Q1434290","display_name":"Flow (mathematics)","level":2,"score":0.47594332695007324},{"id":"https://openalex.org/C2776036281","wikidata":"https://www.wikidata.org/wiki/Q48769818","display_name":"Constraint (computer-aided design)","level":2,"score":0.450281023979187},{"id":"https://openalex.org/C77553402","wikidata":"https://www.wikidata.org/wiki/Q13222579","display_name":"Upper and lower bounds","level":2,"score":0.4215674102306366},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.29834622144699097},{"id":"https://openalex.org/C80444323","wikidata":"https://www.wikidata.org/wiki/Q2878974","display_name":"Theoretical computer science","level":1,"score":0.14447268843650818},{"id":"https://openalex.org/C132525143","wikidata":"https://www.wikidata.org/wiki/Q141488","display_name":"Graph","level":2,"score":0.12641167640686035},{"id":"https://openalex.org/C173870130","wikidata":"https://www.wikidata.org/wiki/Q8548","display_name":"Dijkstra's algorithm","level":4,"score":0.09013459086418152},{"id":"https://openalex.org/C22590252","wikidata":"https://www.wikidata.org/wiki/Q1058754","display_name":"Shortest path problem","level":3,"score":0.0810914933681488},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.06326594948768616},{"id":"https://openalex.org/C127413603","wikidata":"https://www.wikidata.org/wiki/Q11023","display_name":"Engineering","level":0,"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/C66938386","wikidata":"https://www.wikidata.org/wiki/Q633538","display_name":"Structural engineering","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}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1002/net.3230190403","is_oa":false,"landing_page_url":"https://doi.org/10.1002/net.3230190403","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/15","display_name":"Life in Land","score":0.6299999952316284}],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":5,"referenced_works":["https://openalex.org/W192774557","https://openalex.org/W2021070553","https://openalex.org/W2034421572","https://openalex.org/W2083050082","https://openalex.org/W2088045969"],"related_works":["https://openalex.org/W2098682899","https://openalex.org/W2080904092","https://openalex.org/W3035974271","https://openalex.org/W4206915070","https://openalex.org/W3161514703","https://openalex.org/W3141113327","https://openalex.org/W2625547693","https://openalex.org/W2531764854","https://openalex.org/W2355612523","https://openalex.org/W2051329268"],"abstract_inverted_index":{"Abstract":[0],"Given":[1],"a":[2,28,70,84],"network":[3,18,71,89],"having":[4],"costs":[5],"and":[6,34,51],"upper":[7],"bound":[8],"constraints":[9],"on":[10],"the":[11,16,36,40,43,56,59,62,88],"flows":[12,25],"in":[13],"its":[14],"arcs,":[15],"minimum\u2010cost":[17],"flow":[19],"problem":[20,63],"is":[21,53,83],"that":[22],"of":[23,39,49,58,87],"finding":[24],"which":[26],"satisfy":[27],"flow\u2010conservation":[29],"constraint":[30],"at":[31,55],"each":[32],"node":[33],"minimize":[35],"total":[37],"cost":[38],"flow.":[41],"If":[42],"arc":[44],"capacities":[45],"vary":[46],"as":[47],"functions":[48],"time,":[50],"storage":[52],"permitted":[54],"nodes":[57],"network,":[60],"then":[61],"becomes":[64],"an":[65,75],"infinitedimensional":[66],"linear":[67],"program":[68],"with":[69],"structure.":[72],"We":[73],"describe":[74],"algorithm":[76,82],"to":[77],"solve":[78],"such":[79],"problems.":[80],"This":[81],"continuuous\u2010time":[85],"version":[86],"simplex":[90],"algorithm.":[91]},"counts_by_year":[{"year":2024,"cited_by_count":1},{"year":2022,"cited_by_count":1},{"year":2021,"cited_by_count":3},{"year":2020,"cited_by_count":1},{"year":2018,"cited_by_count":2},{"year":2017,"cited_by_count":1},{"year":2015,"cited_by_count":1},{"year":2014,"cited_by_count":5},{"year":2013,"cited_by_count":1},{"year":2012,"cited_by_count":1}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}