{"id":"https://openalex.org/W7162777039","doi":"https://doi.org/10.1007/s10479-026-07289-5","title":"On choosing the number of look-ahead stages in the rolling-horizon procedure for multistage stochastic programming","display_name":"On choosing the number of look-ahead stages in the rolling-horizon procedure for multistage stochastic programming","publication_year":2026,"publication_date":"2026-05-30","ids":{"openalex":"https://openalex.org/W7162777039","doi":"https://doi.org/10.1007/s10479-026-07289-5"},"language":"en","primary_location":{"id":"doi:10.1007/s10479-026-07289-5","doi":"https://doi.org/10.1007/s10479-026-07289-5","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s10479-026-07289-5","pdf_url":"https://link.springer.com/content/pdf/10.1007/s10479-026-07289-5.pdf","source":{"id":"https://openalex.org/S57667410","display_name":"Annals of Operations Research","issn_l":"0254-5330","issn":["0254-5330","1572-9338"],"is_oa":false,"is_in_doaj":false,"is_core":true,"listed_in":["abdc-a","anvur-class-a","anvur-scientific","cwts-core","fnege-2","jufo-1","ki-jl-1","norway-1","poland-70","russia-white-list-1","vabb-shw"],"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Annals of Operations Research","raw_type":"journal-article"},"volume":null,"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"hybrid","oa_url":"https://link.springer.com/content/pdf/10.1007/s10479-026-07289-5.pdf","any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5058780455","display_name":"Murwan Siddig","orcid":null,"observed_orcids":[]},"institutions":[{"id":"https://openalex.org/I33213144","display_name":"University of Florida","ror":"https://ror.org/02y3ad647","country_code":"US","type":"education","lineage":["https://openalex.org/I33213144"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Murwan Siddig","raw_affiliation_strings":["Department of Systems and Industrial Engineering, University of Florida, 303 Weil Hall, Gainesville, 32603, Florida, USA"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Systems and Industrial Engineering, University of Florida, 303 Weil Hall, Gainesville, 32603, Florida, USA","institution_ids":["https://openalex.org/I33213144"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5122904308","display_name":"Yongjia Song","orcid":"https://orcid.org/0000-0001-6839-522X","observed_orcids":["https://orcid.org/0000-0001-6839-522X"]},"institutions":[{"id":"https://openalex.org/I8078737","display_name":"Clemson University","ror":"https://ror.org/037s24f05","country_code":"US","type":"education","lineage":["https://openalex.org/I8078737"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"Yongjia Song","raw_affiliation_strings":["Department of Industrial Engineering, Clemson University, 211 Fernow St., Clemson, 29631, SC, USA"],"raw_orcid":"https://orcid.org/0000-0001-6839-522X","affiliations":[{"raw_affiliation_string":"Department of Industrial Engineering, Clemson University, 211 Fernow St., Clemson, 29631, SC, USA","institution_ids":["https://openalex.org/I8078737"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5137364164","display_name":"Amin Khademi","orcid":"https://orcid.org/0000-0002-5281-8715","observed_orcids":["https://orcid.org/0000-0002-5281-8715"]},"institutions":[{"id":"https://openalex.org/I8078737","display_name":"Clemson University","ror":"https://ror.org/037s24f05","country_code":"US","type":"education","lineage":["https://openalex.org/I8078737"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Amin Khademi","raw_affiliation_strings":["Department of Industrial Engineering, Clemson University, 211 Fernow St., Clemson, 29631, SC, USA"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Industrial Engineering, Clemson University, 211 Fernow St., Clemson, 29631, SC, USA","institution_ids":["https://openalex.org/I8078737"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5122904308"],"corresponding_institution_ids":["https://openalex.org/I8078737"],"apc_list":{"value":3090,"currency":"USD","value_usd":3090},"apc_paid":{"value":3090,"currency":"USD","value_usd":3090},"fwci":0.0,"has_fulltext":true,"cited_by_count":0,"citation_normalized_percentile":{"value":0.35725485,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":null,"issue":null,"first_page":null,"last_page":null},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11413","display_name":"Risk and Portfolio Optimization","score":0.9150000214576721,"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":0.9150000214576721,"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/T10791","display_name":"Advanced Control Systems Optimization","score":0.01679999940097332,"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/T10963","display_name":"Advanced Optimization Algorithms Research","score":0.01140000019222498,"subfield":{"id":"https://openalex.org/subfields/2612","display_name":"Numerical Analysis"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/multistage-stochastic-programming","display_name":"multistage