{"id":"https://openalex.org/W2549872480","doi":"https://doi.org/10.1109/tac.2016.2626790","title":"Optimal Policies for Brownian Inventory Systems With a Piecewise Linear Ordering Cost","display_name":"Optimal Policies for Brownian Inventory Systems With a Piecewise Linear Ordering Cost","publication_year":2016,"publication_date":"2016-11-09","ids":{"openalex":"https://openalex.org/W2549872480","doi":"https://doi.org/10.1109/tac.2016.2626790","mag":"2549872480"},"language":"en","primary_location":{"id":"doi:10.1109/tac.2016.2626790","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tac.2016.2626790","pdf_url":null,"source":{"id":"https://openalex.org/S184954342","display_name":"IEEE Transactions on Automatic Control","issn_l":"0018-9286","issn":["0018-9286","1558-2523","2334-3303"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319808","host_organization_name":"Institute of Electrical and Electronics Engineers","host_organization_lineage":["https://openalex.org/P4310319808"],"host_organization_lineage_names":["Institute of Electrical and Electronics Engineers"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"IEEE Transactions on Automatic Control","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/A5053767105","display_name":"Dacheng Yao","orcid":"https://orcid.org/0000-0001-5893-5595"},"institutions":[{"id":"https://openalex.org/I19820366","display_name":"Chinese Academy of Sciences","ror":"https://ror.org/034t30j35","country_code":"CN","type":"government","lineage":["https://openalex.org/I19820366"]},{"id":"https://openalex.org/I4210120485","display_name":"Academy of Mathematics and Systems Science","ror":"https://ror.org/02jkmyk67","country_code":"CN","type":"facility","lineage":["https://openalex.org/I19820366","https://openalex.org/I4210120485"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Dacheng Yao","raw_affiliation_strings":["Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing, China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing, China","institution_ids":["https://openalex.org/I4210120485","https://openalex.org/I19820366"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5067974546","display_name":"Xiuli Chao","orcid":"https://orcid.org/0000-0001-5233-4385"},"institutions":[{"id":"https://openalex.org/I27837315","display_name":"University of Michigan","ror":"https://ror.org/00jmfr291","country_code":"US","type":"education","lineage":["https://openalex.org/I27837315"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Xiuli Chao","raw_affiliation_strings":["Department of Industrial and Operations Engineering, University of Michigan, Ann Arbor, MI, USA"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Industrial and Operations Engineering, University of Michigan, Ann Arbor, MI, USA","institution_ids":["https://openalex.org/I27837315"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5050746445","display_name":"Jingchen Wu","orcid":null},"institutions":[{"id":"https://openalex.org/I27837315","display_name":"University of Michigan","ror":"https://ror.org/00jmfr291","country_code":"US","type":"education","lineage":["https://openalex.org/I27837315"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Jingchen Wu","raw_affiliation_strings":["Mathematics Department, University of Michigan, Ann Arbor, MI, USA"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Mathematics Department, University of Michigan, Ann Arbor, MI, USA","institution_ids":["https://openalex.org/I27837315"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":3,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":1.9218,"has_fulltext":false,"cited_by_count":8,"citation_normalized_percentile":{"value":0.88459893,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":96},"biblio":{"volume":"62","issue":"7","first_page":"3235","last_page":"3248"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10328","display_name":"Supply Chain and Inventory Management","score":0.9991999864578247,"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"}},"topics":[{"id":"https://openalex.org/T10328","display_name":"Supply Chain and Inventory Management","score":0.9991999864578247,"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/T10974","display_name":"Advanced Queuing Theory Analysis","score":0.9944000244140625,"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/T10551","display_name":"Scheduling and Optimization Algorithms","score":0.9553999900817871,"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/piecewise-linear-function","display_name":"Piecewise