{"id":"https://openalex.org/W2032027865","doi":"https://doi.org/10.1002/net.3230210606","title":"Approximate solutions of capacitated fixed\u2010charge minimum cost network flow problems","display_name":"Approximate solutions of capacitated fixed\u2010charge minimum cost network flow problems","publication_year":1991,"publication_date":"1991-10-01","ids":{"openalex":"https://openalex.org/W2032027865","doi":"https://doi.org/10.1002/net.3230210606","mag":"2032027865"},"language":"en","primary_location":{"id":"doi:10.1002/net.3230210606","is_oa":false,"landing_page_url":"https://doi.org/10.1002/net.3230210606","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/A5111906984","display_name":"Do Ba Khang","orcid":null},"institutions":[{"id":"https://openalex.org/I38538140","display_name":"Asian Institute of Technology","ror":"https://ror.org/0403qcr87","country_code":"TH","type":"education","lineage":["https://openalex.org/I38538140"]}],"countries":["TH"],"is_corresponding":true,"raw_author_name":"Do Ba Khang","raw_affiliation_strings":["Division of Industrial Engineering and Management, Asian Institute of Technology, P.O. Box 2754, Bangkok, 10501 Thailand"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Division of Industrial Engineering and Management, Asian Institute of Technology, P.O. Box 2754, Bangkok, 10501 Thailand","institution_ids":["https://openalex.org/I38538140"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5022679054","display_name":"Okitsugu Fujiwara","orcid":null},"institutions":[{"id":"https://openalex.org/I38538140","display_name":"Asian Institute of Technology","ror":"https://ror.org/0403qcr87","country_code":"TH","type":"education","lineage":["https://openalex.org/I38538140"]}],"countries":["TH"],"is_corresponding":false,"raw_author_name":"Okitsugu Fujiwara","raw_affiliation_strings":["Division of Industrial Engineering and Management, Asian Institute of Technology, P.O. Box 2754, Bangkok, 10501 Thailand"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Division of Industrial Engineering and Management, Asian Institute of Technology, P.O. Box 2754, Bangkok, 10501 Thailand","institution_ids":["https://openalex.org/I38538140"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5111906984"],"corresponding_institution_ids":["https://openalex.org/I38538140"],"apc_list":{"value":3400,"currency":"USD","value_usd":3400},"apc_paid":null,"fwci":0.771,"has_fulltext":false,"cited_by_count":29,"citation_normalized_percentile":{"value":0.73630354,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":96},"biblio":{"volume":"21","issue":"6","first_page":"689","last_page":"704"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T12709","display_name":"Optimization and Mathematical Programming","score":0.9934999942779541,"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"}},"topics":[{"id":"https://openalex.org/T12709","display_name":"Optimization and Mathematical Programming","score":0.9934999942779541,"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/T12546","display_name":"Smart Parking Systems Research","score":0.9800000190734863,"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"}},{"id":"https://openalex.org/T10698","display_name":"Transportation Planning and Optimization","score":0.9589999914169312,"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/subgradient-method","display_name":"Subgradient method","score":0.7704123258590698},{"id":"https://openalex.org/keywords/fixed-charge","display_name":"Fixed charge","score":0.7230817079544067},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.6602880954742432},{"id":"https://openalex.org/keywords/lagrange-multiplier","display_name":"Lagrange multiplier","score":0.6218345165252686},{"id":"https://openalex.org/keywords/upper-and-lower-bounds","display_name":"Upper and lower bounds","score":0.6086576581001282},{"id":"https://openalex.org/keywords/relaxation","display_name":"Relaxation (psychology)","score":0.5697932839393616},{"id":"https://openalex.org/keywords/heuristic","display_name":"Heuristic","score":0.5355702638626099},{"id":"https://openalex.org/keywords/linear-programming-relaxation","display_name":"Linear programming relaxation","score":0.5189356803894043},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.49437665939331055},{"id":"https://openalex.org/keywords/flow-network","display_name":"Flow network","score":0.48834750056266785},{"id":"https://openalex.org/keywords/flow","display_name":"Flow (mathematics)","score":0.4637971520423889},{"id":"https://openalex.org/keywords/simple","display_name":"Simple (philosophy)","score":0.4484442174434662},{"id":"https://openalex.org/keywords/minimum-cost-flow-problem","display_name":"Minimum-cost flow problem","score":0.4448113441467285},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.38641178607940674},{"id":"https://openalex.org/keywords/linear-programming","display_name":"Linear programming","score":0.2820301055908203}],"concepts":[{"id":"https://openalex.org/C158968445","wikidata":"https://www.wikidata.org/wiki/Q7631150","display_name":"Subgradient method","level":2,"score":0.7704123258590698},{"id":"https://openalex.org/C2984553159","wikidata":"https://www.wikidata.org/wiki/Q13579421","display_name":"Fixed charge","level":2,"score":0.7230817079544067},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.6602880954742432},{"id":"https://openalex.org/C73684929","wikidata":"https://www.wikidata.org/wiki/Q598870","display_name":"Lagrange