{"id":"https://openalex.org/W4389632012","doi":"https://doi.org/10.4236/ajcm.2023.134033","title":"Analysis of the Impact of Optimal Solutions to the Transportation Problems for Variations in Cost Using Two Reliable Approaches","display_name":"Analysis of the Impact of Optimal Solutions to the Transportation Problems for Variations in Cost Using Two Reliable Approaches","publication_year":2023,"publication_date":"2023-01-01","ids":{"openalex":"https://openalex.org/W4389632012","doi":"https://doi.org/10.4236/ajcm.2023.134033"},"language":"en","primary_location":{"id":"doi:10.4236/ajcm.2023.134033","doi":"https://doi.org/10.4236/ajcm.2023.134033","is_oa":true,"landing_page_url":"https://doi.org/10.4236/ajcm.2023.134033","pdf_url":"https://www.scirp.org/pdf/ajcm_2023121216400610.pdf","source":{"id":"https://openalex.org/S2764880020","display_name":"American Journal of Computational Mathematics","issn_l":"2161-1203","issn":["2161-1203","2161-1211"],"is_oa":true,"is_in_doaj":false,"is_core":true,"listed_in":["cwts-core"],"host_organization":"https://openalex.org/P4310320480","host_organization_name":"Scientific Research Publishing","host_organization_lineage":["https://openalex.org/P4310320480"],"host_organization_lineage_names":["Scientific Research Publishing"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"American Journal of Computational Mathematics","raw_type":"journal-article"},"volume":null,"type":"article","is_traditional":true,"indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"diamond","oa_url":"https://www.scirp.org/pdf/ajcm_2023121216400610.pdf","any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5026330632","display_name":"Abdur Rashid","orcid":"https://orcid.org/0000-0001-9810-8738","observed_orcids":["https://orcid.org/0000-0001-9810-8738"]},"institutions":[{"id":"https://openalex.org/I46080048","display_name":"Jahangirnagar University","ror":"https://ror.org/04ywb0864","country_code":"BD","type":"education","lineage":["https://openalex.org/I46080048"]}],"countries":["BD"],"is_corresponding":false,"raw_author_name":"Abdur Rashid","raw_affiliation_strings":["Department of Mathematics, Jahangirnagar University, Dhaka, Bangladesh"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics, Jahangirnagar University, Dhaka, Bangladesh","institution_ids":["https://openalex.org/I46080048"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5100778463","display_name":"Md. Amirul Islam","orcid":"https://orcid.org/0000-0002-2359-3887","observed_orcids":["https://orcid.org/0000-0002-2359-3887"]},"institutions":[{"id":"https://openalex.org/I205200222","display_name":"Uttara University","ror":"https://ror.org/035zypg15","country_code":"BD","type":"education","lineage":["https://openalex.org/I205200222"]}],"countries":["BD"],"is_corresponding":false,"raw_author_name":"Md. Amirul Islam","raw_affiliation_strings":["Department of Mathematics, Uttara University, Dhaka, Bangladesh"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics, Uttara University, Dhaka, Bangladesh","institution_ids":["https://openalex.org/I205200222"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":0.2927,"has_fulltext":true,"cited_by_count":2,"citation_normalized_percentile":{"value":0.51983189,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":88,"max":95},"biblio":{"volume":"13","issue":"04","first_page":"607","last_page":"618"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T12709","display_name":"Optimization and Mathematical Programming","score":0.9980000257492065,"subfield":{"id":"https://openalex.org/subfields/1803","display_name":"Management Science and Operations Research"},"field":{"id":"https://openalex.org/fields/18","display_name":"Decision Sciences"},"domain":{"id":"https://openalex.org/domains/2","display_name":"Social Sciences"}},"topics":[{"id":"https://openalex.org/T12709","display_name":"Optimization and Mathematical Programming","score":0.9980000257492065,"subfield":{"id":"https://openalex.org/subfields/1803","display_name":"Management Science and Operations Research"},"field":{"id":"https://openalex.org/fields/18","display_name":"Decision