stochastic programming","score":0.953000009059906},{"id":"https://openalex.org/keywords/surrogate-modeling","display_name":"surrogate models","score":0.8190000057220459},{"id":"https://openalex.org/keywords/discount-factor","display_name":"discount factor","score":0.8730000257492065},{"id":"https://openalex.org/keywords/infinite-horizon-problems","display_name":"infinite horizon problems","score":0.6990000009536743},{"id":"https://openalex.org/keywords/decision-policies","display_name":"decision policies","score":0.5649999976158142},{"id":"https://openalex.org/keywords/supervised-learning","display_name":"supervised learning","score":0.871999979019165},{"id":"https://openalex.org/keywords/sequential-decision-making-under-uncertainty","display_name":"sequential decision making under uncertainty","score":0.824999988079071}],"concepts":[{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.7055000066757202},{"id":"https://openalex.org/C24858836","wikidata":"https://www.wikidata.org/wiki/Q844718","display_name":"Theory of computation","level":2,"score":0.6758000254631042},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.5756999850273132},{"id":"https://openalex.org/C2777212361","wikidata":"https://www.wikidata.org/wiki/Q5127848","display_name":"Class (philosophy)","level":2,"score":0.5313000082969666},{"id":"https://openalex.org/C137631369","wikidata":"https://www.wikidata.org/wiki/Q7617831","display_name":"Stochastic programming","level":2,"score":0.5038999915122986},{"id":"https://openalex.org/C111335779","wikidata":"https://www.wikidata.org/wiki/Q3454686","display_name":"Reduction (mathematics)","level":2,"score":0.49320000410079956},{"id":"https://openalex.org/C48103436","wikidata":"https://www.wikidata.org/wiki/Q599031","display_name":"State (computer science)","level":2,"score":0.4458000063896179},{"id":"https://openalex.org/C37404715","wikidata":"https://www.wikidata.org/wiki/Q380679","display_name":"Dynamic programming","level":2,"score":0.42260000109672546},{"id":"https://openalex.org/C106189395","wikidata":"https://www.wikidata.org/wiki/Q176789","display_name":"Markov decision process","level":3,"score":0.35749998688697815},{"id":"https://openalex.org/C115988155","wikidata":"https://www.wikidata.org/wiki/Q3262192","display_name":"Decision problem","level":2,"score":0.3434999883174896},{"id":"https://openalex.org/C2779530757","wikidata":"https://www.wikidata.org/wiki/Q1207505","display_name":"Quality (philosophy)","level":2,"score":0.336899995803833},{"id":"https://openalex.org/C41045048","wikidata":"https://www.wikidata.org/wiki/Q202843","display_name":"Linear programming","level":2,"score":0.3151000142097473},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.2946000099182129},{"id":"https://openalex.org/C77553402","wikidata":"https://www.wikidata.org/wiki/Q13222579","display_name":"Upper and lower bounds","level":2,"score":0.29440000653266907},{"id":"https://openalex.org/C127491075","wikidata":"https://www.wikidata.org/wiki/Q7617825","display_name":"Stochastic modelling","level":2,"score":0.2838999927043915},{"id":"https://openalex.org/C97541855","wikidata":"https://www.wikidata.org/wiki/Q830687","display_name":"Reinforcement learning","level":2,"score":0.2815999984741211},{"id":"https://openalex.org/C123860398","wikidata":"https://www.wikidata.org/wiki/Q6934605","display_name":"Multiclass classification","level":3,"score":0.26660001277923584},{"id":"https://openalex.org/C179799912","wikidata":"https://www.wikidata.org/wiki/Q205084","display_name":"Computational complexity theory","level":2,"score":0.26330000162124634},{"id":"https://openalex.org/C119857082","wikidata":"https://www.wikidata.org/wiki/Q2539","display_name":"Machine learning","level":1,"score":0.257099986076355},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.2529999911785126},{"id":"https://openalex.org/C150325174","wikidata":"https://www.wikidata.org/wiki/Q4335500","display_name":"Optimal decision","level":3,"score":0.25049999356269836}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1007/s10479-026-07289-5","doi":"https://doi.org/10.1007/s10479-026-07289-5","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s10479-026-07289-5","pdf_url":"https://link.springer.com/content/pdf/10.1007/s10479-026-07289-5.pdf","source":{"id":"https://openalex.org/S57667410","display_name":"Annals of Operations Research","issn_l":"0254-5330","issn":["0254-5330","1572-9338"],"is_oa":false,"is_in_doaj":false,"is_core":true,"listed_in":["abdc-a","anvur-class-a","anvur-scientific","cwts-core","fnege-2","jufo-1","ki-jl-1","norway-1","poland-70","russia-white-list-1","vabb-shw"],"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Annals of Operations Research","raw_type":"journal-article"}],"best_oa_location":{"id":"doi:10.1007/s10479-026-07289-5","doi":"https://doi.org/10.1007/s10479-026-07289-5","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s10479-026-07289-5","pdf_url":"https://link.springer.com/content/pdf/10.1007/s10479-026-07289-5.pdf","source":{"id":"https://openalex.org/S57667410","display_name":"Annals