{"id":"https://openalex.org/W2069433571","doi":"https://doi.org/10.1080/01621459.1962.10482155","title":"Chance Constraints and Normal Deviates","display_name":"Chance Constraints and Normal Deviates","publication_year":1962,"publication_date":"1962-03-01","ids":{"openalex":"https://openalex.org/W2069433571","doi":"https://doi.org/10.1080/01621459.1962.10482155","mag":"2069433571"},"language":"en","primary_location":{"id":"doi:10.1080/01621459.1962.10482155","doi":"https://doi.org/10.1080/01621459.1962.10482155","is_oa":false,"landing_page_url":"https://doi.org/10.1080/01621459.1962.10482155","pdf_url":null,"source":{"id":"https://openalex.org/S4394736638","display_name":"Journal of the American Statistical Association","issn_l":"0162-1459","issn":["0162-1459","1537-274X"],"is_oa":false,"is_in_doaj":false,"is_core":true,"listed_in":["abdc-a-star","anvur-class-a","anvur-scientific","cwts-core","dongbi-a","doyens","jufo-3","ki-jl-3","norway-2","poland-200","russia-white-list-1","vabb-shw"],"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Journal of the American Statistical Association","raw_type":"journal-article"},"volume":null,"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/A5043185084","display_name":"A. Charnes","orcid":null,"observed_orcids":[]},"institutions":[{"id":"https://openalex.org/I111979921","display_name":"Northwestern University","ror":"https://ror.org/000e0be47","country_code":"US","type":"education","lineage":["https://openalex.org/I111979921"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"A. Charnes","raw_affiliation_strings":["Northwestern University, USA"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Northwestern University, USA","institution_ids":["https://openalex.org/I111979921"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5109004846","display_name":"William White Cooper","orcid":null,"observed_orcids":[]},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"W. W. Cooper","raw_affiliation_strings":["Carnegie Institute of Technology, USA"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Carnegie Institute of Technology, USA","institution_ids":[]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":3.1581,"has_fulltext":false,"cited_by_count":207,"citation_normalized_percentile":{"value":0.90726817,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":97,"max":100},"biblio":{"volume":"57","issue":"297","first_page":"134","last_page":"134"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11413","display_name":"Risk and Portfolio Optimization","score":0.9663000106811523,"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":0.9663000106811523,"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":0.02800000086426735,"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/T13706","display_name":"Management and Optimization Techniques","score":0.000699999975040555,"subfield":{"id":"https://openalex.org/subfields/1408","display_name":"Strategy and 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"}}],"keywords":[{"id":"https://openalex.org/keywords/chance-constrained-programming","display_name":"chance-constrained programming","score":0.906000018119812},{"id":"https://openalex.org/keywords/linear-programming","display_name":"linear programming","score":0.8130000233650208},{"id":"https://openalex.org/keywords/duality","display_name":"duality","score":0.7200000286102295},{"id":"https://openalex.org/keywords/ship-chartering","display_name":"ship chartering","score":0.5720000267028809},{"id":"https://openalex.org/keywords/demand-uncertainty","display_name":"demand uncertainty","score":0.6970000267028809},{"id":"https://openalex.org/keywords/linear-decision-rules","display_name":"linear decision rules","score":0.8389999866485596},{"id":"https://openalex.org/keywords/risk-assessment","display_name":"risk assessment","score":0.8379999995231628},{"id":"https://openalex.org/keywords/quality-levels","display_name":"quality levels","score":0.5260000228881836},{"id":"https://openalex.org/keywords/chance-constraints","display_name":"chance constraints","score":0.5389999747276306}],"concepts":[{"id":"https://openalex.org/C41045048","wikidata":"https://www.wikidata.org/wiki/Q202843","display_name":"Linear programming","level":2,"score":0.6329101324081421},{"id":"https://openalex.org/C2777212361","wikidata":"https://www.wikidata.org/wiki/Q5127848","display_name":"Class (philosophy)","level":2,"score":0.6291978359222412},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.6139749884605408},{"id":"https://openalex.org/C2778023678","wikidata":"https://www.wikidata.org/wiki/Q554403","display_name":"Duality (order theory)","level":2,"score":0.6118955016136169},{"id":"https://openalex.org/C2779343474","wikidata":"https://www.wikidata.org/wiki/Q3109175","display_name":"Context (archaeology)","level":2,"score":0.5314491987228394},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.48958882689476013},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.46473148465156555},{"id":"https://openalex.org/C84135550","wikidata":"https://www.wikidata.org/wiki/Q3154022","display_name":"Linear inequality","level":3,"score":0.4576219320297241},{"id":"https://openalex.org/C115527620","wikidata":"https://www.wikidata.org/wiki/Q769909","display_name":"Nonlinear