{"id":"https://openalex.org/W2115158534","doi":"https://doi.org/10.1142/s1793830912500498","title":"THE ALGORITHM OF FINDING ALL PARADOXICAL PAIRS IN A LINEAR TRANSPORTATION PROBLEM","display_name":"THE ALGORITHM OF FINDING ALL PARADOXICAL PAIRS IN A LINEAR TRANSPORTATION PROBLEM","publication_year":2012,"publication_date":"2012-10-29","ids":{"openalex":"https://openalex.org/W2115158534","doi":"https://doi.org/10.1142/s1793830912500498","mag":"2115158534"},"language":"en","primary_location":{"id":"doi:10.1142/s1793830912500498","is_oa":false,"landing_page_url":"https://doi.org/10.1142/s1793830912500498","pdf_url":null,"source":{"id":"https://openalex.org/S178434951","display_name":"Discrete Mathematics Algorithms and Applications","issn_l":"1793-8309","issn":["1793-8309","1793-8317"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319815","host_organization_name":"World Scientific","host_organization_lineage":["https://openalex.org/P4310319815"],"host_organization_lineage_names":["World Scientific"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Discrete Mathematics, Algorithms 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/A5110280536","display_name":"Manjusri Basu","orcid":null},"institutions":[{"id":"https://openalex.org/I77501641","display_name":"University of Kalyani","ror":"https://ror.org/03v783k16","country_code":"IN","type":"education","lineage":["https://openalex.org/I77501641"]}],"countries":["IN"],"is_corresponding":false,"raw_author_name":"MANJUSRI BASU","raw_affiliation_strings":["Department of Mathematics, University of Kalyani, Kalyani-741235, India"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics, University of Kalyani, Kalyani-741235, India","institution_ids":["https://openalex.org/I77501641"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5000668381","display_name":"Debiprasad Acharya","orcid":"https://orcid.org/0000-0002-0758-1683"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"DEBIPRASAD ACHARYA","raw_affiliation_strings":["Department of Mathematics, N.V.College, Nabadwip, Nadia, W.B., India"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics, N.V.College, Nabadwip, Nadia, W.B., India","institution_ids":[]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5087865015","display_name":"Atanu Das","orcid":"https://orcid.org/0000-0002-7694-4345"},"institutions":[{"id":"https://openalex.org/I77501641","display_name":"University of Kalyani","ror":"https://ror.org/03v783k16","country_code":"IN","type":"education","lineage":["https://openalex.org/I77501641"]}],"countries":["IN"],"is_corresponding":false,"raw_author_name":"ATANU DAS","raw_affiliation_strings":["Department of Mathematics, University of Kalyani, Kalyani-741235, India"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics, University of Kalyani, Kalyani-741235, India","institution_ids":["https://openalex.org/I77501641"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":3,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":0.5685,"has_fulltext":false,"cited_by_count":1,"citation_normalized_percentile":{"value":0.75875975,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":94},"biblio":{"volume":"04","issue":"04","first_page":"1250049","last_page":"1250049"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T12709","display_name":"Optimization and Mathematical Programming","score":0.9991999864578247,"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":0.9991999864578247,"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/T13855","display_name":"Aerospace Engineering and Control Systems","score":0.9830999970436096,"subfield":{"id":"https://openalex.org/subfields/2202","display_name":"Aerospace 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/T10545","display_name":"Optimization and Variational Analysis","score":0.9368000030517578,"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/transportation-theory","display_name":"Transportation theory","score":0.5810530781745911},{"id":"https://openalex.org/keywords/range","display_name":"Range (aeronautics)","score":0.5390339493751526},{"id":"https://openalex.org/keywords/linear-programming","display_name":"Linear