multiplier","level":2,"score":0.6218345165252686},{"id":"https://openalex.org/C77553402","wikidata":"https://www.wikidata.org/wiki/Q13222579","display_name":"Upper and lower bounds","level":2,"score":0.6086576581001282},{"id":"https://openalex.org/C2776029896","wikidata":"https://www.wikidata.org/wiki/Q3935810","display_name":"Relaxation (psychology)","level":2,"score":0.5697932839393616},{"id":"https://openalex.org/C173801870","wikidata":"https://www.wikidata.org/wiki/Q201413","display_name":"Heuristic","level":2,"score":0.5355702638626099},{"id":"https://openalex.org/C25360446","wikidata":"https://www.wikidata.org/wiki/Q1512771","display_name":"Linear programming relaxation","level":3,"score":0.5189356803894043},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.49437665939331055},{"id":"https://openalex.org/C114809511","wikidata":"https://www.wikidata.org/wiki/Q1412924","display_name":"Flow network","level":2,"score":0.48834750056266785},{"id":"https://openalex.org/C38349280","wikidata":"https://www.wikidata.org/wiki/Q1434290","display_name":"Flow (mathematics)","level":2,"score":0.4637971520423889},{"id":"https://openalex.org/C2780586882","wikidata":"https://www.wikidata.org/wiki/Q7520643","display_name":"Simple (philosophy)","level":2,"score":0.4484442174434662},{"id":"https://openalex.org/C99545648","wikidata":"https://www.wikidata.org/wiki/Q2897180","display_name":"Minimum-cost flow problem","level":3,"score":0.4448113441467285},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.38641178607940674},{"id":"https://openalex.org/C41045048","wikidata":"https://www.wikidata.org/wiki/Q202843","display_name":"Linear programming","level":2,"score":0.2820301055908203},{"id":"https://openalex.org/C41999313","wikidata":"https://www.wikidata.org/wiki/Q489328","display_name":"Molecular physics","level":1,"score":0.0},{"id":"https://openalex.org/C111472728","wikidata":"https://www.wikidata.org/wiki/Q9471","display_name":"Epistemology","level":1,"score":0.0},{"id":"https://openalex.org/C77805123","wikidata":"https://www.wikidata.org/wiki/Q161272","display_name":"Social psychology","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/C15744967","wikidata":"https://www.wikidata.org/wiki/Q9418","display_name":"Psychology","level":0,"score":0.0},{"id":"https://openalex.org/C138885662","wikidata":"https://www.wikidata.org/wiki/Q5891","display_name":"Philosophy","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/C185592680","wikidata":"https://www.wikidata.org/wiki/Q2329","display_name":"Chemistry","level":0,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1002/net.3230210606","is_oa":false,"landing_page_url":"https://doi.org/10.1002/net.3230210606","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":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":26,"referenced_works":["https://openalex.org/W223605966","https://openalex.org/W1576264907","https://openalex.org/W1973312272","https://openalex.org/W1996431511","https://openalex.org/W2002111665","https://openalex.org/W2016218947","https://openalex.org/W2017697298","https://openalex.org/W2033249500","https://openalex.org/W2038676869","https://openalex.org/W2041603754","https://openalex.org/W2053723217","https://openalex.org/W2053913299","https://openalex.org/W2081833829","https://openalex.org/W2096586036","https://openalex.org/W2149342630","https://openalex.org/W2150855695","https://openalex.org/W2151525839","https://openalex.org/W2157924277","https://openalex.org/W2160408584","https://openalex.org/W2171985270","https://openalex.org/W2172121397","https://openalex.org/W2505968561","https://openalex.org/W2800875754","https://openalex.org/W4236384091","https://openalex.org/W4247600029","https://openalex.org/W6986697800"],"related_works":["https://openalex.org/W3141113327","https://openalex.org/W2080904092","https://openalex.org/W3035974271","https://openalex.org/W3161514703","https://openalex.org/W3207627914","https://openalex.org/W2270959725","https://openalex.org/W2151525839","https://openalex.org/W648253840","https://openalex.org/W2051329268","https://openalex.org/W2172105006"],"abstract_inverted_index":{"Abstract":[0],"This":[1],"article":[2,64],"proposes":[3],"two":[4],"approximate":[5,77],"methods":[6],"to":[7,27,38,50,72,85],"solve":[8],"capacitated,":[9],"single\u2010commodity":[10],"and":[11,69,76],"fixed\u2010charge":[12],"network":[13],"flow":[14],"problems.":[15],"First,":[16],"relaxed":[17],"problems":[18],"obtained":[19],"by":[20,54],"the":[21,39,56,63,86],"Lagrange":[22,57],"relaxation":[23],"method":[24],"are":[25],"shown":[26],"form":[28],"a":[29,35,66,74],"minimum":[30],"spanning":[31],"tree":[32],"problem,":[33],"yielding":[34],"lower":[36],"bound":[37,53,84],"original":[40,87],"problem.":[41,88],"The":[42,59],"subgradient":[43],"optimization":[44],"technique":[45],"can":[46],"be":[47],"then":[48],"applied":[49],"improve":[51],"this":[52],"updating":[55],"multipliers.":[58],"second":[60],"part":[61],"of":[62],"presents":[65],"new,":[67],"simple,":[68],"efficient":[70],"heuristic":[71],"find":[73],"feasible":[75],"solution":[78],"that":[79],"is":[80],"also":[81],"an":[82],"upper":[83]},"counts_by_year":[{"year":2025,"cited_by_count":2},{"year":2021,"cited_by_count":2},{"year":2018,"cited_by_count":1},{"year":2015,"cited_by_count":1},{"year":2014,"cited_by_count":1}],"updated_date":"2026-05-21T09:19:25.381259","created_date":"2025-10-10T00:00:00"}
