{"id":"https://openalex.org/W1501025159","doi":"https://doi.org/10.1023/a:1013867331662","title":"D.C. programming approach for multicommodity network optimization problems with step increasing cost functions","display_name":"D.C. programming approach for multicommodity network optimization problems with step increasing cost functions","publication_year":2002,"publication_date":"2002-01-01","ids":{"openalex":"https://openalex.org/W1501025159","doi":"https://doi.org/10.1023/a:1013867331662","mag":"1501025159"},"language":"en","primary_location":{"id":"doi:10.1023/a:1013867331662","is_oa":false,"landing_page_url":"https://doi.org/10.1023/a:1013867331662","pdf_url":null,"source":{"id":"https://openalex.org/S115925768","display_name":"Journal of Global Optimization","issn_l":"0925-5001","issn":["0925-5001","1573-2916"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Journal of Global Optimization","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/A5042936176","display_name":"Hoai An Le Thi","orcid":"https://orcid.org/0000-0002-2239-2100"},"institutions":[{"id":"https://openalex.org/I4210145753","display_name":"Institute for Applied Science","ror":"https://ror.org/03yy8am44","country_code":"GB","type":"nonprofit","lineage":["https://openalex.org/I4210145753"]},{"id":"https://openalex.org/I4210089412","display_name":"Applied Optimization (United States)","ror":"https://ror.org/004b0n253","country_code":"US","type":"company","lineage":["https://openalex.org/I4210089412"]},{"id":"https://openalex.org/I196454796","display_name":"Institut National des Sciences Appliqu\u00e9es de Toulouse","ror":"https://ror.org/01h8pf755","country_code":"FR","type":"education","lineage":["https://openalex.org/I196454796","https://openalex.org/I4405258862"]}],"countries":["FR","GB","US"],"is_corresponding":true,"raw_author_name":"Le Thi Hoai An","raw_affiliation_strings":["Modelling, Applied Optimization and Operations Research Group, Laboratory of Mathematics, National Institute for Applied Sciences-Rouen, BP 8, F 76 131, Mont Saint Aignan, France","Modelling, Applied Optimization and Operations Research Group, Laboratory of Mathematics, National Institute for Applied Sciences-Rouen, BP 8, F 76 131 Mont Saint Aignan Cedex, FranceE-mail: #TAB#"],"affiliations":[{"raw_affiliation_string":"Modelling, Applied Optimization and Operations Research Group, Laboratory of Mathematics, National Institute for Applied Sciences-Rouen, BP 8, F 76 131, Mont Saint Aignan, France","institution_ids":["https://openalex.org/I4210145753"]},{"raw_affiliation_string":"Modelling, Applied Optimization and Operations Research Group, Laboratory of Mathematics, National Institute for Applied Sciences-Rouen, BP 8, F 76 131 Mont Saint Aignan Cedex, FranceE-mail: #TAB#","institution_ids":["https://openalex.org/I4210145753","https://openalex.org/I196454796","https://openalex.org/I4210089412"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5110051598","display_name":"Pham Dinh Tao","orcid":null},"institutions":[{"id":"https://openalex.org/I196454796","display_name":"Institut National des Sciences Appliqu\u00e9es de Toulouse","ror":"https://ror.org/01h8pf755","country_code":"FR","type":"education","lineage":["https://openalex.org/I196454796","https://openalex.org/I4405258862"]},{"id":"https://openalex.org/I4210089412","display_name":"Applied Optimization (United States)","ror":"https://ror.org/004b0n253","country_code":"US","type":"company","lineage":["https://openalex.org/I4210089412"]},{"id":"https://openalex.org/I4210145753","display_name":"Institute for Applied Science","ror":"https://ror.org/03yy8am44","country_code":"GB","type":"nonprofit","lineage":["https://openalex.org/I4210145753"]}],"countries":["FR","GB","US"],"is_corresponding":false,"raw_author_name":"Pham Dinh Tao","raw_affiliation_strings":["Modelling, Applied Optimization and Operations Research Group, Laboratory of Mathematics, National Institute for Applied Sciences-Rouen, BP 8, F 76 131, Mont Saint Aignan, France","Modelling, Applied Optimization and Operations Research Group, Laboratory of Mathematics, National Institute for Applied Sciences-Rouen, BP 8, F 76 131 Mont Saint Aignan Cedex, FranceE-mail: #TAB#"],"affiliations":[{"raw_affiliation_string":"Modelling, Applied Optimization and Operations Research Group, Laboratory of