programming","score":0.5151530504226685},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.5135960578918457},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.4478887617588043},{"id":"https://openalex.org/keywords/flow","display_name":"Flow (mathematics)","score":0.42346060276031494},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.42236804962158203},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.4090661108493805},{"id":"https://openalex.org/keywords/mathematical-economics","display_name":"Mathematical economics","score":0.32642054557800293},{"id":"https://openalex.org/keywords/engineering","display_name":"Engineering","score":0.155528724193573}],"concepts":[{"id":"https://openalex.org/C31829261","wikidata":"https://www.wikidata.org/wiki/Q1929885","display_name":"Transportation theory","level":2,"score":0.5810530781745911},{"id":"https://openalex.org/C204323151","wikidata":"https://www.wikidata.org/wiki/Q905424","display_name":"Range (aeronautics)","level":2,"score":0.5390339493751526},{"id":"https://openalex.org/C41045048","wikidata":"https://www.wikidata.org/wiki/Q202843","display_name":"Linear programming","level":2,"score":0.5151530504226685},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.5135960578918457},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.4478887617588043},{"id":"https://openalex.org/C38349280","wikidata":"https://www.wikidata.org/wiki/Q1434290","display_name":"Flow (mathematics)","level":2,"score":0.42346060276031494},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.42236804962158203},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.4090661108493805},{"id":"https://openalex.org/C144237770","wikidata":"https://www.wikidata.org/wiki/Q747534","display_name":"Mathematical economics","level":1,"score":0.32642054557800293},{"id":"https://openalex.org/C127413603","wikidata":"https://www.wikidata.org/wiki/Q11023","display_name":"Engineering","level":0,"score":0.155528724193573},{"id":"https://openalex.org/C146978453","wikidata":"https://www.wikidata.org/wiki/Q3798668","display_name":"Aerospace engineering","level":1,"score":0.0},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1142/s1793830912500498","is_oa":false,"landing_page_url":"https://doi.org/10.1142/s1793830912500498","pdf_url":null,"source":{"id":"https://openalex.org/S178434951","display_name":"Discrete Mathematics Algorithms and Applications","issn_l":"1793-8309","issn":["1793-8309","1793-8317"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319815","host_organization_name":"World Scientific","host_organization_lineage":["https://openalex.org/P4310319815"],"host_organization_lineage_names":["World Scientific"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Discrete Mathematics, Algorithms and Applications","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":11,"referenced_works":["https://openalex.org/W1965899202","https://openalex.org/W1991616395","https://openalex.org/W2020898537","https://openalex.org/W2030665787","https://openalex.org/W2063824979","https://openalex.org/W2150988245","https://openalex.org/W2328725012","https://openalex.org/W2734583511","https://openalex.org/W2800137643","https://openalex.org/W4232353591","https://openalex.org/W4301216918"],"related_works":["https://openalex.org/W2196900565","https://openalex.org/W4281745638","https://openalex.org/W2389150017","https://openalex.org/W3202999461","https://openalex.org/W4214624958","https://openalex.org/W4205332774","https://openalex.org/W2386102873","https://openalex.org/W1987173310","https://openalex.org/W313296872","https://openalex.org/W2053611849"],"abstract_inverted_index":{"In":[0],"this":[1],"paper,":[2],"we":[3,12,28],"discuss":[4],"paradox":[5,21],"in":[6,22,48],"a":[7,14,23,45],"linear":[8,24],"Transportation":[9],"Problem.":[10],"Thereby,":[11],"establish":[13],"sufficient":[15],"condition":[16],"for":[17],"the":[18,32,51],"existence":[19],"of":[20,40,50],"transportation":[25],"problem.":[26],"Next":[27],"find":[29],"out":[30],"all":[31],"Paradoxical":[33],"pairs":[34],"as":[35,37],"well":[36],"paradoxical":[38],"range":[39],"flow.":[41],"We":[42],"also":[43],"illustrate":[44],"numerical":[46],"example":[47],"support":[49],"theory.":[52]},"counts_by_year":[{"year":2015,"cited_by_count":1}],"updated_date":"2026-06-11T09:08:48.828518","created_date":"2025-10-10T00:00:00"}