Sciences"},"domain":{"id":"https://openalex.org/domains/2","display_name":"Social Sciences"}},{"id":"https://openalex.org/T10567","display_name":"Vehicle Routing Optimization Methods","score":0.000699999975040555,"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/T10720","display_name":"Complexity and Algorithms in Graphs","score":0.0005000000237487257,"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-problem","display_name":"transportation problem","score":0.9929999709129333},{"id":"https://openalex.org/keywords/optimal-solution","display_name":"optimal solution","score":0.8230000138282776},{"id":"https://openalex.org/keywords/cost-variation","display_name":"cost variation","score":0.5789999961853027},{"id":"https://openalex.org/keywords/cost-efficiency","display_name":"cost efficiency","score":0.621999979019165},{"id":"https://openalex.org/keywords/resource-allocation","display_name":"resource allocation","score":0.5370000004768372}],"concepts":[{"id":"https://openalex.org/C2779343474","wikidata":"https://www.wikidata.org/wiki/Q3109175","display_name":"Context (archaeology)","level":2,"score":0.6260261535644531},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.621298611164093},{"id":"https://openalex.org/C31829261","wikidata":"https://www.wikidata.org/wiki/Q1929885","display_name":"Transportation theory","level":2,"score":0.5952565670013428},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.5945528745651245},{"id":"https://openalex.org/C26517878","wikidata":"https://www.wikidata.org/wiki/Q228039","display_name":"Key (lock)","level":2,"score":0.5119510889053345},{"id":"https://openalex.org/C206345919","wikidata":"https://www.wikidata.org/wiki/Q20380951","display_name":"Resource (disambiguation)","level":2,"score":0.46794265508651733},{"id":"https://openalex.org/C2780595030","wikidata":"https://www.wikidata.org/wiki/Q3860309","display_name":"Multiplication (music)","level":2,"score":0.45309948921203613},{"id":"https://openalex.org/C68060419","wikidata":"https://www.wikidata.org/wiki/Q40754","display_name":"Subtraction","level":2,"score":0.4262383282184601},{"id":"https://openalex.org/C42475967","wikidata":"https://www.wikidata.org/wiki/Q194292","display_name":"Operations research","level":1,"score":0.3899648189544678},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.1786012053489685},{"id":"https://openalex.org/C94375191","wikidata":"https://www.wikidata.org/wiki/Q11205","display_name":"Arithmetic","level":1,"score":0.0},{"id":"https://openalex.org/C31258907","wikidata":"https://www.wikidata.org/wiki/Q1301371","display_name":"Computer network","level":1,"score":0.0},{"id":"https://openalex.org/C151730666","wikidata":"https://www.wikidata.org/wiki/Q7205","display_name":"Paleontology","level":1,"score":0.0},{"id":"https://openalex.org/C86803240","wikidata":"https://www.wikidata.org/wiki/Q420","display_name":"Biology","level":0,"score":0.0},{"id":"https://openalex.org/C38652104","wikidata":"https://www.wikidata.org/wiki/Q3510521","display_name":"Computer security","level":1,"score":0.0},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.4236/ajcm.2023.134033","doi":"https://doi.org/10.4236/ajcm.2023.134033","is_oa":true,"landing_page_url":"https://doi.org/10.4236/ajcm.2023.134033","pdf_url":"https://www.scirp.org/pdf/ajcm_2023121216400610.pdf","source":{"id":"https://openalex.org/S2764880020","display_name":"American Journal of Computational Mathematics","issn_l":"2161-1203","issn":["2161-1203","2161-1211"],"is_oa":true,"is_in_doaj":false,"is_core":true,"listed_in":["cwts-core"],"host_organization":"https://openalex.org/P4310320480","host_organization_name":"Scientific Research Publishing","host_organization_lineage":["https://openalex.org/P4310320480"],"host_organization_lineage_names":["Scientific Research Publishing"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"American Journal of Computational Mathematics","raw_type":"journal-article"}],"best_oa_location":{"id":"doi:10.4236/ajcm.2023.134033","doi":"https://doi.org/10.4236/ajcm.2023.134033","is_oa":true,"landing_page_url":"https://doi.org/10.4236/ajcm.2023.134033","pdf_url":"https://www.scirp.org/pdf/ajcm_2023121216400610.pdf","source":{"id":"https://openalex.org/S2764880020","display_name":"American