linear function","score":0.6636474132537842},{"id":"https://openalex.org/keywords/average-cost","display_name":"Average cost","score":0.6045596599578857},{"id":"https://openalex.org/keywords/brownian-motion","display_name":"Brownian motion","score":0.6040604710578918},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.557031512260437},{"id":"https://openalex.org/keywords/monotone-polygon","display_name":"Monotone polygon","score":0.5499687194824219},{"id":"https://openalex.org/keywords/economies-of-scale","display_name":"Economies of scale","score":0.5372173190116882},{"id":"https://openalex.org/keywords/holding-cost","display_name":"Holding cost","score":0.5303939580917358},{"id":"https://openalex.org/keywords/piecewise","display_name":"Piecewise","score":0.4898388087749481},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.4632924795150757},{"id":"https://openalex.org/keywords/stochastic-control","display_name":"Stochastic control","score":0.46280258893966675},{"id":"https://openalex.org/keywords/regular-polygon","display_name":"Regular polygon","score":0.46134358644485474},{"id":"https://openalex.org/keywords/economics","display_name":"Economics","score":0.32007700204849243},{"id":"https://openalex.org/keywords/optimal-control","display_name":"Optimal control","score":0.3180069923400879},{"id":"https://openalex.org/keywords/statistics","display_name":"Statistics","score":0.10054600238800049},{"id":"https://openalex.org/keywords/microeconomics","display_name":"Microeconomics","score":0.08582678437232971}],"concepts":[{"id":"https://openalex.org/C17095337","wikidata":"https://www.wikidata.org/wiki/Q2375229","display_name":"Piecewise linear function","level":2,"score":0.6636474132537842},{"id":"https://openalex.org/C2780958618","wikidata":"https://www.wikidata.org/wiki/Q945621","display_name":"Average cost","level":2,"score":0.6045596599578857},{"id":"https://openalex.org/C112401455","wikidata":"https://www.wikidata.org/wiki/Q178036","display_name":"Brownian motion","level":2,"score":0.6040604710578918},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.557031512260437},{"id":"https://openalex.org/C2834757","wikidata":"https://www.wikidata.org/wiki/Q4925424","display_name":"Monotone polygon","level":2,"score":0.5499687194824219},{"id":"https://openalex.org/C29321873","wikidata":"https://www.wikidata.org/wiki/Q5970087","display_name":"Economies of scale","level":2,"score":0.5372173190116882},{"id":"https://openalex.org/C192365026","wikidata":"https://www.wikidata.org/wiki/Q5046829","display_name":"Holding cost","level":2,"score":0.5303939580917358},{"id":"https://openalex.org/C164660894","wikidata":"https://www.wikidata.org/wiki/Q2037833","display_name":"Piecewise","level":2,"score":0.4898388087749481},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.4632924795150757},{"id":"https://openalex.org/C170131372","wikidata":"https://www.wikidata.org/wiki/Q7617811","display_name":"Stochastic control","level":3,"score":0.46280258893966675},{"id":"https://openalex.org/C112680207","wikidata":"https://www.wikidata.org/wiki/Q714886","display_name":"Regular polygon","level":2,"score":0.46134358644485474},{"id":"https://openalex.org/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","level":0,"score":0.32007700204849243},{"id":"https://openalex.org/C91575142","wikidata":"https://www.wikidata.org/wiki/Q1971426","display_name":"Optimal control","level":2,"score":0.3180069923400879},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.10054600238800049},{"id":"https://openalex.org/C175444787","wikidata":"https://www.wikidata.org/wiki/Q39072","display_name":"Microeconomics","level":1,"score":0.08582678437232971},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","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}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1109/tac.2016.2626790","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tac.2016.2626790","pdf_url":null,"source":{"id":"https://openalex.org/S184954342","display_name":"IEEE Transactions on Automatic Control","issn_l":"0018-9286","issn":["0018-9286","1558-2523","2334-3303"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319808","host_organization_name":"Institute of Electrical and Electronics Engineers","host_organization_lineage":["https://openalex.org/P4310319808"],"host_organization_lineage_names":["Institute of Electrical and Electronics