{"id":"https://openalex.org/W1982280823","doi":"https://doi.org/10.1145/1122480.1122493","title":"Approximation algorithms for 2-stage stochastic optimization problems","display_name":"Approximation algorithms for 2-stage stochastic optimization problems","publication_year":2006,"publication_date":"2006-03-01","ids":{"openalex":"https://openalex.org/W1982280823","doi":"https://doi.org/10.1145/1122480.1122493","mag":"1982280823"},"language":"en","primary_location":{"id":"doi:10.1145/1122480.1122493","is_oa":false,"landing_page_url":"https://doi.org/10.1145/1122480.1122493","pdf_url":null,"source":{"id":"https://openalex.org/S4210206003","display_name":"ACM SIGACT News","issn_l":"0163-5700","issn":["0163-5700","1943-5827"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319798","host_organization_name":"Association for Computing Machinery","host_organization_lineage":["https://openalex.org/P4310319798"],"host_organization_lineage_names":["Association for Computing Machinery"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"ACM SIGACT News","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/A5031968426","display_name":"Chaitanya Swamy","orcid":"https://orcid.org/0000-0003-1108-7941"},"institutions":[{"id":"https://openalex.org/I122411786","display_name":"California Institute of Technology","ror":"https://ror.org/05dxps055","country_code":"US","type":"education","lineage":["https://openalex.org/I122411786"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"Chaitanya Swamy","raw_affiliation_strings":["Center for the Mathematics of Information, Caltech, Pasadena, CA"],"affiliations":[{"raw_affiliation_string":"Center for the Mathematics of Information, Caltech, Pasadena, CA","institution_ids":["https://openalex.org/I122411786"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5030030349","display_name":"David B. Shmoys","orcid":"https://orcid.org/0000-0003-3882-901X"},"institutions":[{"id":"https://openalex.org/I205783295","display_name":"Cornell University","ror":"https://ror.org/05bnh6r87","country_code":"US","type":"education","lineage":["https://openalex.org/I205783295"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"David B. Shmoys","raw_affiliation_strings":["Cornell University, Ithaca, NY","Cornell University (Ithaca, NY);"],"affiliations":[{"raw_affiliation_string":"Cornell University, Ithaca, NY","institution_ids":["https://openalex.org/I205783295"]},{"raw_affiliation_string":"Cornell University (Ithaca, NY);","institution_ids":["https://openalex.org/I205783295"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5031968426"],"corresponding_institution_ids":["https://openalex.org/I122411786"],"apc_list":null,"apc_paid":null,"fwci":13.4703,"has_fulltext":false,"cited_by_count":83,"citation_normalized_percentile":{"value":0.98337322,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":89,"max":99},"biblio":{"volume":"37","issue":"1","first_page":"33","last_page":"46"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10698","display_name":"Transportation Planning and Optimization","score":0.9980999827384949,"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"}},"topics":[{"id":"https://openalex.org/T10698","display_name":"Transportation Planning and Optimization","score":0.9980999827384949,"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"}},{"id":"https://openalex.org/T10328","display_name":"Supply Chain and Inventory Management","score":0.9957000017166138,"subfield":{"id":"https://openalex.org/subfields/1404","display_name":"Management Information Systems"},"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/T10567","display_name":"Vehicle Routing Optimization Methods","score":0.9955999851226807,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/stochastic-programming","display_name":"Stochastic programming","score":0.6868054866790771},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.6810217499732971},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.5363458395004272},{"id":"https://openalex.org/keywords/variety","display_name":"Variety (cybernetics)","score":0.4989888668060303},{"id":"https://openalex.org/keywords/stochastic-optimization","display_name":"Stochastic optimization","score":0.47243818640708923},{"id":"https://openalex.org/keywords/field","display_name":"Field (mathematics)","score":0.47091174125671387},{"id":"https://openalex.org/keywords/probability-distribution","display_name":"Probability distribution","score":0.4404347240924835},{"id":"https://openalex.org/keywords/noise","display_name":"Noise (video)","score":0.4346623718738556},{"id":"https://openalex.org/keywords/robust-optimization","display_name":"Robust optimization","score":0.4111118018627167},{"id":"https://openalex.org/keywords/operations-research","display_name":"Operations research","score":0.36023756861686707},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.16169297695159912},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.12209773063659668}],"concepts":[{"id":"https://openalex.org/C137631369","wikidata":"https://www.wikidata.org/wiki/Q7617831","display_name":"Stochastic