{"id":"https://openalex.org/W4285022204","doi":"https://doi.org/10.1155/2022/7596736","title":"Additive Slack-Based Measure for a Two-Stage Structure with Shared Inputs and Undesirable Feedback","display_name":"Additive Slack-Based Measure for a Two-Stage Structure with Shared Inputs and Undesirable Feedback","publication_year":2022,"publication_date":"2022-07-11","ids":{"openalex":"https://openalex.org/W4285022204","doi":"https://doi.org/10.1155/2022/7596736"},"language":"en","primary_location":{"id":"doi:10.1155/2022/7596736","is_oa":true,"landing_page_url":"https://doi.org/10.1155/2022/7596736","pdf_url":"https://downloads.hindawi.com/journals/aor/2022/7596736.pdf","source":{"id":"https://openalex.org/S33782831","display_name":"Advances in Operations Research","issn_l":"1687-9147","issn":["1687-9147","1687-9155"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319869","host_organization_name":"Hindawi Publishing Corporation","host_organization_lineage":["https://openalex.org/P4310319869"],"host_organization_lineage_names":["Hindawi Publishing Corporation"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Advances in Operations Research","raw_type":"journal-article"},"type":"article","indexed_in":["crossref","doaj"],"open_access":{"is_oa":true,"oa_status":"hybrid","oa_url":"https://downloads.hindawi.com/journals/aor/2022/7596736.pdf","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5054974568","display_name":"Maziar Salahi","orcid":"https://orcid.org/0000-0002-0430-3063"},"institutions":[{"id":"https://openalex.org/I877176835","display_name":"University of Guilan","ror":"https://ror.org/01bdr6121","country_code":"IR","type":"education","lineage":["https://openalex.org/I877176835"]}],"countries":["IR"],"is_corresponding":true,"raw_author_name":"M. Salahi","raw_affiliation_strings":["Center of Excellence for Mathematical Modeling, Optimization and Combinatorial Computing (MMOCC), University of Guilan, P.O. Box 1914, Rasht, Iran","Department of Applied Mathematics, Faculty of Mathematical Sciences, University of Guilan, P.O. Box 1914, Rasht, Iran"],"raw_orcid":"https://orcid.org/0000-0002-0430-3063","affiliations":[{"raw_affiliation_string":"Center of Excellence for Mathematical Modeling, Optimization and Combinatorial Computing (MMOCC), University of Guilan, P.O. Box 1914, Rasht, Iran","institution_ids":["https://openalex.org/I877176835"]},{"raw_affiliation_string":"Department of Applied Mathematics, Faculty of Mathematical Sciences, University of Guilan, P.O. Box 1914, Rasht, Iran","institution_ids":["https://openalex.org/I877176835"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5024085924","display_name":"Ali Jamalian","orcid":"https://orcid.org/0000-0001-6237-3118"},"institutions":[{"id":"https://openalex.org/I877176835","display_name":"University of Guilan","ror":"https://ror.org/01bdr6121","country_code":"IR","type":"education","lineage":["https://openalex.org/I877176835"]}],"countries":["IR"],"is_corresponding":false,"raw_author_name":"A. Jamalian","raw_affiliation_strings":["Department of Computer Science, Faculty of Mathematical Sciences, University of Guilan, P.O. Box 1914, Rasht, Iran"],"raw_orcid":"https://orcid.org/0000-0001-6237-3118","affiliations":[{"raw_affiliation_string":"Department of Computer Science, Faculty of Mathematical Sciences, University of Guilan, P.O. Box 1914, Rasht, Iran","institution_ids":["https://openalex.org/I877176835"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5015993534","display_name":"Rita Shakouri","orcid":"https://orcid.org/0000-0003-2175-1519"},"institutions":[{"id":"https://openalex.org/I4210089766","display_name":"Technical and Vocational University","ror":"https://ror.org/00854zy02","country_code":"IR","type":"education","lineage":["https://openalex.org/I4210089766"]}],"countries":["IR"],"is_corresponding":false,"raw_author_name":"R. Shakouri","raw_affiliation_strings":["Department of Computer Engineering, Faculty of Mathematical Sciences, Technical and Vocational University (TVU), Tehran, Iran"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Computer Engineering, Faculty of Mathematical Sciences, Technical and Vocational University (TVU), Tehran, Iran","institution_ids":["https://openalex.org/I4210089766"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5074923210","display_name":"Keyvan Asanimoghadam","orcid":null},"institutions":[{"id":"https://openalex.org/I877176835","display_name":"University