of Operations Research","issn_l":"0254-5330","issn":["0254-5330","1572-9338"],"is_oa":false,"is_in_doaj":false,"is_core":true,"listed_in":["abdc-a","anvur-class-a","anvur-scientific","cwts-core","fnege-2","jufo-1","ki-jl-1","norway-1","poland-70","russia-white-list-1","vabb-shw"],"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Annals of Operations Research","raw_type":"journal-article"},"sustainable_development_goals":[],"sustainable_development_goals_aurora":[{"display_name":"Peace, justice, and strong institutions","id":"https://metadata.un.org/sdg/16","score":0.7972347140312195}],"study_designs":[],"awards":[{"id":"https://openalex.org/G4876451744","display_name":"An Adaptive Partition-based Approach for Solving Large-Scale Stochastic Programs","funder_award_id":"1854960","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"},{"id":"https://openalex.org/G85566416","display_name":null,"funder_award_id":"1854960","funder_id":"https://openalex.org/F4320332170","funder_display_name":"Directorate for Engineering"}],"funders":[{"id":"https://openalex.org/F4320306076","display_name":"National Science Foundation","ror":"https://ror.org/021nxhr62"},{"id":"https://openalex.org/F4320332170","display_name":"Directorate for Engineering","ror":"https://ror.org/00b6sbb32"},{"id":"https://openalex.org/F4320337391","display_name":"Division of Civil, Mechanical and Manufacturing Innovation","ror":"https://ror.org/028yd4c30"}],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W7162777039.pdf","grobid_xml":"https://content.openalex.org/works/W7162777039.grobid-xml"},"referenced_works_count":20,"referenced_works":["https://openalex.org/W1918816242","https://openalex.org/W1976667494","https://openalex.org/W1989567750","https://openalex.org/W2002219970","https://openalex.org/W2016167804","https://openalex.org/W2019233828","https://openalex.org/W2019710194","https://openalex.org/W2033182080","https://openalex.org/W2152545378","https://openalex.org/W2186356962","https://openalex.org/W2304662403","https://openalex.org/W2487770199","https://openalex.org/W2772593466","https://openalex.org/W2803144101","https://openalex.org/W2803443353","https://openalex.org/W2915771420","https://openalex.org/W2942709498","https://openalex.org/W3047197922","https://openalex.org/W3133324912","https://openalex.org/W3203981230"],"related_works":[],"abstract_inverted_index":{"Abstract":[0],"Multistage":[1],"stochastic":[2],"programming":[3],"(MSP)":[4],"is":[5,33,43,59,69],"a":[6,44,63,73,140,153,161,177],"class":[7],"of":[8,55,76,95,101,112,172,189,199,205,220],"models":[9],"for":[10,19,118,191],"sequential":[11],"decision-making":[12],"under":[13],"uncertainty.":[14],"MSP":[15,50,146,150],"problems":[16],"are":[17],"known":[18],"their":[20],"computational":[21],"difficulties,":[22],"and":[23],"one":[24],"common":[25],"approach":[26,180],"to":[27,34,36,61,87,108,116,133,143,167,184],"find":[28],"an":[29,49,109,148,169,186],"approximate":[30],"decision":[31,104],"policy":[32],"resort":[35],"the":[37,79,90,93,99,102,123,144,197,200,206,218,221],"rolling-horizon":[38],"procedure":[39],"(RHP).":[40],"The":[41,66],"RHP":[42],"method":[45],"that":[46,181],"involves":[47],"solving":[48],"problem":[51,151],"at":[52],"each":[53,119,192,203],"roll":[54,204],"its":[56],"procedure,":[57],"which":[58,158,163],"referred":[60],"as":[62,147],"look-ahead":[64,67,120,193],"model.":[65],"model":[68,121,142,194],"typically":[70],"defined":[71],"with":[72,152],"smaller":[74],"number":[75,94,171,188],"stages":[77,96,115,190],"than":[78],"original":[80,145],"MSP,":[81],"making":[82],"them":[83],"computationally":[84],"less":[85],"demanding":[86],"solve.":[88],"However,":[89],"reduction":[91],"in":[92,122,202],"may":[97],"compromise":[98],"quality":[100],"resulting":[103],"policy.":[105],"This":[106],"leads":[107],"important":[110],"question":[111],"how":[113,183],"many":[114],"use":[117],"RHP.":[124],"In":[125],"this":[126,135],"paper,":[127],"we":[128,138,159,175],"propose":[129,139,176],"two":[130],"alternative":[131],"approaches":[132,223],"address":[134],"question.":[136],"First,":[137],"surrogate":[141],"infinite-horizon":[149],"certain":[154],"discount":[155],"factor,":[156],"from":[157,211],"derive":[160],"bound":[162],"can":[164],"be":[165],"used":[166],"prescribe":[168],"appropriate":[170,187],"stages.":[173],"Alternatively,":[174],"supervised":[178],"learning":[179],"learns":[182],"choose":[185],"based":[195],"on":[196,224],"state":[198],"system":[201],"RHP,":[207],"using":[208],"data":[209],"collected":[210],"offline":[212],"experiments.":[213],"Our":[214],"numerical":[215],"experiments":[216],"demonstrate":[217],"effectiveness":[219],"proposed":[222],"these":[225],"problems.":[226]},"counts_by_year":[],"updated_date":"2026-10-14T16:39:01.820549","created_date":"2026-05-30T00:00:00"}
