{"id":"https://openalex.org/W7117464169","doi":"https://doi.org/10.1007/s10957-025-02890-3","title":"Approximating Split Delivery Path Routing Problems","display_name":"Approximating Split Delivery Path Routing Problems","publication_year":2025,"publication_date":"2025-12-29","ids":{"openalex":"https://openalex.org/W7117464169","doi":"https://doi.org/10.1007/s10957-025-02890-3"},"language":"en","primary_location":{"id":"doi:10.1007/s10957-025-02890-3","is_oa":false,"landing_page_url":"https://doi.org/10.1007/s10957-025-02890-3","pdf_url":null,"source":{"id":"https://openalex.org/S52430896","display_name":"Journal of Optimization Theory and Applications","issn_l":"0022-3239","issn":["0022-3239","1573-2878"],"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 Optimization Theory and Applications","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/A5121508084","display_name":"Jun Wu","orcid":null},"institutions":[{"id":"https://openalex.org/I277688954","display_name":"Universit\u00e9 Paris-Saclay","ror":"https://ror.org/03xjwb503","country_code":"FR","type":"education","lineage":["https://openalex.org/I277688954"]},{"id":"https://openalex.org/I4210107733","display_name":"Informatique, BioInformatique, Syst\u00e8mes Complexes","ror":"https://ror.org/01aqxgr98","country_code":"FR","type":"facility","lineage":["https://openalex.org/I277688954","https://openalex.org/I277688954","https://openalex.org/I4210107733","https://openalex.org/I88467170"]},{"id":"https://openalex.org/I87445476","display_name":"Xi'an Jiaotong University","ror":"https://ror.org/017zhmm22","country_code":"CN","type":"education","lineage":["https://openalex.org/I87445476"]}],"countries":["CN","FR"],"is_corresponding":false,"raw_author_name":"Jun Wu","raw_affiliation_strings":["IBISC, Univ \u00c9vry, University of Paris-Saclay, 91025, \u00c9vry, France","School of Management, Xi\u2019an Jiaotong University, 710049, Xi\u2019an, China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"IBISC, Univ \u00c9vry, University of Paris-Saclay, 91025, \u00c9vry, France","institution_ids":["https://openalex.org/I277688954","https://openalex.org/I4210107733"]},{"raw_affiliation_string":"School of Management, Xi\u2019an Jiaotong University, 710049, Xi\u2019an, China","institution_ids":["https://openalex.org/I87445476"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5121457839","display_name":"Feng Chu","orcid":null},"institutions":[{"id":"https://openalex.org/I277688954","display_name":"Universit\u00e9 Paris-Saclay","ror":"https://ror.org/03xjwb503","country_code":"FR","type":"education","lineage":["https://openalex.org/I277688954"]},{"id":"https://openalex.org/I4210107733","display_name":"Informatique, BioInformatique, Syst\u00e8mes Complexes","ror":"https://ror.org/01aqxgr98","country_code":"FR","type":"facility","lineage":["https://openalex.org/I277688954","https://openalex.org/I277688954","https://openalex.org/I4210107733","https://openalex.org/I88467170"]}],"countries":["FR"],"is_corresponding":false,"raw_author_name":"Feng Chu","raw_affiliation_strings":["IBISC, Univ \u00c9vry, University of Paris-Saclay, 91025, \u00c9vry, France"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"IBISC, Univ \u00c9vry, University of Paris-Saclay, 91025, \u00c9vry, France","institution_ids":["https://openalex.org/I277688954","https://openalex.org/I4210107733"]}]},{"author_position":"middle","author":{"id":null,"display_name":"Zhen Yang","orcid":"https://orcid.org/0000-0001-9871-8851"},"institutions":[{"id":"https://openalex.org/I87445476","display_name":"Xi'an Jiaotong University","ror":"https://ror.org/017zhmm22","country_code":"CN","type":"education","lineage":["https://openalex.org/I87445476"]}],"countries":["CN"],"is_corresponding":true,"raw_author_name":"Zhen Yang","raw_affiliation_strings":["Logistics Science and Technology Innovation Integrated Development Research Center, Xi\u2019an Jiaotong University, 710049, Xi\u2019an, China","School of Management, Xi\u2019an Jiaotong University, 710049, Xi\u2019an, China","State Key Lab for Manufacturing Systems Engineering, 710049, Xi\u2019an, China"],"raw_orcid":"https://orcid.org/0000-0001-9871-8851","affiliations":[{"raw_affiliation_string":"Logistics Science and Technology Innovation Integrated Development Research Center, Xi\u2019an Jiaotong University, 710049, Xi\u2019an, China","institution_ids":["https://openalex.org/I87445476"]},{"raw_affiliation_string":"School of Management, Xi\u2019an Jiaotong