{"id":"https://openalex.org/W2024826662","doi":"https://doi.org/10.1142/s021759591250011x","title":"A LINEAR BILEVEL PROGRAMMING PROBLEM FOR OBTAINING THE CLOSEST TARGETS AND MINIMUM DISTANCE OF A UNIT FROM THE STRONG EFFICIENT FRONTIER","display_name":"A LINEAR BILEVEL PROGRAMMING PROBLEM FOR OBTAINING THE CLOSEST TARGETS AND MINIMUM DISTANCE OF A UNIT FROM THE STRONG EFFICIENT FRONTIER","publication_year":2012,"publication_date":"2012-04-01","ids":{"openalex":"https://openalex.org/W2024826662","doi":"https://doi.org/10.1142/s021759591250011x","mag":"2024826662"},"language":"en","primary_location":{"id":"doi:10.1142/s021759591250011x","is_oa":false,"landing_page_url":"https://doi.org/10.1142/s021759591250011x","pdf_url":null,"source":{"id":"https://openalex.org/S1254427","display_name":"Asia Pacific Journal of Operational Research","issn_l":"0217-5959","issn":["0217-5959","1793-7019"],"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":"Asia-Pacific Journal of 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/A5075892810","display_name":"G.R. Jahanshahloo","orcid":"https://orcid.org/0000-0003-0380-6416"},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"G. R. JAHANSHAHLOO","raw_affiliation_strings":["Faculty of Mathematical and Computer Sciences, Teacher Training University, 599 Taleghani Avenue, 15618 Tehran, Iran"],"affiliations":[{"raw_affiliation_string":"Faculty of Mathematical and Computer Sciences, Teacher Training University, 599 Taleghani Avenue, 15618 Tehran, Iran","institution_ids":[]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5101616289","display_name":"Javad Vakili","orcid":"https://orcid.org/0000-0002-7100-8961"},"institutions":[{"id":"https://openalex.org/I41832843","display_name":"University of Tabriz","ror":"https://ror.org/01papkj44","country_code":"IR","type":"education","lineage":["https://openalex.org/I41832843"]}],"countries":["IR"],"is_corresponding":false,"raw_author_name":"J. VAKILI","raw_affiliation_strings":["Faculty of Mathematical Sciences and Computer, Tabriz University, 29 Bahman Avenue, Tabriz, Iran","Faculty of Mathematical and Computer Sciences, Teacher Training University, 599 Taleghani Avenue, 15618 Tehran, Iran"],"affiliations":[{"raw_affiliation_string":"Faculty of Mathematical Sciences and Computer, Tabriz University, 29 Bahman Avenue, Tabriz, Iran","institution_ids":["https://openalex.org/I41832843"]},{"raw_affiliation_string":"Faculty of Mathematical and Computer Sciences, Teacher Training University, 599 Taleghani Avenue, 15618 Tehran, Iran","institution_ids":[]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5075003661","display_name":"Masoud Zarepisheh","orcid":"https://orcid.org/0000-0001-6616-5949"},"institutions":[{"id":"https://openalex.org/I158248296","display_name":"Amirkabir University of Technology","ror":"https://ror.org/04gzbav43","country_code":"IR","type":"education","lineage":["https://openalex.org/I158248296"]}],"countries":["IR"],"is_corresponding":false,"raw_author_name":"M. ZAREPISHEH","raw_affiliation_strings":["Faculty of Mathematical Sciences and Computer, Amirkabir University, Tehran, Iran"],"affiliations":[{"raw_affiliation_string":"Faculty of Mathematical Sciences and Computer, Amirkabir University, Tehran, Iran","institution_ids":["https://openalex.org/I158248296"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5075892810"],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":3.3118,"has_fulltext":false,"cited_by_count":29,"citation_normalized_percentile":{"value":0.91878627,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":90,"max":99},"biblio":{"volume":"29","issue":"02","first_page":"1250011","last_page":"1250011"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10357","display_name":"Efficiency Analysis Using DEA","score":0.9997000098228455,"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/T10357","display_name":"Efficiency Analysis Using DEA","score":0.9997000098228455,"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/T12709","display_name":"Optimization and Mathematical Programming","score":0.9939000010490417,"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/T11770","display_name":"Fiscal Policy and Economic Growth","score":0.9855999946594238,"subfield":{"id":"https://openalex.org/subfields/2002","display_name":"Economics and Econometrics"},"field":{"id":"https://openalex.org/fields/20","display_name":"Economics, Econometrics