programming","level":3,"score":0.4293242394924164},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.38533875346183777},{"id":"https://openalex.org/C45555294","wikidata":"https://www.wikidata.org/wiki/Q28113351","display_name":"Inequality","level":2,"score":0.2811274528503418},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.1089925467967987},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.1038038432598114},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.0},{"id":"https://openalex.org/C151730666","wikidata":"https://www.wikidata.org/wiki/Q7205","display_name":"Paleontology","level":1,"score":0.0},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.0},{"id":"https://openalex.org/C86803240","wikidata":"https://www.wikidata.org/wiki/Q420","display_name":"Biology","level":0,"score":0.0},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1080/01621459.1962.10482155","doi":"https://doi.org/10.1080/01621459.1962.10482155","is_oa":false,"landing_page_url":"https://doi.org/10.1080/01621459.1962.10482155","pdf_url":null,"source":{"id":"https://openalex.org/S4394736638","display_name":"Journal of the American Statistical Association","issn_l":"0162-1459","issn":["0162-1459","1537-274X"],"is_oa":false,"is_in_doaj":false,"is_core":true,"listed_in":["abdc-a-star","anvur-class-a","anvur-scientific","cwts-core","dongbi-a","doyens","jufo-3","ki-jl-3","norway-2","poland-200","russia-white-list-1","vabb-shw"],"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Journal of the American Statistical Association","raw_type":"journal-article"},{"id":"doi:10.2307/2282444","doi":"https://doi.org/10.2307/2282444","is_oa":false,"landing_page_url":"https://doi.org/10.2307/2282444","pdf_url":null,"source":{"id":"https://openalex.org/S4394736638","display_name":"Journal of the American Statistical Association","issn_l":"0162-1459","issn":["0162-1459","1537-274X"],"is_oa":false,"is_in_doaj":false,"is_core":true,"listed_in":["abdc-a-star","anvur-class-a","anvur-scientific","cwts-core","dongbi-a","doyens","jufo-3","ki-jl-3","norway-2","poland-200","russia-white-list-1","vabb-shw"],"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Journal of the American Statistical Association","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[],"study_designs":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":14,"referenced_works":["https://openalex.org/W2002804835","https://openalex.org/W2049606892","https://openalex.org/W2132670515","https://openalex.org/W2142123535","https://openalex.org/W2143863355","https://openalex.org/W2152358062","https://openalex.org/W2158550687","https://openalex.org/W2307105123","https://openalex.org/W2316506176","https://openalex.org/W2341171179","https://openalex.org/W4231530765","https://openalex.org/W4248313157","https://openalex.org/W4255783720","https://openalex.org/W4285719527"],"related_works":["https://openalex.org/W2032031645","https://openalex.org/W3033874439","https://openalex.org/W6958765370","https://openalex.org/W2161835748","https://openalex.org/W2012862353","https://openalex.org/W2083350518","https://openalex.org/W4388004315","https://openalex.org/W3013727788","https://openalex.org/W4255135958","https://openalex.org/W2069508999"],"abstract_inverted_index":{"Linear":[0],"programming":[1,48,125,131],"as":[2],"a":[3,7,76,107,122,129],"problem":[4,78],"in":[5,56,72,79,92],"optimizing":[6],"linear":[8,12,111,130],"functional":[9],"subject":[10,40],"to":[11,29,41,50,63,97,117,121,128],"inequality":[13],"constraints":[14],"is":[15,70],"first":[16,120],"discussed":[17],"along":[18],"with":[19,31],"possible":[20,116],"uses":[21],"of":[22,36,53,75,94,106,110,135,146],"the":[23,37,51,73,86,95,104,136],"resulting":[24,137],"duality":[25,138],"relations.":[26],"Various":[27],"approaches":[28],"dealing":[30],"such":[32,54],"problems":[33],"when":[34],"parts":[35],"data":[38],"are":[39,43,60,149],"error":[42],"briefly":[44,151],"reviewed.":[45],"Chance":[46],"constrained":[47],"refers":[49],"class":[52,109],"cases":[55],"which":[57,80],"contraint":[58],"violations":[59],"admissible":[61],"up":[62],"pre-":[64],"assigned":[65],"probability":[66],"levels.":[67],"This":[68],"topic":[69],"elaborated":[71],"context":[74],"ship-chartering":[77],"independent":[81],"normally":[82],"distributed":[83],"deviates":[84],"from":[85],"(known)":[87],"average":[88],"demands":[89],"may":[90],"occur":[91],"any":[93],"periods":[96],"be":[98],"considered.":[99],"Certain":[100],"additional":[101],"assumptions":[102],"(including":[103],"use":[105,134],"specified":[108],"decision":[112],"rules)":[113],"make":[114],"it":[115],"effect":[118],"reductions":[119],"nonlinear":[123],"(mathematical)":[124],"and":[126,143],"then":[127,150],"problem.":[132],"The":[133],"relations":[139],"for":[140],"evaluating":[141],"risk":[142],"quality":[144],"levels":[145],"planned":[147],"performance":[148],"examined.":[152]},"counts_by_year":[{"year":2026,"cited_by_count":5},{"year":2025,"cited_by_count":8},{"year":2024,"cited_by_count":7},{"year":2023,"cited_by_count":6},{"year":2022,"cited_by_count":9},{"year":2021,"cited_by_count":5},{"year":2020,"cited_by_count":9},{"year":2019,"cited_by_count":6},{"year":2018,"cited_by_count":6},{"year":2017,"cited_by_count":6},{"year":2016,"cited_by_count":5},{"year":2015,"cited_by_count":15},{"year":2014,"cited_by_count":4},{"year":2013,"cited_by_count":6},{"year":2012,"cited_by_count":4}],"updated_date":"2026-10-30T12:39:25.321706","created_date":"2016-06-24T00:00:00"}