{"id":"https://openalex.org/W2107879048","doi":"https://doi.org/10.1051/ro/2010010","title":"Lexicographic<i>\u03b1</i>-robustness: an application to the 1-median problem","display_name":"Lexicographic<i>\u03b1</i>-robustness: an application to the 1-median problem","publication_year":2010,"publication_date":"2010-04-01","ids":{"openalex":"https://openalex.org/W2107879048","doi":"https://doi.org/10.1051/ro/2010010","mag":"2107879048"},"language":"en","primary_location":{"id":"doi:10.1051/ro/2010010","is_oa":false,"landing_page_url":"https://doi.org/10.1051/ro/2010010","pdf_url":null,"source":{"id":"https://openalex.org/S20631277","display_name":"RAIRO - Operations Research","issn_l":"0399-0559","issn":["0399-0559","1290-3868"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319748","host_organization_name":"EDP Sciences","host_organization_lineage":["https://openalex.org/P4310319748"],"host_organization_lineage_names":["EDP Sciences"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"RAIRO - Operations 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/A5029743603","display_name":"Rim Kala\u00ef","orcid":null},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"R. Kala\u00ef","raw_affiliation_strings":["Rouen Business School, 1 rue du Mar\u00e9chal Juin, BP 215 \u2013 76825 Mont Saint Aignan Cedex, France; rkj@rouenbs.fr"],"affiliations":[{"raw_affiliation_string":"Rouen Business School, 1 rue du Mar\u00e9chal Juin, BP 215 \u2013 76825 Mont Saint Aignan Cedex, France; rkj@rouenbs.fr","institution_ids":[]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5064116931","display_name":"Mohamed Ali Aloulou","orcid":null},"institutions":[{"id":"https://openalex.org/I56435720","display_name":"Universit\u00e9 Paris Dauphine-PSL","ror":"https://ror.org/052bz7812","country_code":"FR","type":"education","lineage":["https://openalex.org/I2746051580","https://openalex.org/I56435720"]}],"countries":["FR"],"is_corresponding":false,"raw_author_name":"M. A. Aloulou","raw_affiliation_strings":["LAMSADE, Universit\u00e9 Paris-Dauphine, Pl. du Mar\u00e9chal de Lattre de Tassigny, 75775 Paris Cedex 16, France"],"affiliations":[{"raw_affiliation_string":"LAMSADE, Universit\u00e9 Paris-Dauphine, Pl. du Mar\u00e9chal de Lattre de Tassigny, 75775 Paris Cedex 16, France","institution_ids":["https://openalex.org/I56435720"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5109216182","display_name":"Ph. Vallin","orcid":null},"institutions":[{"id":"https://openalex.org/I56435720","display_name":"Universit\u00e9 Paris Dauphine-PSL","ror":"https://ror.org/052bz7812","country_code":"FR","type":"education","lineage":["https://openalex.org/I2746051580","https://openalex.org/I56435720"]}],"countries":["FR"],"is_corresponding":false,"raw_author_name":"Ph. Vallin","raw_affiliation_strings":["LAMSADE, Universit\u00e9 Paris-Dauphine, Pl. du Mar\u00e9chal de Lattre de Tassigny, 75775 Paris Cedex 16, France"],"affiliations":[{"raw_affiliation_string":"LAMSADE, Universit\u00e9 Paris-Dauphine, Pl. du Mar\u00e9chal de Lattre de Tassigny, 75775 Paris Cedex 16, France","institution_ids":["https://openalex.org/I56435720"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5061295470","display_name":"Daniel Vanderpooten","orcid":"https://orcid.org/0000-0002-5934-0603"},"institutions":[{"id":"https://openalex.org/I56435720","display_name":"Universit\u00e9 Paris Dauphine-PSL","ror":"https://ror.org/052bz7812","country_code":"FR","type":"education","lineage":["https://openalex.org/I2746051580","https://openalex.org/I56435720"]}],"countries":["FR"],"is_corresponding":false,"raw_author_name":"D. Vanderpooten","raw_affiliation_strings":["LAMSADE, Universit\u00e9 Paris-Dauphine, Pl. du Mar\u00e9chal de Lattre de Tassigny, 75775 Paris Cedex 16, France"],"affiliations":[{"raw_affiliation_string":"LAMSADE, Universit\u00e9 Paris-Dauphine, Pl. du Mar\u00e9chal de Lattre de Tassigny, 75775 Paris Cedex 