{"id":"https://openalex.org/W4409889871","doi":"https://doi.org/10.1080/03155986.2025.2492739","title":"Investigation of a multi-objective fixed charge transportation problem with quantity dependent transportation cost and discount policy <i>via</i> metaheuristics","display_name":"Investigation of a multi-objective fixed charge transportation problem with quantity dependent transportation cost and discount policy <i>via</i> metaheuristics","publication_year":2025,"publication_date":"2025-04-28","ids":{"openalex":"https://openalex.org/W4409889871","doi":"https://doi.org/10.1080/03155986.2025.2492739"},"language":"en","primary_location":{"id":"doi:10.1080/03155986.2025.2492739","is_oa":false,"landing_page_url":"https://doi.org/10.1080/03155986.2025.2492739","pdf_url":null,"source":{"id":"https://openalex.org/S155959304","display_name":"INFOR Information Systems and Operational Research","issn_l":"0315-5986","issn":["0315-5986","1916-0615"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320547","host_organization_name":"Taylor & Francis","host_organization_lineage":["https://openalex.org/P4310320547"],"host_organization_lineage_names":["Taylor & Francis"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"INFOR: Information Systems and Operational Research","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/A5108875096","display_name":"M. S. Mondal","orcid":"https://orcid.org/0009-0006-9863-2605"},"institutions":[{"id":"https://openalex.org/I132359460","display_name":"University of Burdwan","ror":"https://ror.org/05cyd8v32","country_code":"IN","type":"education","lineage":["https://openalex.org/I132359460"]}],"countries":["IN"],"is_corresponding":false,"raw_author_name":"Manas Mondal","raw_affiliation_strings":["Department of Mathematics, The University of Burdwan"],"raw_orcid":"https://orcid.org/0009-0006-9863-2605","affiliations":[{"raw_affiliation_string":"Department of Mathematics, The University of Burdwan","institution_ids":["https://openalex.org/I132359460"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5004475917","display_name":"Goutam Mandal","orcid":"https://orcid.org/0000-0002-9212-5200"},"institutions":[{"id":"https://openalex.org/I132359460","display_name":"University of Burdwan","ror":"https://ror.org/05cyd8v32","country_code":"IN","type":"education","lineage":["https://openalex.org/I132359460"]},{"id":"https://openalex.org/I74786994","display_name":"Kitware (United States)","ror":"https://ror.org/02s2acn37","country_code":"US","type":"company","lineage":["https://openalex.org/I74786994"]}],"countries":["IN","US"],"is_corresponding":false,"raw_author_name":"Goutam Mandal","raw_affiliation_strings":["Department of Mathematics, Brainware University","Department of Mathematics, The University of Burdwan"],"raw_orcid":"https://orcid.org/0000-0002-9212-5200","affiliations":[{"raw_affiliation_string":"Department of Mathematics, Brainware University","institution_ids":["https://openalex.org/I74786994"]},{"raw_affiliation_string":"Department of Mathematics, The University of Burdwan","institution_ids":["https://openalex.org/I132359460"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5046327670","display_name":"Ali Akbar Shaikh","orcid":"https://orcid.org/0000-0001-6479-7002"},"institutions":[{"id":"https://openalex.org/I132359460","display_name":"University of Burdwan","ror":"https://ror.org/05cyd8v32","country_code":"IN","type":"education","lineage":["https://openalex.org/I132359460"]}],"countries":["IN"],"is_corresponding":true,"raw_author_name":"Ali Akbar Shaikh","raw_affiliation_strings":["Department of Mathematics, The University of Burdwan"],"raw_orcid":"https://orcid.org/0000-0001-6479-7002","affiliations":[{"raw_affiliation_string":"Department of Mathematics, The University of Burdwan","institution_ids":["https://openalex.org/I132359460"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5048665354","display_name":"Asoke Kumar Bhunia","orcid":"https://orcid.org/0000-0001-8193-3141"},"institutions":[{"id":"https://openalex.org/I132359460","display_name":"University of Burdwan","ror":"https://ror.org/05cyd8v32","country_code":"IN","type":"education","lineage":["https://openalex.org/I132359460"]}],"countries":["IN"],"is_corresponding":false,"raw_author_name":"Asoke Kumar Bhunia","raw_affiliation_strings":["Department of Mathematics, The University of Burdwan"],"raw_orcid":"https://orcid.org/0000-0001-8193-3141","affiliations":[{"raw_affiliation_string":"Department of Mathematics, The University of Burdwan","institution_ids":["https://openalex.org/I132359460"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":4,"corresponding_author_ids":["https://openalex.org/A5046327670"],"corresponding_institution_ids":["https://openalex.org/I132359460"],"apc_list":null,"apc_paid":null,"fwci":1.7711,"has_fulltext":false,"cited_by_count":2,"citation_normalized_percentile":{"value":0.84008596,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":91,"max":98},"biblio":{"volume":"63","issue":"3","first_page":"562","last_page":"591"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T12709","display_name":"Optimization