of Guilan","ror":"https://ror.org/01bdr6121","country_code":"IR","type":"education","lineage":["https://openalex.org/I877176835"]}],"countries":["IR"],"is_corresponding":false,"raw_author_name":"K. Asanimoghadam","raw_affiliation_strings":["Center of Excellence for Mathematical Modeling, Optimization and Combinatorial Computing (MMOCC), University of Guilan, P.O. Box 1914, Rasht, Iran","Department of Applied Mathematics, Faculty of Mathematical Sciences, University of Guilan, P.O. Box 1914, Rasht, Iran"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Center of Excellence for Mathematical Modeling, Optimization and Combinatorial Computing (MMOCC), University of Guilan, P.O. Box 1914, Rasht, Iran","institution_ids":["https://openalex.org/I877176835"]},{"raw_affiliation_string":"Department of Applied Mathematics, Faculty of Mathematical Sciences, University of Guilan, P.O. Box 1914, Rasht, Iran","institution_ids":["https://openalex.org/I877176835"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":4,"corresponding_author_ids":["https://openalex.org/A5054974568"],"corresponding_institution_ids":["https://openalex.org/I877176835"],"apc_list":{"value":1025,"currency":"USD","value_usd":1025},"apc_paid":{"value":1025,"currency":"USD","value_usd":1025},"fwci":1.0132,"has_fulltext":true,"cited_by_count":6,"citation_normalized_percentile":{"value":0.78114683,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":97},"biblio":{"volume":"2022","issue":null,"first_page":"1","last_page":"14"},"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/T10050","display_name":"Multi-Criteria Decision Making","score":0.9767000079154968,"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":0.9598000049591064,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/weighting","display_name":"Weighting","score":0.6928989291191101},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.6457504034042358},{"id":"https://openalex.org/keywords/data-envelopment-analysis","display_name":"Data envelopment analysis","score":0.6382092237472534},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.6137641072273254},{"id":"https://openalex.org/keywords/measure","display_name":"Measure (data warehouse)","score":0.5998640060424805},{"id":"https://openalex.org/keywords/sensitivity","display_name":"Sensitivity (control systems)","score":0.5334620475769043},{"id":"https://openalex.org/keywords/additive-model","display_name":"Additive model","score":0.4677486717700958},{"id":"https://openalex.org/keywords/parametric-statistics","display_name":"Parametric statistics","score":0.4565538763999939},{"id":"https://openalex.org/keywords/goal-programming","display_name":"Goal programming","score":0.450197696685791},{"id":"https://openalex.org/keywords/parametric-programming","display_name":"Parametric programming","score":0.4296118915081024},{"id":"https://openalex.org/keywords/multi-objective-optimization","display_name":"Multi-objective optimization","score":0.4128572344779968},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.23970061540603638},{"id":"https://openalex.org/keywords/data-mining","display_name":"Data mining","score":0.14243084192276},{"id":"https://openalex.org/keywords/statistics","display_name":"Statistics","score":0.13085150718688965}],"concepts":[{"id":"https://openalex.org/C183115368","wikidata":"https://www.wikidata.org/wiki/Q856577","display_name":"Weighting","level":2,"score":0.6928989291191101},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.6457504034042358},{"id":"https://openalex.org/C22088475","wikidata":"https://www.wikidata.org/wiki/Q647974","display_name":"Data envelopment analysis","level":2,"score":0.6382092237472534},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.6137641072273254},{"id":"https://openalex.org/C2780009758","wikidata":"https://www.wikidata.org/wiki/Q6804172","display_name":"Measure (data warehouse)","level":2,"score":0.5998640060424805},{"id":"https://openalex.org/C21200559","wikidata":"https://www.wikidata.org/wiki/Q7451068","display_name":"Sensitivity (control systems)","level":2,"score":0.5334620475769043},{"id":"https://openalex.org/C203223496","wikidata":"https://www.wikidata.org/wiki/Q4681344","display_name":"Additive model","level":2,"score":0.4677486717700958},{"id":"https://openalex.org/C117251300","wikidata":"https://www.wikidata.org/wiki/Q1849855","display_name":"Parametric