16, France","institution_ids":["https://openalex.org/I56435720"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":4,"corresponding_author_ids":["https://openalex.org/A5029743603"],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":1.1731,"has_fulltext":false,"cited_by_count":5,"citation_normalized_percentile":{"value":0.82306447,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":94},"biblio":{"volume":"44","issue":"2","first_page":"119","last_page":"138"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11413","display_name":"Risk and Portfolio Optimization","score":0.9983999729156494,"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/T11413","display_name":"Risk and Portfolio Optimization","score":0.9983999729156494,"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/T11502","display_name":"Facility Location and Emergency Management","score":0.9983999729156494,"subfield":{"id":"https://openalex.org/subfields/1407","display_name":"Organizational Behavior and Human Resource Management"},"field":{"id":"https://openalex.org/fields/14","display_name":"Business, Management and Accounting"},"domain":{"id":"https://openalex.org/domains/2","display_name":"Social Sciences"}},{"id":"https://openalex.org/T10050","display_name":"Multi-Criteria Decision Making","score":0.9973999857902527,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/robustness","display_name":"Robustness (evolution)","score":0.8921011090278625},{"id":"https://openalex.org/keywords/regret","display_name":"Regret","score":0.7354141473770142},{"id":"https://openalex.org/keywords/lexicographical-order","display_name":"Lexicographical order","score":0.6619157791137695},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.6125546097755432},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.495456337928772},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.39521509408950806},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.3297537565231323},{"id":"https://openalex.org/keywords/machine-learning","display_name":"Machine learning","score":0.150888592004776}],"concepts":[{"id":"https://openalex.org/C63479239","wikidata":"https://www.wikidata.org/wiki/Q7353546","display_name":"Robustness (evolution)","level":3,"score":0.8921011090278625},{"id":"https://openalex.org/C50817715","wikidata":"https://www.wikidata.org/wiki/Q79895177","display_name":"Regret","level":2,"score":0.7354141473770142},{"id":"https://openalex.org/C159254197","wikidata":"https://www.wikidata.org/wiki/Q1144915","display_name":"Lexicographical order","level":2,"score":0.6619157791137695},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.6125546097755432},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.495456337928772},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.39521509408950806},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.3297537565231323},{"id":"https://openalex.org/C119857082","wikidata":"https://www.wikidata.org/wiki/Q2539","display_name":"Machine learning","level":1,"score":0.150888592004776},{"id":"https://openalex.org/C185592680","wikidata":"https://www.wikidata.org/wiki/Q2329","display_name":"Chemistry","level":0,"score":0.0},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.0},{"id":"https://openalex.org/C104317684","wikidata":"https://www.wikidata.org/wiki/Q7187","display_name":"Gene","level":2,"score":0.0},{"id":"https://openalex.org/C55493867","wikidata":"https://www.wikidata.org/wiki/Q7094","display_name":"Biochemistry","level":1,"score":0.0}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.1051/ro/2010010","is_oa":false,"landing_page_url":"https://doi.org/10.1051/ro/2010010","pdf_url":null,"source":{"id":"https://openalex.org/S20631277","display_name":"RAIRO - Operations Research","issn_l":"0399-0559","issn":["0399-0559","1290-3868"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319748","host_organization_name":"EDP Sciences","host_organization_lineage":["https://openalex.org/P4310319748"],"host_organization_lineage_names":["EDP Sciences"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"RAIRO - Operations Research","raw_type":"journal-article"},{"id":"pmh:oai:HAL:hal-00565530v1","is_oa":false,"landing_page_url":"https://hal.science/hal-00565530","pdf_url":null,"source":{"id":"https://openalex.org/S4306402512","display_name":"HAL (Le Centre pour la Communication