and Finance"},"domain":{"id":"https://openalex.org/domains/2","display_name":"Social Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/data-envelopment-analysis","display_name":"Data envelopment analysis","score":0.8528631329536438},{"id":"https://openalex.org/keywords/linear-programming","display_name":"Linear programming","score":0.7322841882705688},{"id":"https://openalex.org/keywords/unit","display_name":"Unit (ring theory)","score":0.685025691986084},{"id":"https://openalex.org/keywords/efficient-frontier","display_name":"Efficient frontier","score":0.6801676154136658},{"id":"https://openalex.org/keywords/point","display_name":"Point (geometry)","score":0.6298537254333496},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.6274287700653076},{"id":"https://openalex.org/keywords/frontier","display_name":"Frontier","score":0.5997234582901001},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.5676896572113037},{"id":"https://openalex.org/keywords/bilevel-optimization","display_name":"Bilevel optimization","score":0.5440248250961304},{"id":"https://openalex.org/keywords/extension","display_name":"Extension (predicate logic)","score":0.4635566473007202},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.2844344973564148},{"id":"https://openalex.org/keywords/optimization-problem","display_name":"Optimization problem","score":0.2106919288635254},{"id":"https://openalex.org/keywords/economics","display_name":"Economics","score":0.11075061559677124}],"concepts":[{"id":"https://openalex.org/C22088475","wikidata":"https://www.wikidata.org/wiki/Q647974","display_name":"Data envelopment analysis","level":2,"score":0.8528631329536438},{"id":"https://openalex.org/C41045048","wikidata":"https://www.wikidata.org/wiki/Q202843","display_name":"Linear programming","level":2,"score":0.7322841882705688},{"id":"https://openalex.org/C122637931","wikidata":"https://www.wikidata.org/wiki/Q118084","display_name":"Unit (ring theory)","level":2,"score":0.685025691986084},{"id":"https://openalex.org/C51485801","wikidata":"https://www.wikidata.org/wiki/Q16966861","display_name":"Efficient frontier","level":3,"score":0.6801676154136658},{"id":"https://openalex.org/C28719098","wikidata":"https://www.wikidata.org/wiki/Q44946","display_name":"Point (geometry)","level":2,"score":0.6298537254333496},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.6274287700653076},{"id":"https://openalex.org/C2778571376","wikidata":"https://www.wikidata.org/wiki/Q1355821","display_name":"Frontier","level":2,"score":0.5997234582901001},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.5676896572113037},{"id":"https://openalex.org/C3309286","wikidata":"https://www.wikidata.org/wiki/Q4907693","display_name":"Bilevel optimization","level":3,"score":0.5440248250961304},{"id":"https://openalex.org/C2778029271","wikidata":"https://www.wikidata.org/wiki/Q5421931","display_name":"Extension (predicate logic)","level":2,"score":0.4635566473007202},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.2844344973564148},{"id":"https://openalex.org/C137836250","wikidata":"https://www.wikidata.org/wiki/Q984063","display_name":"Optimization problem","level":2,"score":0.2106919288635254},{"id":"https://openalex.org/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","level":0,"score":0.11075061559677124},{"id":"https://openalex.org/C2780821815","wikidata":"https://www.wikidata.org/wiki/Q5340806","display_name":"Portfolio","level":2,"score":0.0},{"id":"https://openalex.org/C145420912","wikidata":"https://www.wikidata.org/wiki/Q853077","display_name":"Mathematics education","level":1,"score":0.0},{"id":"https://openalex.org/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","level":1,"score":0.0},{"id":"https://openalex.org/C95457728","wikidata":"https://www.wikidata.org/wiki/Q309","display_name":"History","level":0,"score":0.0},{"id":"https://openalex.org/C166957645","wikidata":"https://www.wikidata.org/wiki/Q23498","display_name":"Archaeology","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},{"id":"https://openalex.org/C106159729","wikidata":"https://www.wikidata.org/wiki/Q2294553","display_name":"Financial economics","level":1,"score":0.0}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.1142/s021759591250011x","is_oa":false,"landing_page_url":"https://doi.org/10.1142/s021759591250011x","pdf_url":null,"source":{"id":"https://openalex.org/S1254427","display_name":"Asia