and Mathematical Programming","score":0.9994000196456909,"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":0.9994000196456909,"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/T13601","display_name":"Urban Transport Systems Analysis","score":0.9140999913215637,"subfield":{"id":"https://openalex.org/subfields/2205","display_name":"Civil and Structural 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/T10698","display_name":"Transportation Planning and Optimization","score":0.9138000011444092,"subfield":{"id":"https://openalex.org/subfields/3313","display_name":"Transportation"},"field":{"id":"https://openalex.org/fields/33","display_name":"Social Sciences"},"domain":{"id":"https://openalex.org/domains/2","display_name":"Social Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/metaheuristic","display_name":"Metaheuristic","score":0.7332918643951416},{"id":"https://openalex.org/keywords/transportation-theory","display_name":"Transportation theory","score":0.6136492490768433},{"id":"https://openalex.org/keywords/fixed-charge","display_name":"Fixed charge","score":0.544093906879425},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.43961647152900696},{"id":"https://openalex.org/keywords/fixed-cost","display_name":"Fixed cost","score":0.4268350601196289},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.4031296372413635},{"id":"https://openalex.org/keywords/economics","display_name":"Economics","score":0.33826708793640137},{"id":"https://openalex.org/keywords/microeconomics","display_name":"Microeconomics","score":0.2741814851760864},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.21755677461624146},{"id":"https://openalex.org/keywords/chemistry","display_name":"Chemistry","score":0.19838005304336548}],"concepts":[{"id":"https://openalex.org/C109718341","wikidata":"https://www.wikidata.org/wiki/Q1385229","display_name":"Metaheuristic","level":2,"score":0.7332918643951416},{"id":"https://openalex.org/C31829261","wikidata":"https://www.wikidata.org/wiki/Q1929885","display_name":"Transportation theory","level":2,"score":0.6136492490768433},{"id":"https://openalex.org/C2984553159","wikidata":"https://www.wikidata.org/wiki/Q13579421","display_name":"Fixed charge","level":2,"score":0.544093906879425},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.43961647152900696},{"id":"https://openalex.org/C42866809","wikidata":"https://www.wikidata.org/wiki/Q466764","display_name":"Fixed cost","level":2,"score":0.4268350601196289},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.4031296372413635},{"id":"https://openalex.org/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","level":0,"score":0.33826708793640137},{"id":"https://openalex.org/C175444787","wikidata":"https://www.wikidata.org/wiki/Q39072","display_name":"Microeconomics","level":1,"score":0.2741814851760864},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.21755677461624146},{"id":"https://openalex.org/C185592680","wikidata":"https://www.wikidata.org/wiki/Q2329","display_name":"Chemistry","level":0,"score":0.19838005304336548},{"id":"https://openalex.org/C41999313","wikidata":"https://www.wikidata.org/wiki/Q489328","display_name":"Molecular physics","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1080/03155986.2025.2492739","is_oa":false,"landing_page_url":"https://doi.org/10.1080/03155986.2025.2492739","pdf_url":null,"source":{"id":"https://openalex.org/S155959304","display_name":"INFOR Information Systems and Operational Research","issn_l":"0315-5986","issn":["0315-5986","1916-0615"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320547","host_organization_name":"Taylor & Francis","host_organization_lineage":["https://openalex.org/P4310320547"],"host_organization_lineage_names":["Taylor & Francis"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"INFOR: Information Systems and Operational