{"id":"https://openalex.org/W3047197922","doi":"https://doi.org/10.1137/19m129406x","title":"Periodical Multistage Stochastic Programs","display_name":"Periodical Multistage Stochastic Programs","publication_year":2020,"publication_date":"2020-01-01","ids":{"openalex":"https://openalex.org/W3047197922","doi":"https://doi.org/10.1137/19m129406x","mag":"3047197922"},"language":"en","primary_location":{"id":"doi:10.1137/19m129406x","is_oa":false,"landing_page_url":"https://doi.org/10.1137/19m129406x","pdf_url":null,"source":{"id":"https://openalex.org/S928796702","display_name":"SIAM Journal on Optimization","issn_l":"1052-6234","issn":["1052-6234","1095-7189"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320508","host_organization_name":"Society for Industrial and Applied Mathematics","host_organization_lineage":["https://openalex.org/P4310320508"],"host_organization_lineage_names":["Society for Industrial and Applied Mathematics"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"SIAM Journal on Optimization","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/A5025917676","display_name":"Alexander Shapiro","orcid":"https://orcid.org/0000-0002-4776-0053"},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Alexander Shapiro","raw_affiliation_strings":[],"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5089110010","display_name":"Lingquan Ding","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Lingquan Ding","raw_affiliation_strings":[],"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5025917676"],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":0.7181,"has_fulltext":false,"cited_by_count":11,"citation_normalized_percentile":{"value":0.7470445,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":100},"biblio":{"volume":"30","issue":"3","first_page":"2083","last_page":"2102"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11413","display_name":"Risk and Portfolio Optimization","score":0.9980000257492065,"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":0.9980000257492065,"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/T12135","display_name":"Fuzzy Systems and Optimization","score":0.9940999746322632,"subfield":{"id":"https://openalex.org/subfields/2613","display_name":"Statistics and Probability"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T12137","display_name":"Economic theories and models","score":0.9842000007629395,"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/mathematics","display_name":"Mathematics","score":0.6796072721481323},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.4620401859283447},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.3356221318244934}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6796072721481323},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.4620401859283447},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.3356221318244934}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1137/19m129406x","is_oa":false,"landing_page_url":"https://doi.org/10.1137/19m129406x","pdf_url":null,"source":{"id":"https://openalex.org/S928796702","display_name":"SIAM Journal on Optimization","issn_l":"1052-6234","issn":["1052-6234","1095-7189"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320508","host_organization_name":"Society for Industrial and Applied Mathematics","host_organization_lineage":["https://openalex.org/P4310320508"],"host_organization_lineage_names":["Society for Industrial and Applied Mathematics"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"SIAM Journal on Optimization","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G3526341773","display_name":null,"funder_award_id":"1633196","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"}],"funders":[{"id":"https://openalex.org/F4320306076","display_name":"National Science Foundation","ror":"https://ror.org/021nxhr62"}],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":9,"referenced_works":["https://openalex.org/W1965328823","https://openalex.org/W2015637491","https://openalex.org/W2019291268","https://openalex.org/W2019710194","https://openalex.org/W2114487363","https://openalex.org/W2170007044","https://openalex.org/W2546532603","https://openalex.org/W2790253573","https://openalex.org/W2964048385"],"related_works":["https://openalex.org/W2351859806","https://openalex.org/W1994109492","https://openalex.org/W4239376463","https://openalex.org/W1996810073","https://openalex.org/W2089811522","https://openalex.org/W1993700123","https://openalex.org/W2092244978","https://openalex.org/W1998839353","https://openalex.org/W2613209927","https://openalex.org/W1996783679"],"abstract_inverted_index":{"In":[0],"some":[1],"applications":[2],"the":[3,24,34,58,66,76],"considered":[4],"multistage":[5],"stochastic":[6,49,59],"programs":[7],"have":[8],"a":[9,30,55],"periodical":[10,31,68],"behavior.":[11],"We":[12],"show":[13],"that":[14],"in":[15,44],"such":[16],"cases":[17],"it":[18],"is":[19],"possible":[20],"to":[21,65],"drastically":[22],"reduce":[23],"number":[25],"of":[26,33,57],"stages":[27],"by":[28],"introducing":[29],"analogue":[32],"so-called":[35],"Bellman":[36,69],"equations":[37],"for":[38,75],"discounted":[39],"infinite":[40],"horizon":[41],"problems":[42],"used":[43],"Markov":[45],"decision":[46],"processes":[47],"and":[48,71],"optimal":[50],"control.":[51],"Furthermore,":[52],"we":[53],"describe":[54],"variant":[56],"dual":[60],"dynamic":[61],"programming":[62],"algorithm,":[63],"applied":[64],"constructed":[67],"equations,":[70],"provide":[72],"numerical":[73],"experiments":[74],"Brazilian":[77],"interconnected":[78],"power":[79],"system":[80],"problem.":[81]},"counts_by_year":[{"year":2026,"cited_by_count":2},{"year":2025,"cited_by_count":3},{"year":2024,"cited_by_count":2},{"year":2022,"cited_by_count":1},{"year":2021,"cited_by_count":3}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}