programming","level":2,"score":0.6868054866790771},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.6810217499732971},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.5363458395004272},{"id":"https://openalex.org/C136197465","wikidata":"https://www.wikidata.org/wiki/Q1729295","display_name":"Variety (cybernetics)","level":2,"score":0.4989888668060303},{"id":"https://openalex.org/C194387892","wikidata":"https://www.wikidata.org/wiki/Q1747770","display_name":"Stochastic optimization","level":2,"score":0.47243818640708923},{"id":"https://openalex.org/C9652623","wikidata":"https://www.wikidata.org/wiki/Q190109","display_name":"Field (mathematics)","level":2,"score":0.47091174125671387},{"id":"https://openalex.org/C149441793","wikidata":"https://www.wikidata.org/wiki/Q200726","display_name":"Probability distribution","level":2,"score":0.4404347240924835},{"id":"https://openalex.org/C99498987","wikidata":"https://www.wikidata.org/wiki/Q2210247","display_name":"Noise (video)","level":3,"score":0.4346623718738556},{"id":"https://openalex.org/C193254401","wikidata":"https://www.wikidata.org/wiki/Q2160088","display_name":"Robust optimization","level":2,"score":0.4111118018627167},{"id":"https://openalex.org/C42475967","wikidata":"https://www.wikidata.org/wiki/Q194292","display_name":"Operations research","level":1,"score":0.36023756861686707},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.16169297695159912},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.12209773063659668},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.0},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.0},{"id":"https://openalex.org/C115961682","wikidata":"https://www.wikidata.org/wiki/Q860623","display_name":"Image (mathematics)","level":2,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1145/1122480.1122493","is_oa":false,"landing_page_url":"https://doi.org/10.1145/1122480.1122493","pdf_url":null,"source":{"id":"https://openalex.org/S4210206003","display_name":"ACM SIGACT News","issn_l":"0163-5700","issn":["0163-5700","1943-5827"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319798","host_organization_name":"Association for Computing Machinery","host_organization_lineage":["https://openalex.org/P4310319798"],"host_organization_lineage_names":["Association for Computing Machinery"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"ACM SIGACT News","raw_type":"journal-article"},{"id":"pmh:oai:authors.library.caltech.edu:73012","is_oa":false,"landing_page_url":"https://authors.library.caltech.edu/73012/","pdf_url":null,"source":{"id":"https://openalex.org/S4306402161","display_name":"CaltechAUTHORS (California Institute of Technology)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I122411786","host_organization_name":"California Institute of Technology","host_organization_lineage":["https://openalex.org/I122411786"],"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":40,"referenced_works":["https://openalex.org/W347166089","https://openalex.org/W569789896","https://openalex.org/W1484951415","https://openalex.org/W1490324987","https://openalex.org/W1523452202","https://openalex.org/W1528210381","https://openalex.org/W1560324410","https://openalex.org/W1569990960","https://openalex.org/W1579824288","https://openalex.org/W1601567149","https://openalex.org/W1696776098","https://openalex.org/W1752958389","https://openalex.org/W1779964607","https://openalex.org/W1974114807","https://openalex.org/W1980412153","https://openalex.org/W1981673685","https://openalex.org/W1983916623","https://openalex.org/W2000257769","https://openalex.org/W2001139415","https://openalex.org/W2002285507","https://openalex.org/W2044081853","https://openalex.org/W2057974767","https://openalex.org/W2090343757","https://openalex.org/W2105088727","https://openalex.org/W2107989318","https://openalex.org/W2109156431","https://openalex.org/W2112058494","https://openalex.org/W2116509768","https://openalex.org/W2117399775","https://openalex.org/W2119297255","https://openalex.org/W2125295283","https://openalex.org/W2131552728","https://openalex.org/W2134396776","https://openalex.org/W2139841919","https://openalex.org/W2140844111","https://openalex.org/W2142092335","https://openalex.org/W2143863355","https://openalex.org/W2502170570","https://openalex.org/W3125256586","https://openalex.org/W4251495539"],"related_works":["https://openalex.org/W175006096","https://openalex.org/W2180949474","https://openalex.org/W4293570283","https://openalex.org/W4389463731","https://openalex.org/W4310823612","https://openalex.org/W2740343970","https://openalex.org/W4317569546","https://openalex.org/W2084062606","https://openalex.org/W2127388103","https://openalex.org/W2105067139"],"abstract_inverted_index":{"Uncertainty":[0],"is":[1,104,133,162,204,253,290,382],"a":[2,31,40,82,205,216,269,272,367