Research","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":40,"referenced_works":["https://openalex.org/W1507872748","https://openalex.org/W1882911873","https://openalex.org/W1978090048","https://openalex.org/W1979519690","https://openalex.org/W2031763823","https://openalex.org/W2057178439","https://openalex.org/W2058324360","https://openalex.org/W2091555994","https://openalex.org/W2110373411","https://openalex.org/W2121501602","https://openalex.org/W2156247500","https://openalex.org/W2394995294","https://openalex.org/W2527287982","https://openalex.org/W2592134595","https://openalex.org/W2611332821","https://openalex.org/W2791170953","https://openalex.org/W2800293417","https://openalex.org/W2943394939","https://openalex.org/W3011016572","https://openalex.org/W3036256279","https://openalex.org/W3095472642","https://openalex.org/W3099238366","https://openalex.org/W3117990902","https://openalex.org/W3118319229","https://openalex.org/W3165201824","https://openalex.org/W3214326829","https://openalex.org/W4220915774","https://openalex.org/W4254857188","https://openalex.org/W4282972627","https://openalex.org/W4283398923","https://openalex.org/W4289884182","https://openalex.org/W4294145498","https://openalex.org/W4308198968","https://openalex.org/W4311827859","https://openalex.org/W4322761032","https://openalex.org/W4376651748","https://openalex.org/W4382938882","https://openalex.org/W4386099988","https://openalex.org/W4386457920","https://openalex.org/W4386914339"],"related_works":["https://openalex.org/W2037829186","https://openalex.org/W2017698890","https://openalex.org/W2069737189","https://openalex.org/W2086797414","https://openalex.org/W2073734055","https://openalex.org/W4253150790","https://openalex.org/W1981364505","https://openalex.org/W2022606608","https://openalex.org/W1998211476","https://openalex.org/W2205233086"],"abstract_inverted_index":{"Efficient":[0],"transportation":[1,38,45,109,134,140,198,302],"of":[2,108,178,186,193,197,209,249],"goods":[3],"is":[4,20,32,59,128,142,199,252],"a":[5,43,71,78,84,100,155,163,206,322],"primary":[6],"economic":[7],"concern":[8],"for":[9,202],"any":[10],"business":[11,156],"organization.":[12],"For":[13,94],"this":[14,69,95,250],"reason,":[15],"research":[16],"on":[17,126,165,170,213],"transportation-related":[18],"issues":[19],"becoming":[21],"increasingly":[22],"important.":[23],"It":[24],"should":[25],"be":[26],"noted":[27],"that":[28,123,145,293],"the":[29,36,56,63,89,92,97,103,131,137,143,149,159,166,171,229,237,255,261,268,280,300,304,309,312,317,331],"shipping":[30],"amount":[31,172],"determined":[33],"by":[34],"taking":[35,236],"unit":[37,64,115,121,133,139],"cost":[39,144,196,240,258],"into":[40,118,242],"account":[41,243],"in":[42,49,68,76,231,286,296],"traditional":[44],"problem":[46],"(TP).":[47],"However,":[48],"reality,":[50],"there":[51],"are":[52,116,180,294,327],"many":[53],"situations":[54],"where":[55],"transported":[57],"quantity":[58,208],"used":[60,279,328],"to":[61,87,91,153,253,298,329],"determine":[62],"cost.":[65],"Regarding":[66],"this,":[67],"work,":[70],"TP":[72],"has":[73,81],"been":[74,221,274],"addressed":[75],"which":[77],"manufacturing":[79],"company":[80],"agreements":[82],"with":[83,158,183,190,205,288],"few":[85,323],"suppliers":[86,98,124,146,161],"deliver":[88],"products":[90,179,182,189],"retailers.":[93],"contract,":[96],"receive":[99],"commission":[101,238],"from":[102],"company.":[104],"Here,":[105,175],"two":[106,176,215,217],"types":[107,177],"costs":[110],"(actual":[111],"and":[112,188,239,259,316],"demanded)":[113],"per":[114],"taken":[117],"account.":[119],"The":[120,195,247],"charge":[122,168],"impose":[125],"retailers":[127],"known":[129],"as":[130,244],"\u2018demanded":[132],"cost\u2019,":[135],"while":[136,235],"\u2018actual":[138],"cost\u2019":[141],"bear":[147],"during":[148],"transportation.":[150],"In":[151],"order":[152],"establish":[154],"relationship":[157],"retailers,":[160],"offer":[162],"discount":[164],"demanded":[167],"based":[169],"they":[173],"receive.":[174],"considered:":[181],"lower":[184],"rate":[185,192],"deterioration":[187],"higher":[191,201],"deterioration.":[194],"relatively":[200],"later":[203],"items":[204],"larger":[207],"deteriorating":[210],"items.":[211],"Based":[212],"these":[214],"categories,":[216],"deterministic":[218],"models":[219,230],"have":[220,226,273,278],"developed":[222],"here.":[223],"Subsequently,":[224],"we":[225,277],"looked":[227],"at":[228],"an":[232],"uncertain":[233],"setting":[234],"parameters":[241],"interval":[245],"numbers.":[246],"objective":[248],"study":[251],"minimize":[254],"retailers\u2019":[256],"overall":[257],"maximize":[260],"suppliers\u2019":[262],"total":[263],"profit":[264],"simultaneously.":[265],"To":[266],"demonstrate":[267],"models,":[269],"four":[270,289],"numerical":[271],"examples":[272],"considered.":[275],"Then":[276],"artificial":[281],"bee":[282],"colony":[283],"(ABC)":[284],"algorithm":[285],"conjunction":[287],"multi-objective":[290,301],"optimization":[291],"techniques":[292],"currently":[295],"use":[297],"solve":[299],"models:":[303],"global":[305],"criterion":[306],"method":[307,315],"(GCM),":[308],"Tchebycheff":[310,314],"method,":[311],"weighted":[313,318],"sum":[319],"method.":[320],"Finally,":[321],"more":[324],"metaheuristic":[325],"algorithms":[326],"compare":[330],"results.":[332]},"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2025,"cited_by_count":1}],"updated_date":"2026-06-14T06:11:07.267592","created_date":"2025-10-10T00:00:00"}
