{"id":"https://openalex.org/W2025533513","doi":"https://doi.org/10.1016/0166-218x(86)90069-7","title":"Conditions for the existence of solutions of the three-dimensional planar transportation problem","display_name":"Conditions for the existence of solutions of the three-dimensional planar transportation problem","publication_year":1986,"publication_date":"1986-01-01","ids":{"openalex":"https://openalex.org/W2025533513","doi":"https://doi.org/10.1016/0166-218x(86)90069-7","mag":"2025533513"},"language":"en","primary_location":{"id":"doi:10.1016/0166-218x(86)90069-7","is_oa":false,"landing_page_url":"https://doi.org/10.1016/0166-218x(86)90069-7","pdf_url":null,"source":{"id":"https://openalex.org/S171741597","display_name":"Discrete Applied Mathematics","issn_l":"0166-218X","issn":["0166-218X","1872-6771"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320990","host_organization_name":"Elsevier BV","host_organization_lineage":["https://openalex.org/P4310320990"],"host_organization_lineage_names":["Elsevier BV"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Discrete Applied Mathematics","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/A5062179552","display_name":"Milan Vlach","orcid":"https://orcid.org/0000-0001-6859-8414"},"institutions":[{"id":"https://openalex.org/I21250087","display_name":"Charles University","ror":"https://ror.org/024d6js02","country_code":"CZ","type":"education","lineage":["https://openalex.org/I21250087"]}],"countries":["CZ"],"is_corresponding":true,"raw_author_name":"Milan Vlach","raw_affiliation_strings":["Dept. of Computer Science and Operations Research, Charles University, Prague, Czechoslovakia"],"affiliations":[{"raw_affiliation_string":"Dept. of Computer Science and Operations Research, Charles University, Prague, Czechoslovakia","institution_ids":["https://openalex.org/I21250087"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5062179552"],"corresponding_institution_ids":["https://openalex.org/I21250087"],"apc_list":{"value":2750,"currency":"USD","value_usd":2750},"apc_paid":null,"fwci":2.4954,"has_fulltext":false,"cited_by_count":66,"citation_normalized_percentile":{"value":0.89863014,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":97},"biblio":{"volume":"13","issue":"1","first_page":"61","last_page":"78"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T12396","display_name":"Advanced Differential Equations and Dynamical Systems","score":0.9735000133514404,"subfield":{"id":"https://openalex.org/subfields/2608","display_name":"Geometry and Topology"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T12396","display_name":"Advanced Differential Equations and Dynamical Systems","score":0.9735000133514404,"subfield":{"id":"https://openalex.org/subfields/2608","display_name":"Geometry and Topology"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T12504","display_name":"Mathematics and Applications","score":0.9555000066757202,"subfield":{"id":"https://openalex.org/subfields/2608","display_name":"Geometry and Topology"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T11777","display_name":"Fixed Point Theorems Analysis","score":0.9060999751091003,"subfield":{"id":"https://openalex.org/subfields/2608","display_name":"Geometry and Topology"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/planar","display_name":"Planar","score":0.8724246025085449},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.8688948154449463},{"id":"https://openalex.org/keywords/transportation-theory","display_name":"Transportation theory","score":0.5403663516044617},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.43047255277633667},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.32760655879974365},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.06393671035766602}],"concepts":[{"id":"https://openalex.org/C134786449","wikidata":"https://www.wikidata.org/wiki/Q3391255","display_name":"Planar","level":2,"score":0.8724246025085449},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8688948154449463},{"id":"https://openalex.org/C31829261","wikidata":"https://www.wikidata.org/wiki/Q1929885","display_name":"Transportation theory","level":2,"score":0.5403663516044617},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.43047255277633667},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.32760655879974365},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.06393671035766602},{"id":"https://openalex.org/C121684516","wikidata":"https://www.wikidata.org/wiki/Q7600677","display_name":"Computer graphics (images)","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1016/0166-218x(86)90069-7","is_oa":false,"landing_page_url":"https://doi.org/10.1016/0166-218x(86)90069-7","pdf_url":null,"source":{"id":"https://openalex.org/S171741597","display_name":"Discrete Applied Mathematics","issn_l":"0166-218X","issn":["0166-218X","1872-6771"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320990","host_organization_name":"Elsevier BV","host_organization_lineage":["https://openalex.org/P4310320990"],"host_organization_lineage_names":["Elsevier BV"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Discrete Applied Mathematics","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":15,"referenced_works":["https://openalex.org/W140486548","https://openalex.org/W1984815404","https://openalex.org/W2032768509","https://openalex.org/W2033424339","https://openalex.org/W2040163622","https://openalex.org/W2079379406","https://openalex.org/W2109798945","https://openalex.org/W2127188720","https://openalex.org/W2149097134","https://openalex.org/W3048253721","https://openalex.org/W3048325135","https://openalex.org/W4255280903","https://openalex.org/W6647777910","https://openalex.org/W6658620974","https://openalex.org/W6781480471"],"related_works":["https://openalex.org/W1979597421","https://openalex.org/W2007980826","https://openalex.org/W4245490552","https://openalex.org/W4225152035","https://openalex.org/W2061531152","https://openalex.org/W4380087116","https://openalex.org/W2913548082","https://openalex.org/W4229678196","https://openalex.org/W3176059562","https://openalex.org/W4295940899"],"abstract_inverted_index":null,"counts_by_year":[{"year":2025,"cited_by_count":1},{"year":2024,"cited_by_count":1},{"year":2023,"cited_by_count":1},{"year":2022,"cited_by_count":2},{"year":2021,"cited_by_count":1},{"year":2020,"cited_by_count":1},{"year":2019,"cited_by_count":3},{"year":2018,"cited_by_count":1},{"year":2017,"cited_by_count":2},{"year":2016,"cited_by_count":1},{"year":2015,"cited_by_count":2},{"year":2014,"cited_by_count":1},{"year":2013,"cited_by_count":1},{"year":2012,"cited_by_count":3}],"updated_date":"2026-04-04T16:13:02.066488","created_date":"2025-10-10T00:00:00"}