Mathematics, National Institute for Applied Sciences-Rouen, BP 8, F 76 131, Mont Saint Aignan, France","institution_ids":["https://openalex.org/I4210145753"]},{"raw_affiliation_string":"Modelling, Applied Optimization and Operations Research Group, Laboratory of Mathematics, National Institute for Applied Sciences-Rouen, BP 8, F 76 131 Mont Saint Aignan Cedex, FranceE-mail: #TAB#","institution_ids":["https://openalex.org/I4210145753","https://openalex.org/I196454796","https://openalex.org/I4210089412"]}]}],"institutions":[],"countries_distinct_count":3,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5042936176"],"corresponding_institution_ids":["https://openalex.org/I196454796","https://openalex.org/I4210089412","https://openalex.org/I4210145753"],"apc_list":{"value":2190,"currency":"EUR","value_usd":2780},"apc_paid":null,"fwci":0.8226,"has_fulltext":false,"cited_by_count":15,"citation_normalized_percentile":{"value":0.71101124,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":94},"biblio":{"volume":"22","issue":"1-4","first_page":"205","last_page":"232"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10567","display_name":"Vehicle Routing Optimization Methods","score":0.9991999864578247,"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":0.9991999864578247,"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/T11502","display_name":"Facility Location and Emergency Management","score":0.9944000244140625,"subfield":{"id":"https://openalex.org/subfields/1407","display_name":"Organizational Behavior and Human Resource Management"},"field":{"id":"https://openalex.org/fields/14","display_name":"Business, Management and Accounting"},"domain":{"id":"https://openalex.org/domains/2","display_name":"Social Sciences"}},{"id":"https://openalex.org/T12546","display_name":"Smart Parking Systems Research","score":0.993399977684021,"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/mathematics","display_name":"Mathematics","score":0.8317583799362183},{"id":"https://openalex.org/keywords/simple","display_name":"Simple (philosophy)","score":0.5811161994934082},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.5772421360015869},{"id":"https://openalex.org/keywords/upper-and-lower-bounds","display_name":"Upper and lower bounds","score":0.5707636475563049},{"id":"https://openalex.org/keywords/linear-programming","display_name":"Linear programming","score":0.5532455444335938},{"id":"https://openalex.org/keywords/function","display_name":"Function (biology)","score":0.5127040147781372},{"id":"https://openalex.org/keywords/convex-optimization","display_name":"Convex optimization","score":0.4839189648628235},{"id":"https://openalex.org/keywords/optimization-problem","display_name":"Optimization problem","score":0.47488540410995483},{"id":"https://openalex.org/keywords/regular-polygon","display_name":"Regular polygon","score":0.4560534656047821},{"id":"https://openalex.org/keywords/convex-function","display_name":"Convex function","score":0.4156584143638611},{"id":"https://openalex.org/keywords/affine-transformation","display_name":"Affine transformation","score":0.4124312400817871},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.3275679051876068},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.09721028804779053}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8317583799362183},{"id":"https://openalex.org/C2780586882","wikidata":"https://www.wikidata.org/wiki/Q7520643","display_name":"Simple (philosophy)","level":2,"score":0.5811161994934082},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.5772421360015869},{"id":"https://openalex.org/C77553402","wikidata":"https://www.wikidata.org/wiki/Q13222579","display_name":"Upper and lower bounds","level":2,"score":0.5707636475563049},{"id":"https://openalex.org/C41045048","wikidata":"https://www.wikidata.org/wiki/Q202843","display_name":"Linear programming","level":2,"score":0.5532455444335938},{"id":"https://openalex.org/C14036430","wikidata":"https://www.wikidata.org/wiki/Q3736076","display_name":"Function (biology)","level":2,"score":0.5127040147781372},{"id":"https://openalex.org/C157972887","wikidata":"https://www.wikidata.org/wiki/Q463359","display_name":"Convex optimization","level":3,"score":0.4839189648628235},{"id":"https://openalex.org/C137836250","wikidata":"https://www.wikidata.org/wiki/Q984063","display_name":"Optimization