Journal of Computational Mathematics","issn_l":"2161-1203","issn":["2161-1203","2161-1211"],"is_oa":true,"is_in_doaj":false,"is_core":true,"listed_in":["cwts-core"],"host_organization":"https://openalex.org/P4310320480","host_organization_name":"Scientific Research Publishing","host_organization_lineage":["https://openalex.org/P4310320480"],"host_organization_lineage_names":["Scientific Research Publishing"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"American Journal of Computational Mathematics","raw_type":"journal-article"},"sustainable_development_goals":[{"score":0.5378999710083008,"id":"https://metadata.un.org/sdg/9","display_name":"Industry, innovation and infrastructure"}],"study_designs":[],"awards":[],"funders":[],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W4389632012.pdf","grobid_xml":"https://content.openalex.org/works/W4389632012.grobid-xml"},"referenced_works_count":14,"referenced_works":["https://openalex.org/W1967486378","https://openalex.org/W2047903283","https://openalex.org/W2096477102","https://openalex.org/W2125994026","https://openalex.org/W2127470768","https://openalex.org/W2212016480","https://openalex.org/W2298738418","https://openalex.org/W2317065341","https://openalex.org/W2328725012","https://openalex.org/W2418477132","https://openalex.org/W2735565064","https://openalex.org/W2914423730","https://openalex.org/W2924884701","https://openalex.org/W3045460713"],"related_works":["https://openalex.org/W7215652217","https://openalex.org/W7016559496","https://openalex.org/W3092776968","https://openalex.org/W2220911353","https://openalex.org/W4206458378","https://openalex.org/W7165169064","https://openalex.org/W7221264424","https://openalex.org/W2068277260","https://openalex.org/W6987544762","https://openalex.org/W4236425129"],"abstract_inverted_index":{"In":[0,22],"this":[1,143],"paper,":[2],"we":[3,90],"have":[4],"used":[5],"two":[6,83,138],"reliable":[7,139],"approaches":[8],"(theorems)":[9],"to":[10,15,30,36,118,152,166],"find":[11],"the":[12,37,41,76,97,112,130,137,154,168],"optimal":[13,34,98],"solutions":[14,35,151],"transportation":[16,25,38,79,109,159],"problems,":[17],"using":[18,87],"variations":[19,44],"in":[20,40,45,66,107,142],"costs.":[21],"real-life":[23],"scenarios,":[24],"costs":[26,110],"can":[27,91],"fluctuate":[28],"due":[29],"different":[31],"factors.":[32],"Finding":[33],"problem":[39],"context":[42],"of":[43,78,105,116,158],"cost":[46,51,131],"is":[47,134],"vital":[48],"for":[49,75,95],"ensuring":[50],"efficiency,":[52],"resource":[53],"allocation,":[54],"customer":[55],"satisfaction,":[56],"competitive":[57],"advantage,":[58],"environmental":[59],"responsibility,":[60],"risk":[61],"mitigation,":[62],"and":[63,101,149,156],"operational":[64],"fortitude":[65],"practical":[67,150],"situations.":[68],"This":[69],"paper":[70],"opens":[71],"up":[72],"new":[73],"directions":[74],"solution":[77,99],"problems":[80],"by":[81,127],"introducing":[82],"key":[84],"theorems.":[85],"By":[86],"these":[88],"theorems,":[89],"develop":[92],"an":[93],"algorithm":[94],"identifying":[96],"attributes":[100],"permitting":[102],"accurate":[103],"quantification":[104],"changes":[106],"overall":[108],"through":[111],"addition":[113],"or":[114,121],"subtraction":[115],"constants":[117,128],"specific":[119],"rows":[120],"columns,":[122],"as":[123,125],"well":[124],"multiplication":[126],"inside":[129],"matrix.":[132],"It":[133],"anticipated":[135],"that":[136],"techniques":[140],"presented":[141,165],"study":[144],"will":[145],"provide":[146],"theoretical":[147],"insights":[148],"enhance":[153],"efficiency":[155],"cost-effectiveness":[157],"systems.":[160],"Finally,":[161],"numerical":[162],"illustrations":[163],"are":[164],"verify":[167],"proposed":[169],"approaches.":[170]},"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2024,"cited_by_count":1}],"updated_date":"2026-11-07T11:25:07.637180","created_date":"2023-12-13T00:00:00"}