,402,410],"facet":[3],"of":[4,46,54,66,85,200,245,248,262],"many":[5],"decision":[6,319],"environments":[7],"and":[8,69,75,93,98,155,191,219,243,250,257,370,423],"might":[9,299],"arise":[10],"for":[11,259,334,419],"various":[12],"reasons,":[13],"such":[14],"as":[15,169],"unpredictable":[16],"information":[17,114,213,310,327],"revealed":[18,158],"in":[19,63,72,81,101,184,321],"the":[20,47,64,73,105,118,130,137,146,152,157,165,172,188,223,228,232,246,287,295,312,316,322,329,335,348,360,375,383,397,420,428],"future,":[21],"or":[22,57,307],"inherent":[23],"fluctuations":[24],"caused":[25],"by":[26,36,39,362],"noise.":[27],"Stochastic":[28],"optimization":[29],"provides":[30],"means":[32],"to":[33,136,150,163,170,187,222,255,275,278,282,302,344,354,373,378],"handle":[34],"uncertainty":[35],"modeling":[37],"it":[38],"probability":[41],"distribution":[42],"over":[43],"possible":[44],"realizations":[45],"actual":[48,131],"data,":[49,119],"called":[50],"scenarios.":[51],"The":[52,160,177,390],"field":[53],"stochastic":[55,58,102,385],"optimization,":[56],"programming,":[59],"has":[60,76,274],"its":[61],"roots":[62],"work":[65],"Dantzig":[67],"[4]":[68],"Beale":[70],"[1]":[71],"1950s,":[74],"since":[77],"increasingly":[78],"found":[79],"application":[80],"wide":[83],"variety":[84],"areas,":[86],"including":[87],"transportation":[88],"models,":[89],"logistics,":[90],"financial":[91],"instruments,":[92],"network":[94],"design.":[95],"An":[96],"important":[97],"widely-used":[99],"model":[100,108],"programming":[103],"2-stage":[106,384],"recourse":[107,140,178,368,391],":":[109],"first,":[110],"given":[111,324],"only":[112,211,325],"distributional":[113,326],"about":[115,311,328],"(some":[116],"of)":[117],"one":[120,298,339],"commits":[121],"on":[122,427],"initial":[123,166],"(":[124],"first-stage":[125],")":[126,149],"actions.":[127],"Then,":[128],"once":[129,347],"data":[132,333],"realized":[134,352,376,429],"according":[135,353],"distribution,":[138,356],"further":[139],"actions":[141,167,179],"can":[142,238,358],"be":[143,239,300,417],"taken":[144],"(in":[145],"second":[147],"stage":[148],"augment":[151],"earlier":[153],"solution":[154,361],"satisfy":[156],"requirements.":[159],"aim":[161],"choose":[164],"so":[168],"minimize":[171],"expected":[173],"total":[174],"cost":[175],"incurred.":[176],"typically":[180],"entail":[181],"making":[182],"decisions":[183,197,221],"rapid":[185],"reaction":[186],"observed":[189],"scenario,":[190],"are":[192,234,351,393],"therefore":[193],"more":[194,364],"costly":[195],"than":[196,396],"made":[198],"ahead":[199],"time.":[201],"Thus":[202],"there":[203],"trade-off":[206],"between":[207],"committing":[208],"initially,":[209],"having":[210],"imprecise":[212],"while":[214],"incurring":[215,366],"lower":[217],"cost,":[218,369],"deferring":[220],"second-stage,":[224],"when":[225],"we":[226,357,371],"know":[227],"input":[229],"precisely":[230,293],"but":[231,297],"costs":[233,392,415],"higher.":[235],"Many":[236],"applications":[237],"modeled":[240],"this":[241,260,355],"way,":[242],"much":[244],"textbook":[247],"Birge":[249],"Louveaux":[251],"[2]":[252],"devoted":[254],"models":[256,306],"algorithms":[258],"class":[261],"problems.":[263],"A":[264],"commonly":[265],"cited":[266],"example":[267],"involves":[268],"setting":[270],"where":[271,277],"company":[273],"decide":[276,341],"set":[279],"up":[280],"facilities":[281,343],"serve":[283],"client":[284,349],"demands.":[285,313],"Typically":[286],"demand":[288],"pattern":[289],"not":[291],"known":[292],"at":[294],"outset,":[296],"able":[301],"obtain,":[303],"through":[304],"simulation":[305],"surveys,":[308],"statistical":[309],"This":[314,381],"motivates":[315],"following":[317],"2-step":[318],"process:":[320],"first-stage,":[323],"demands":[330,350,377],"(and":[331],"deterministic":[332],"facility":[336,387,403],"opening":[337,363,401],"costs),":[338],"must":[340],"which":[342],"open":[345,379],"initially;":[346],"extend":[359],"facilities,":[365,422],"have":[372],"assign":[374],"facilities.":[380],"uncapacitated":[386],"location":[388],"problem.":[389],"usually":[394],"higher":[395],"original":[398],"ones":[399],"(because":[400],"later":[404],"would":[405],"involve":[406],"deploying":[407],"resources":[408],"with":[409],"small":[411],"lead":[412],"time);":[413],"these":[414],"could":[416,424],"different":[418,421],"even":[425],"depend":[426],"scenario.":[430]},"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2025,"cited_by_count":1},{"year":2024,"cited_by_count":3},{"year":2023,"cited_by_count":2},{"year":2022,"cited_by_count":5},{"year":2021,"cited_by_count":3},{"year":2020,"cited_by_count":3},{"year":2019,"cited_by_count":2},{"year":2018,"cited_by_count":3},{"year":2017,"cited_by_count":3},{"year":2016,"cited_by_count":6},{"year":2015,"cited_by_count":3},{"year":2014,"cited_by_count":4},{"year":2013,"cited_by_count":4},{"year":2012,"cited_by_count":1}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}