problem","level":2,"score":0.47488540410995483},{"id":"https://openalex.org/C112680207","wikidata":"https://www.wikidata.org/wiki/Q714886","display_name":"Regular polygon","level":2,"score":0.4560534656047821},{"id":"https://openalex.org/C145446738","wikidata":"https://www.wikidata.org/wiki/Q319913","display_name":"Convex function","level":3,"score":0.4156584143638611},{"id":"https://openalex.org/C92757383","wikidata":"https://www.wikidata.org/wiki/Q382497","display_name":"Affine transformation","level":2,"score":0.4124312400817871},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.3275679051876068},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.09721028804779053},{"id":"https://openalex.org/C86803240","wikidata":"https://www.wikidata.org/wiki/Q420","display_name":"Biology","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/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","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/C78458016","wikidata":"https://www.wikidata.org/wiki/Q840400","display_name":"Evolutionary biology","level":1,"score":0.0},{"id":"https://openalex.org/C138885662","wikidata":"https://www.wikidata.org/wiki/Q5891","display_name":"Philosophy","level":0,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1023/a:1013867331662","is_oa":false,"landing_page_url":"https://doi.org/10.1023/a:1013867331662","pdf_url":null,"source":{"id":"https://openalex.org/S115925768","display_name":"Journal of Global Optimization","issn_l":"0925-5001","issn":["0925-5001","1573-2916"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Journal of Global Optimization","raw_type":"journal-article"},{"id":"pmh:oai:HAL:hal-01636771v1","is_oa":false,"landing_page_url":"https://hal.univ-lorraine.fr/hal-01636771","pdf_url":null,"source":{"id":"https://openalex.org/S4306402512","display_name":"HAL (Le Centre pour la Communication Scientifique Directe)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I1294671590","host_organization_name":"Centre National de la Recherche Scientifique","host_organization_lineage":["https://openalex.org/I1294671590"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Journal of Global Optimization, 2002, 22, pp.205 - 232. &#x27E8;10.1023/A:1013867331662&#x27E9;","raw_type":"Journal articles"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":37,"referenced_works":["https://openalex.org/W81972919","https://openalex.org/W202383464","https://openalex.org/W246680905","https://openalex.org/W390418894","https://openalex.org/W610675618","https://openalex.org/W625539078","https://openalex.org/W1513964715","https://openalex.org/W1553702074","https://openalex.org/W1564250817","https://openalex.org/W1589133845","https://openalex.org/W1974650454","https://openalex.org/W1977545325","https://openalex.org/W1986298157","https://openalex.org/W2002111665","https://openalex.org/W2016885155","https://openalex.org/W2021136283","https://openalex.org/W2022483727","https://openalex.org/W2023452967","https://openalex.org/W2030731960","https://openalex.org/W2038497950","https://openalex.org/W2051664786","https://openalex.org/W2052092601","https://openalex.org/W2063317370","https://openalex.org/W2090532016","https://openalex.org/W2104431850","https://openalex.org/W2111329184","https://openalex.org/W2115785179","https://openalex.org/W2144014315","https://openalex.org/W2149705873","https://openalex.org/W2155113352","https://openalex.org/W2301746362","https://openalex.org/W2585337112","https://openalex.org/W4249667877","https://openalex.org/W4299984265","https://openalex.org/W4300987062","https://openalex.org/W4379512177","https://openalex.org/W6619663078"],"related_works":["https://openalex.org/W2756132392","https://openalex.org/W2510140549","https://openalex.org/W2187449906","https://openalex.org/W4285101096","https://openalex.org/W4382725876","https://openalex.org/W2084892497","https://openalex.org/W2115614142","https://openalex.org/W4320477335","https://openalex.org/W1561889708","https://openalex.org/W2275184629"],"abstract_inverted_index":null,"counts_by_year":[{"year":2024,"cited_by_count":1},{"year":2020,"cited_by_count":1},{"year":2018,"cited_by_count":1},{"year":2017,"cited_by_count":1},{"year":2013,"cited_by_count":1}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2016-06-24T00:00:00"}