Engineers"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"IEEE Transactions on Automatic Control","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[{"display_name":"Decent work and economic growth","id":"https://metadata.un.org/sdg/8","score":0.4699999988079071}],"awards":[{"id":"https://openalex.org/G5317936097","display_name":null,"funder_award_id":"CMMI-1362619","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"},{"id":"https://openalex.org/G5866076622","display_name":null,"funder_award_id":"11401566","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G8761512307","display_name":null,"funder_award_id":"CMMI-1131249","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"},{"id":"https://openalex.org/F4320321001","display_name":"National Natural Science Foundation of China","ror":"https://ror.org/01h0zpd94"},{"id":"https://openalex.org/F4320337391","display_name":"Division of Civil, Mechanical and Manufacturing Innovation","ror":"https://ror.org/028yd4c30"}],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":39,"referenced_works":["https://openalex.org/W561749035","https://openalex.org/W1568914899","https://openalex.org/W1577527822","https://openalex.org/W1595980179","https://openalex.org/W1963775509","https://openalex.org/W1969906947","https://openalex.org/W1970741704","https://openalex.org/W1971766344","https://openalex.org/W1975772205","https://openalex.org/W1982806220","https://openalex.org/W1983058804","https://openalex.org/W1990111368","https://openalex.org/W1996540573","https://openalex.org/W2003338056","https://openalex.org/W2007179722","https://openalex.org/W2018328814","https://openalex.org/W2028256316","https://openalex.org/W2034864849","https://openalex.org/W2057097347","https://openalex.org/W2071191354","https://openalex.org/W2080461826","https://openalex.org/W2096676480","https://openalex.org/W2105091108","https://openalex.org/W2109595427","https://openalex.org/W2130873555","https://openalex.org/W2131275591","https://openalex.org/W2132973642","https://openalex.org/W2134906701","https://openalex.org/W2140067350","https://openalex.org/W2144032829","https://openalex.org/W2147736135","https://openalex.org/W2162094362","https://openalex.org/W2171320369","https://openalex.org/W2506219953","https://openalex.org/W3005205613","https://openalex.org/W4247893708","https://openalex.org/W4253453450","https://openalex.org/W6681205470","https://openalex.org/W6725015421"],"related_works":["https://openalex.org/W90202410","https://openalex.org/W2140067350","https://openalex.org/W2242279817","https://openalex.org/W2489899567","https://openalex.org/W3123432389","https://openalex.org/W2372265497","https://openalex.org/W2108054346","https://openalex.org/W4312847924","https://openalex.org/W3178355381","https://openalex.org/W2034002595"],"abstract_inverted_index":{"We":[0],"consider":[1],"a":[2,18,123],"stochastic":[3],"inventory":[4],"system":[5,78,92],"with":[6],"general":[7],"piecewise":[8],"linear":[9],"ordering":[10,23,47,75,103],"cost.":[11],"The":[12,22],"cumulative":[13],"demand":[14],"is":[15,26,38,87,113,117],"modeled":[16],"as":[17,69],"Brownian":[19],"motion":[20],"process.":[21],"cost":[24,48,93,104],"function":[25],"neither":[27],"convex":[28],"nor":[29],"concave;":[30],"it":[31,37,44,116],"may":[32],"not":[33,39],"be":[34],"monotone;":[35],"and":[36,43,65,84],"even":[40],"necessarily":[41],"continuous,":[42],"includes":[45],"most":[46],"functions":[49],"studied":[50],"in":[51,101],"the":[52,77,80,85,90,99,102],"literature,":[53],"e.g.,":[54],"economies-of-scale":[55],"or":[56,62,122],"dis-economies":[57],"of":[58,96],"scale,":[59],"all-unit":[60],"discount":[61],"incremental":[63],"discount,":[64],"multiple":[66],"setup":[67],"costs,":[68],"special":[70],"cases.":[71],"In":[72],"addition":[73],"to":[74,88],"cost,":[76,83],"incurs":[79],"usual":[81],"holding/shortage":[82],"objective":[86],"minimize":[89],"average":[91],"per":[94],"unit":[95],"time.":[97],"Despite":[98],"complexity":[100],"function,":[105],"we":[106],"show":[107],"that":[108],"an":[109,119],"optimal":[110],"control":[111,126],"policy":[112,121],"very":[114],"simple:":[115],"either":[118],"(s,S)":[120],"one-sided":[124],"singular":[125],"policy.":[127]},"counts_by_year":[{"year":2022,"cited_by_count":2},{"year":2021,"cited_by_count":1},{"year":2020,"cited_by_count":1},{"year":2019,"cited_by_count":2},{"year":2018,"cited_by_count":1},{"year":2017,"cited_by_count":1}],"updated_date":"2026-06-11T09:08:48.828518","created_date":"2025-10-10T00:00:00"}