Pacific Journal of Operational Research","issn_l":"0217-5959","issn":["0217-5959","1793-7019"],"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":"Asia-Pacific Journal of Operational Research","raw_type":"journal-article"},{"id":"pmh:oai:RePEc:wsi:apjorx:v:29:y:2012:i:02:n:s021759591250011x","is_oa":false,"landing_page_url":"http://www.worldscientific.com/doi/abs/10.1142/S021759591250011X","pdf_url":null,"source":{"id":"https://openalex.org/S4306401271","display_name":"RePEc: Research Papers in Economics","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I77793887","host_organization_name":"Federal Reserve Bank of St. Louis","host_organization_lineage":["https://openalex.org/I77793887"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"article"},{"id":"pmh:oai:RePEc:wsi:apjorx:v:29:y:2012:i:02:p:1250011-1-1250011-19","is_oa":false,"landing_page_url":"http://www.worldscinet.com/cgi-bin/details.cgi?type=html&id=pii:S021759591250011X","pdf_url":null,"source":{"id":"https://openalex.org/S4306401271","display_name":"RePEc: Research Papers in Economics","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I77793887","host_organization_name":"Federal Reserve Bank of St. Louis","host_organization_lineage":["https://openalex.org/I77793887"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":25,"referenced_works":["https://openalex.org/W28739319","https://openalex.org/W1495821235","https://openalex.org/W1557851371","https://openalex.org/W1588628884","https://openalex.org/W1605422376","https://openalex.org/W1965703251","https://openalex.org/W1969500956","https://openalex.org/W1976703982","https://openalex.org/W1983202079","https://openalex.org/W2010997912","https://openalex.org/W2015040770","https://openalex.org/W2035726060","https://openalex.org/W2061228544","https://openalex.org/W2062626207","https://openalex.org/W2070657573","https://openalex.org/W2073702850","https://openalex.org/W2076452041","https://openalex.org/W2079173630","https://openalex.org/W2079849653","https://openalex.org/W2110250287","https://openalex.org/W2129763896","https://openalex.org/W2152358062","https://openalex.org/W2163504867","https://openalex.org/W2164679440","https://openalex.org/W4205881252"],"related_works":["https://openalex.org/W1646002931","https://openalex.org/W2392236356","https://openalex.org/W98418551","https://openalex.org/W2101331924","https://openalex.org/W1980707780","https://openalex.org/W2011801048","https://openalex.org/W2364237663","https://openalex.org/W2060124870","https://openalex.org/W2015124671","https://openalex.org/W1534463048"],"abstract_inverted_index":{"Data":[0],"envelopment":[1],"analysis":[2],"(DEA)":[3],"can":[4],"be":[5,108],"used":[6],"for":[7,19,58,94],"assessing":[8],"the":[9,28,60,70,95,100,111,118],"relative":[10],"efficiency":[11],"of":[12,15,66,92,99,117],"a":[13,22,40,53,67],"number":[14],"operating":[16,24],"units,":[17],"finding,":[18],"each":[20],"unit,":[21],"target":[23],"point":[25],"lying":[26],"on":[27],"strong":[29,71],"efficient":[30,72],"frontier.":[31],"Most":[32],"DEA":[33],"models":[34],"project":[35],"an":[36,115],"inefficient":[37],"unit":[38,68],"onto":[39],"most":[41],"distant":[42],"target,":[43],"which":[44],"makes":[45],"its":[46],"attainment":[47],"more":[48],"difficult.":[49],"In":[50],"this":[51,82],"paper,":[52],"linear":[54],"bilevel":[55],"programming":[56],"problem":[57],"obtaining":[59],"closest":[61],"targets":[62,87],"and":[63,97],"minimum":[64],"distance":[65],"from":[69],"frontier":[73],"by":[74],"different":[75],"norms":[76],"is":[77,84,114],"provided.":[78],"The":[79],"idea":[80],"behind":[81],"approach":[83],"that":[85,110],"closer":[86],"determine":[88],"less":[89],"demanding":[90],"levels":[91],"operation":[93],"inputs":[96],"outputs":[98],"units":[101],"to":[102],"perform":[103],"efficiently.":[104],"Finally,":[105],"it":[106],"will":[107],"shown":[109],"proposed":[112],"method":[113],"extension":[116],"existing":[119],"methods.":[120]},"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2025,"cited_by_count":1},{"year":2023,"cited_by_count":1},{"year":2022,"cited_by_count":3},{"year":2021,"cited_by_count":4},{"year":2020,"cited_by_count":3},{"year":2019,"cited_by_count":4},{"year":2018,"cited_by_count":4},{"year":2015,"cited_by_count":2},{"year":2014,"cited_by_count":3},{"year":2013,"cited_by_count":3}],"updated_date":"2026-04-05T17:49:38.594831","created_date":"2025-10-10T00:00:00"}