statistics","level":2,"score":0.4565538763999939},{"id":"https://openalex.org/C61157135","wikidata":"https://www.wikidata.org/wiki/Q1345279","display_name":"Goal programming","level":2,"score":0.450197696685791},{"id":"https://openalex.org/C2776045410","wikidata":"https://www.wikidata.org/wiki/Q25111241","display_name":"Parametric programming","level":3,"score":0.4296118915081024},{"id":"https://openalex.org/C68781425","wikidata":"https://www.wikidata.org/wiki/Q2052203","display_name":"Multi-objective optimization","level":2,"score":0.4128572344779968},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.23970061540603638},{"id":"https://openalex.org/C124101348","wikidata":"https://www.wikidata.org/wiki/Q172491","display_name":"Data mining","level":1,"score":0.14243084192276},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.13085150718688965},{"id":"https://openalex.org/C24326235","wikidata":"https://www.wikidata.org/wiki/Q126095","display_name":"Electronic engineering","level":1,"score":0.0},{"id":"https://openalex.org/C126838900","wikidata":"https://www.wikidata.org/wiki/Q77604","display_name":"Radiology","level":1,"score":0.0},{"id":"https://openalex.org/C127413603","wikidata":"https://www.wikidata.org/wiki/Q11023","display_name":"Engineering","level":0,"score":0.0},{"id":"https://openalex.org/C119857082","wikidata":"https://www.wikidata.org/wiki/Q2539","display_name":"Machine learning","level":1,"score":0.0},{"id":"https://openalex.org/C71924100","wikidata":"https://www.wikidata.org/wiki/Q11190","display_name":"Medicine","level":0,"score":0.0}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.1155/2022/7596736","is_oa":true,"landing_page_url":"https://doi.org/10.1155/2022/7596736","pdf_url":"https://downloads.hindawi.com/journals/aor/2022/7596736.pdf","source":{"id":"https://openalex.org/S33782831","display_name":"Advances in Operations Research","issn_l":"1687-9147","issn":["1687-9147","1687-9155"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319869","host_organization_name":"Hindawi Publishing Corporation","host_organization_lineage":["https://openalex.org/P4310319869"],"host_organization_lineage_names":["Hindawi Publishing Corporation"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Advances in Operations Research","raw_type":"journal-article"},{"id":"pmh:oai:RePEc:hin:jnlaor:7596736","is_oa":false,"landing_page_url":"http://downloads.hindawi.com/journals/aor/2022/7596736.xml","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:doaj.org/article:66ab89ab528e405bbe78963ca5f8c62f","is_oa":true,"landing_page_url":"https://doaj.org/article/66ab89ab528e405bbe78963ca5f8c62f","pdf_url":null,"source":{"id":"https://openalex.org/S4306401280","display_name":"DOAJ (DOAJ: Directory of Open Access Journals)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by-sa","license_id":"https://openalex.org/licenses/cc-by-sa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Advances in Operations Research, Vol 2022 (2022)","raw_type":"article"}],"best_oa_location":{"id":"doi:10.1155/2022/7596736","is_oa":true,"landing_page_url":"https://doi.org/10.1155/2022/7596736","pdf_url":"https://downloads.hindawi.com/journals/aor/2022/7596736.pdf","source":{"id":"https://openalex.org/S33782831","display_name":"Advances in Operations Research","issn_l":"1687-9147","issn":["1687-9147","1687-9155"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319869","host_organization_name":"Hindawi Publishing Corporation","host_organization_lineage":["https://openalex.org/P4310319869"],"host_organization_lineage_names":["Hindawi Publishing Corporation"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Advances in Operations Research","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[],"funders":[{"id":"https://openalex.org/F4320310963","display_name":"University of