University, 710049, Xi\u2019an, China","institution_ids":["https://openalex.org/I87445476"]},{"raw_affiliation_string":"State Key Lab for Manufacturing Systems Engineering, 710049, Xi\u2019an, China","institution_ids":["https://openalex.org/I87445476"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5068123051","display_name":"Yongxi Cheng","orcid":"https://orcid.org/0000-0003-0405-5263"},"institutions":[{"id":"https://openalex.org/I87445476","display_name":"Xi'an Jiaotong University","ror":"https://ror.org/017zhmm22","country_code":"CN","type":"education","lineage":["https://openalex.org/I87445476"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Yongxi Cheng","raw_affiliation_strings":["School of Management, Xi\u2019an Jiaotong University, 710049, Xi\u2019an, China","State Key Lab for Manufacturing Systems Engineering, 710049, Xi\u2019an, China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"School of Management, Xi\u2019an Jiaotong University, 710049, Xi\u2019an, China","institution_ids":["https://openalex.org/I87445476"]},{"raw_affiliation_string":"State Key Lab for Manufacturing Systems Engineering, 710049, Xi\u2019an, China","institution_ids":["https://openalex.org/I87445476"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":3,"corresponding_author_ids":[],"corresponding_institution_ids":["https://openalex.org/I87445476"],"apc_list":{"value":2990,"currency":"USD","value_usd":2990},"apc_paid":null,"fwci":0.5997,"has_fulltext":false,"cited_by_count":1,"citation_normalized_percentile":{"value":0.75981305,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":94,"max":97},"biblio":{"volume":"208","issue":"2","first_page":null,"last_page":null},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10567","display_name":"Vehicle Routing Optimization Methods","score":0.9959999918937683,"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":0.9959999918937683,"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/T11223","display_name":"Maritime Ports and Logistics","score":0.0003000000142492354,"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/T11814","display_name":"Advanced Manufacturing and Logistics Optimization","score":0.0003000000142492354,"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/theory-of-computation","display_name":"Theory of computation","score":0.6657000184059143},{"id":"https://openalex.org/keywords/routing","display_name":"Routing (electronic design automation)","score":0.6349999904632568},{"id":"https://openalex.org/keywords/parameterized-complexity","display_name":"Parameterized complexity","score":0.5595999956130981},{"id":"https://openalex.org/keywords/range","display_name":"Range (aeronautics)","score":0.5515999794006348},{"id":"https://openalex.org/keywords/vehicle-routing-problem","display_name":"Vehicle routing problem","score":0.527400016784668},{"id":"https://openalex.org/keywords/path","display_name":"Path (computing)","score":0.508899986743927},{"id":"https://openalex.org/keywords/approximation-algorithm","display_name":"Approximation algorithm","score":0.4453999996185303}],"concepts":[{"id":"https://openalex.org/C24858836","wikidata":"https://www.wikidata.org/wiki/Q844718","display_name":"Theory of computation","level":2,"score":0.6657000184059143},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.6496999859809875},{"id":"https://openalex.org/C74172769","wikidata":"https://www.wikidata.org/wiki/Q1446839","display_name":"Routing (electronic design automation)","level":2,"score":0.6349999904632568},{"id":"https://openalex.org/C165464430","wikidata":"https://www.wikidata.org/wiki/Q1570441","display_name":"Parameterized complexity","level":2,"score":0.5595999956130981},{"id":"https://openalex.org/C204323151","wikidata":"https://www.wikidata.org/wiki/Q905424","display_name":"Range (aeronautics)","level":2,"score":0.5515999794006348},{"id":"https://openalex.org/C123784306","wikidata":"https://www.wikidata.org/wiki/Q944041","display_name":"Vehicle routing problem","level":3,"score":0.527400016784668},{"id":"https://openalex.org/C2777735758","wikidata":"https://www.wikidata.org/wiki/Q817765","display_name":"Path (computing)","level":2,"score":0.508899986743927},{"id":"https://openalex.org/C148764684","wikidata":"https://www.wikidata.org/wiki/Q621751","display_name":"Approximation algorithm","level":2,"score":0.4453999996185303},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.43459999561309814},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.4124000072479248},{"id":"https://openalex.org/C2778029271","wikidata":"https://www.wikidata.org/wiki/Q5421931","display_name":"Extension (predicate logic)","level":2,"score":0.4074000120162964},{"id":"https://openalex.org/C18762648","wikidata":"https://www.wikidata.org/wiki/Q42213","display_name":"Work (physics)","level":2,"score":0.38260000944137573},{"id":"https://openalex.org/C22590252","wikidata":"https://www.wikidata.org/wiki/Q1058754","display_name":"Shortest path problem","level":3,"score":0.3109000027179718},{"id":"https://openalex.org/C76522221","wikidata":"https://www.wikidata.org/wiki/Q5035396","display_name":"Multipath routing","level":5,"score":0.30660000443458557},{"id":"https://openalex.org/C115443555","wikidata":"https://www.wikidata.org/wiki/Q5367790","display_name":"Equal-cost multi-path routing","level":5,"score":0.29829999804496765},{"id":"https://openalex.org/C42475967","wikidata":"https://www.wikidata.org/wiki/Q194292","display_name":"Operations research","level":1,"score":0.28870001435279846},{"id":"https://openalex.org/C2777705401","wikidata":"https://www.wikidata.org/wiki/Q6457570","display_name":"LEAPS","level":2,"score":0.2874999940395355}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1007/s10957-025-02890-3","is_oa":false,"landing_page_url":"https://doi.org/10.1007/s10957-025-02890-3","pdf_url":null,"source":{"id":"https://openalex.org/S52430896","display_name":"Journal of Optimization Theory and Applications","issn_l":"0022-3239","issn":["0022-3239","1573-2878"],"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 Optimization Theory and Applications","raw_type":"journal-article"},{"id":"pmh:oai:HAL:hal-05438814v1","is_oa":false,"landing_page_url":"https://univ-evry.hal.science/hal-05438814","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 Optimization Theory and Applications, 2026, 208 (2), pp.73. ⟨10.1007/s10957-025-02890-3⟩","raw_type":"info:eu-repo/semantics/article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G4972362988","display_name":"\u57fa\u4e8e\u5206\u7c7b\u7684\u57ce\u5e02\u751f\u6d3b\u5783\u573e\u56de\u6536\u7cfb\u7edf\u7f51\u7edc\u8bbe\u8ba1\u4e0e\u4f18\u5316\u7814\u7a76","funder_award_id":"71971167","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G735607534","display_name":null,"funder_award_id":"202206280182","funder_id":"https://openalex.org/F4320322725","funder_display_name":"China Scholarship Council"}],"funders":[{"id":"https://openalex.org/F4320321001","display_name":"National Natural Science Foundation of China","ror":"https://ror.org/01h0zpd94"},{"id":"https://openalex.org/F4320322725","display_name":"China Scholarship Council","ror":"https://ror.org/04atp4p48"}],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":44,"referenced_works":["https://openalex.org/W863933106","https://openalex.org/W1541543614","https://openalex.org/W1552693528","https://openalex.org/W1857333123","https://openalex.org/W1966209162","https://openalex.org/W1969481197","https://openalex.org/W1980809300","https://openalex.org/W1988345713","https://openalex.org/W1994271251","https://openalex.org/W1996875951","https://openalex.org/W2016699485","https://openalex.org/W2018679674","https://openalex.org/W2027678739","https://openalex.org/W2034097982","https://openalex.org/W2056299576","https://openalex.org/W2056897184","https://openalex.org/W2062045653","https://openalex.org/W2077326088","https://openalex.org/W2090245401","https://openalex.org/W2109335081","https://openalex.org/W2111563176","https://openalex.org/W2123213336","https://openalex.org/W2131338629","https://openalex.org/W2162750432","https://openalex.org/W2165515547","https://openalex.org/W2509664953","https://openalex.org/W2600233134","https://openalex.org/W2603042788","https://openalex.org/W2620314292","https://openalex.org/W2734566198","https://openalex.org/W2774653136","https://openalex.org/W2800453060","https://openalex.org/W2924970388","https://openalex.org/W2944803716","https://openalex.org/W2948333404","https://openalex.org/W2999840680","https://openalex.org/W3125642975","https://openalex.org/W3174352199","https://openalex.org/W4200391575","https://openalex.org/W4252801674","https://openalex.org/W4292230561","https://openalex.org/W4378220009","https://openalex.org/W4385075968","https://openalex.org/W4391741341"],"related_works":[],"abstract_inverted_index":null,"counts_by_year":[{"year":2026,"cited_by_count":1}],"updated_date":"2026-07-23T08:03:31.855105","created_date":"2025-12-29T00:00:00"}