Scientifique Directe)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I1294671590","host_organization_name":"Centre National de la Recherche Scientifique","host_organization_lineage":["https://openalex.org/I1294671590"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"RAIRO - Operations Research, 2010, vol. 44, n\u00b02, pp. 119-138. &#x27E8;10.1051/ro/2010010&#x27E9;","raw_type":"Journal articles"},{"id":"pmh:oai:numdam.org:RO_2010__44_2_119_0","is_oa":false,"landing_page_url":"https://www.numdam.org/articles/10.1051/ro/2010010/","pdf_url":null,"source":{"id":"https://openalex.org/S4306402264","display_name":"French digital mathematics library (Numdam)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I70900168","host_organization_name":"Universit\u00e9 Savoie Mont Blanc","host_organization_lineage":["https://openalex.org/I70900168"],"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":"Text"}],"best_oa_location":null,"sustainable_development_goals":[{"score":0.7799999713897705,"display_name":"Peace, Justice and strong institutions","id":"https://metadata.un.org/sdg/16"}],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":32,"referenced_works":["https://openalex.org/W124714043","https://openalex.org/W275341628","https://openalex.org/W1514117420","https://openalex.org/W1963888335","https://openalex.org/W1970531677","https://openalex.org/W1973862684","https://openalex.org/W1988104153","https://openalex.org/W2005183677","https://openalex.org/W2007208809","https://openalex.org/W2008959214","https://openalex.org/W2013924799","https://openalex.org/W2017571998","https://openalex.org/W2017572120","https://openalex.org/W2022249252","https://openalex.org/W2034083313","https://openalex.org/W2038730428","https://openalex.org/W2039665408","https://openalex.org/W2044028040","https://openalex.org/W2057223621","https://openalex.org/W2063511957","https://openalex.org/W2064646997","https://openalex.org/W2065055074","https://openalex.org/W2098157133","https://openalex.org/W2102750402","https://openalex.org/W2107131517","https://openalex.org/W2127331687","https://openalex.org/W2128751223","https://openalex.org/W2153381804","https://openalex.org/W2165775468","https://openalex.org/W4213074663","https://openalex.org/W4238714550","https://openalex.org/W4253347690"],"related_works":["https://openalex.org/W2971351794","https://openalex.org/W4376155396","https://openalex.org/W1947085858","https://openalex.org/W2174986909","https://openalex.org/W2527791220","https://openalex.org/W2101991911","https://openalex.org/W2155070487","https://openalex.org/W4311589891","https://openalex.org/W3123835761","https://openalex.org/W118270247"],"abstract_inverted_index":{"In":[0,14,48],"the":[1,22,63,69,77,97,112],"last":[2],"decade,":[3],"several":[4],"robustness":[5,25,55],"approaches":[6],"have":[7],"been":[8],"developed":[9],"to":[10,76,92,111],"deal":[11],"with":[12],"uncertainty.":[13],"decision":[15],"problems,":[16,21],"and":[17,86],"particularly":[18],"in":[19,96],"location":[20,79],"most":[23],"used":[24],"approach":[26,75],"rely":[27],"either":[28],"on":[29,33,68,83],"maximal":[30,34],"cost":[31],"or":[32],"regret":[35],"criteria.":[36],"However,":[37],"it":[38],"is":[39],"well":[40],"known":[41],"that":[42,105],"these":[43],"criteria":[44,66],"are":[45],"too":[46],"conservative.":[47],"this":[49,74,106],"paper,":[50],"we":[51,87],"present":[52],"a":[53,89,100,115],"new":[54],"approach,":[56],"called":[57],"lexicographic":[58],"\u03b1-robustness,":[59],"which":[60],"compensates":[61],"for":[62],"drawbacks":[64],"of":[65,99,114],"based":[67],"worst":[70],"case.":[71],"We":[72,102],"apply":[73],"1-median":[78],"problem":[80],"under":[81],"uncertainty":[82],"node":[84],"weights":[85],"give":[88],"specific":[90],"algorithm":[91,107],"determine":[93],"robust":[94],"solutions":[95],"case":[98,113],"tree.":[101],"also":[103],"show":[104],"can":[108],"be":[109],"extended":[110],"general":[116],"network.":[117]},"counts_by_year":[{"year":2019,"cited_by_count":1},{"year":2013,"cited_by_count":1},{"year":2012,"cited_by_count":1}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}