Guilan","ror":"https://ror.org/01bdr6121"}],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W4285022204.pdf","grobid_xml":"https://content.openalex.org/works/W4285022204.grobid-xml"},"referenced_works_count":42,"referenced_works":["https://openalex.org/W1549121604","https://openalex.org/W1880945528","https://openalex.org/W1971326325","https://openalex.org/W1993147828","https://openalex.org/W2007148289","https://openalex.org/W2009366868","https://openalex.org/W2028035046","https://openalex.org/W2029070506","https://openalex.org/W2030083085","https://openalex.org/W2033229193","https://openalex.org/W2038622556","https://openalex.org/W2052228606","https://openalex.org/W2076452041","https://openalex.org/W2081384722","https://openalex.org/W2098704515","https://openalex.org/W2274876774","https://openalex.org/W2506753585","https://openalex.org/W2510861287","https://openalex.org/W2757025317","https://openalex.org/W2783217860","https://openalex.org/W2793441897","https://openalex.org/W2804484902","https://openalex.org/W2807052537","https://openalex.org/W2894410346","https://openalex.org/W2895123307","https://openalex.org/W2900084105","https://openalex.org/W2907814553","https://openalex.org/W2924808362","https://openalex.org/W2940868936","https://openalex.org/W2947048163","https://openalex.org/W2973498489","https://openalex.org/W2992655797","https://openalex.org/W2993008480","https://openalex.org/W3035144317","https://openalex.org/W3044708479","https://openalex.org/W3091978616","https://openalex.org/W3110986569","https://openalex.org/W3154521658","https://openalex.org/W3179690408","https://openalex.org/W3215224923","https://openalex.org/W4200350189","https://openalex.org/W4243871258"],"related_works":["https://openalex.org/W2801360836","https://openalex.org/W2120745168","https://openalex.org/W1992157395","https://openalex.org/W3135346546","https://openalex.org/W99158474","https://openalex.org/W3035598753","https://openalex.org/W228145510","https://openalex.org/W1538731551","https://openalex.org/W4379507615","https://openalex.org/W2939422270"],"abstract_inverted_index":{"The":[0,116],"two-stage":[1,19,25],"data":[2],"envelopment":[3],"analysis":[4,243],"models":[5,148],"are":[6,55,199],"among":[7],"the":[8,16,47,64,80,92,99,108,146,150,153,176,179,184,187,194,203,211,219,226,233,236],"widely":[9],"used":[10],"mathematical":[11],"programming":[12,103],"approaches":[13],"to":[14,45,111,137,231],"evaluate":[15,46],"performance":[17,162],"of":[18,101,107,114,164,178,186,235],"structures.":[20],"In":[21,78],"this":[22],"paper,":[23],"a":[24,123,129,142,165,240],"structure":[26],"with":[27,225],"shared":[28],"inputs":[29],"and":[30,49,160,190],"feedback":[31],"is":[32,43,120,128,141,156,222,244],"studied.":[33],"To":[34],"reduce":[35],"undesirable":[36,53,88],"outputs,":[37,89],"an":[38],"additive":[39],"slack-based":[40],"measure":[41],"model":[42,110,119,155],"proposed":[44,81,117,154],"stages":[48,189],"overall":[50,180,220],"efficiencies,":[51,69],"while":[52],"outputs":[54,86],"weakly":[56],"disposable.":[57],"As":[58],"it":[59],"does":[60],"not":[61],"require":[62],"determining":[63],"weights":[65],"for":[66,94,158,191],"combining":[67],"stages\u2019":[68,73],"all":[70,192],"Pareto":[71],"optimal":[72],"efficiencies":[74,185],"can":[75,83,134],"be":[76,135],"gained.":[77],"addition,":[79],"approach":[82],"identify":[84],"desirable":[85],"from":[87,98],"thereby":[90],"avoiding":[91],"need":[93],"weighting.":[95],"This":[96,140],"advantage":[97],"aspect":[100],"multiobjective":[102],"helps":[104],"internal":[105],"evaluation":[106],"network":[109],"match":[112],"priorities":[113],"managers.":[115],"nonlinear":[118],"reformulated":[121],"as":[122],"second-order":[124],"cone":[125],"program,":[126],"which":[127],"convex":[130],"optimization":[131],"problem":[132],"that":[133,175,218],"solved":[136],"global":[138],"optimality.":[139],"computational":[143],"improvement":[144],"over":[145],"parametric":[147],"in":[149,170,207],"literature.":[151],"Furthermore,":[152],"applied":[157],"country-wise":[159],"area-wise":[161],"evaluations":[163],"real":[166],"industrial":[167],"application":[168],"dataset":[169],"mainland":[171],"China.":[172],"Results":[173],"show":[174,217,232],"efficiency":[177,197,221],"system":[181],"relies":[182],"between":[183],"two":[188],"DMUs,":[193],"first":[195],"stage\u2019s":[196],"scores":[198],"always":[200],"higher":[201],"than":[202],"second":[204],"stage":[205],"ones":[206],"both":[208],"evaluations.":[209],"Also,":[210],"Pearson":[212],"correlation":[213],"coefficient":[214],"test":[215],"results":[216],"more":[223],"correlated":[224],"waste":[227],"disposal":[228],"stage.":[229],"Finally,":[230],"effect":[234],"decision":[237],"maker\u2019s":[238],"preference,":[239],"detailed":[241],"sensitivity":[242],"performed.":[245]},"counts_by_year":[{"year":2025,"cited_by_count":1},{"year":2024,"cited_by_count":3},{"year":2023,"cited_by_count":1},{"year":2022,"cited_by_count":1}],"updated_date":"2026-05-21T06:26:12.895304","created_date":"2025-10-10T00:00:00"}