{"id":"https://openalex.org/W2106372920","doi":"https://doi.org/10.1109/tac.2010.2049913","title":"Optimization Based Production Planning With Hybrid Dynamics and Constraints","display_name":"Optimization Based Production Planning With Hybrid Dynamics and Constraints","publication_year":2010,"publication_date":"2010-05-12","ids":{"openalex":"https://openalex.org/W2106372920","doi":"https://doi.org/10.1109/tac.2010.2049913","mag":"2106372920"},"language":"en","primary_location":{"id":"doi:10.1109/tac.2010.2049913","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tac.2010.2049913","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/A5032033256","display_name":"Qiaozhu Zhai","orcid":"https://orcid.org/0000-0002-7312-4923"},"institutions":[{"id":"https://openalex.org/I87445476","display_name":"Xi'an Jiaotong University","ror":"https://ror.org/017zhmm22","country_code":"CN","type":"education","lineage":["https://openalex.org/I87445476"]}],"countries":["CN"],"is_corresponding":true,"raw_author_name":"Qiaozhu Zhai","raw_affiliation_strings":["Systems Engineering Institute, MOE KLINNS Laboratory and SKLMSE Laboratory, Xi'an Jiaotong University, Shaanxi, China"],"affiliations":[{"raw_affiliation_string":"Systems Engineering Institute, MOE KLINNS Laboratory and SKLMSE Laboratory, Xi'an Jiaotong University, Shaanxi, China","institution_ids":["https://openalex.org/I87445476"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5075845093","display_name":"Xiaohong Guan","orcid":"https://orcid.org/0000-0002-8826-0362"},"institutions":[{"id":"https://openalex.org/I87445476","display_name":"Xi'an Jiaotong University","ror":"https://ror.org/017zhmm22","country_code":"CN","type":"education","lineage":["https://openalex.org/I87445476"]},{"id":"https://openalex.org/I99065089","display_name":"Tsinghua University","ror":"https://ror.org/03cve4549","country_code":"CN","type":"education","lineage":["https://openalex.org/I99065089"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Xiaohong Guan","raw_affiliation_strings":["Center of Intelligent and Networked Systems, Tsinghua University, Beijing, China","Systems Engineering Institute, MOE KLINNS Laboratory and SKLMSE Laboratory, Xi'an Jiaotong University, Shaanxi, China"],"affiliations":[{"raw_affiliation_string":"Center of Intelligent and Networked Systems, Tsinghua University, Beijing, China","institution_ids":["https://openalex.org/I99065089"]},{"raw_affiliation_string":"Systems Engineering Institute, MOE KLINNS Laboratory and SKLMSE Laboratory, Xi'an Jiaotong University, Shaanxi, China","institution_ids":["https://openalex.org/I87445476"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5048293972","display_name":"Feng Gao","orcid":"https://orcid.org/0000-0002-4969-5195"},"institutions":[{"id":"https://openalex.org/I87445476","display_name":"Xi'an Jiaotong University","ror":"https://ror.org/017zhmm22","country_code":"CN","type":"education","lineage":["https://openalex.org/I87445476"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Feng Gao","raw_affiliation_strings":["Systems Engineering Institute, MOE KLINNS Laboratory and SKLMSE Laboratory, Xi'an Jiaotong University, Shaanxi, China"],"affiliations":[{"raw_affiliation_string":"Systems Engineering Institute, MOE KLINNS Laboratory and SKLMSE Laboratory, Xi'an Jiaotong University, Shaanxi, China","institution_ids":["https://openalex.org/I87445476"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5032033256"],"corresponding_institution_ids":["https://openalex.org/I87445476"],"apc_list":null,"apc_paid":null,"fwci":2.0205,"has_fulltext":false,"cited_by_count":16,"citation_normalized_percentile":{"value":0.87755766,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":97},"biblio":{"volume":"55","issue":"12","first_page":"2778","last_page":"2792"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10424","display_name":"Electric Power System Optimization","score":0.9987000226974487,"subfield":{"id":"https://openalex.org/subfields/2208","display_name":"Electrical and Electronic Engineering"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T10424","display_name":"Electric Power System Optimization","score":0.9987000226974487,"subfield":{"id":"https://openalex.org/subfields/2208","display_name":"Electrical and Electronic 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/T10551","display_name":"Scheduling and Optimization Algorithms","score":0.9975000023841858,"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"}},{"id":"https://openalex.org/T10603","display_name":"Smart Grid Energy Management","score":0.9965999722480774,"subfield":{"id":"https://openalex.org/subfields/2208","display_name":"Electrical and Electronic 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/mathematical-optimization","display_name":"Mathematical optimization","score":0.7784461975097656},{"id":"https://openalex.org/keywords/discretization","display_name":"Discretization","score":0.7333979606628418},{"id":"https://openalex.org/keywords/production-planning","display_name":"Production planning","score":0.6528118252754211},{"id":"https://openalex.org/keywords/lagrangian-relaxation","display_name":"Lagrangian relaxation","score":0.5460016131401062},{"id":"https://openalex.org/keywords/relaxation","display_name":"Relaxation (psychology)","score":0.540073812007904},{"id":"https://openalex.org/keywords/limit","display_name":"Limit (mathematics)","score":0.5102884769439697},{"id":"https://openalex.org/keywords/lagrange-multiplier","display_name":"Lagrange multiplier","score":0.49320071935653687},{"id":"https://openalex.org/keywords/optimization-problem","display_name":"Optimization problem","score":0.482030987739563},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.4569121301174164},{"id":"https://openalex.org/keywords/discrete-time-and-continuous-time","display_name":"Discrete time and continuous time","score":0.4539378583431244},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.4114489257335663},{"id":"https://openalex.org/keywords/production","display_name":"Production (economics)","score":0.3755219578742981}],"concepts":[{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.7784461975097656},{"id":"https://openalex.org/C73000952","wikidata":"https://www.wikidata.org/wiki/Q17007827","display_name":"Discretization","level":2,"score":0.7333979606628418},{"id":"https://openalex.org/C2777909354","wikidata":"https://www.wikidata.org/wiki/Q1386523","display_name":"Production planning","level":3,"score":0.6528118252754211},{"id":"https://openalex.org/C91765299","wikidata":"https://www.wikidata.org/wiki/Q3424292","display_name":"Lagrangian relaxation","level":2,"score":0.5460016131401062},{"id":"https://openalex.org/C2776029896","wikidata":"https://www.wikidata.org/wiki/Q3935810","display_name":"Relaxation (psychology)","level":2,"score":0.540073812007904},{"id":"https://openalex.org/C151201525","wikidata":"https://www.wikidata.org/wiki/Q177239","display_name":"Limit (mathematics)","level":2,"score":0.5102884769439697},{"id":"https://openalex.org/C73684929","wikidata":"https://www.wikidata.org/wiki/Q598870","display_name":"Lagrange multiplier","level":2,"score":0.49320071935653687},{"id":"https://openalex.org/C137836250","wikidata":"https://www.wikidata.org/wiki/Q984063","display_name":"Optimization problem","level":2,"score":0.482030987739563},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.4569121301174164},{"id":"https://openalex.org/C55689738","wikidata":"https://www.wikidata.org/wiki/Q15963867","display_name":"Discrete time and continuous time","level":2,"score":0.4539378583431244},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.4114489257335663},{"id":"https://openalex.org/C2778348673","wikidata":"https://www.wikidata.org/wiki/Q739302","display_name":"Production (economics)","level":2,"score":0.3755219578742981},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.0},{"id":"https://openalex.org/C15744967","wikidata":"https://www.wikidata.org/wiki/Q9418","display_name":"Psychology","level":0,"score":0.0},{"id":"https://openalex.org/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","level":0,"score":0.0},{"id":"https://openalex.org/C139719470","wikidata":"https://www.wikidata.org/wiki/Q39680","display_name":"Macroeconomics","level":1,"score":0.0},{"id":"https://openalex.org/C77805123","wikidata":"https://www.wikidata.org/wiki/Q161272","display_name":"Social psychology","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.2010.2049913","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tac.2010.2049913","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":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":55,"referenced_works":["https://openalex.org/W74203006","https://openalex.org/W651998970","https://openalex.org/W1506895795","https://openalex.org/W1948613015","https://openalex.org/W1968143987","https://openalex.org/W1982928246","https://openalex.org/W1987678257","https://openalex.org/W1987728044","https://openalex.org/W1993750689","https://openalex.org/W2007223237","https://openalex.org/W2007255736","https://openalex.org/W2017697298","https://openalex.org/W2039725020","https://openalex.org/W2052885299","https://openalex.org/W2069279462","https://openalex.org/W2072479366","https://openalex.org/W2074104008","https://openalex.org/W2076400379","https://openalex.org/W2077151392","https://openalex.org/W2081371078","https://openalex.org/W2092775568","https://openalex.org/W2096703248","https://openalex.org/W2101775529","https://openalex.org/W2105749069","https://openalex.org/W2107164313","https://openalex.org/W2111414899","https://openalex.org/W2117799989","https://openalex.org/W2119606476","https://openalex.org/W2126310855","https://openalex.org/W2132056139","https://openalex.org/W2133996598","https://openalex.org/W2139211712","https://openalex.org/W2147185189","https://openalex.org/W2148652465","https://openalex.org/W2158023072","https://openalex.org/W2158547185","https://openalex.org/W2163089379","https://openalex.org/W2164297615","https://openalex.org/W2168324649","https://openalex.org/W2168858968","https://openalex.org/W2505968561","https://openalex.org/W2588401480","https://openalex.org/W2764796714","https://openalex.org/W2764818801","https://openalex.org/W4236384091","https://openalex.org/W4239664064","https://openalex.org/W4241358655","https://openalex.org/W4242130683","https://openalex.org/W4242710730","https://openalex.org/W4243245739","https://openalex.org/W4248597148","https://openalex.org/W4251695001","https://openalex.org/W4375905903","https://openalex.org/W6640399676","https://openalex.org/W6676251673"],"related_works":["https://openalex.org/W2002102264","https://openalex.org/W4237964977","https://openalex.org/W1996993548","https://openalex.org/W4285149922","https://openalex.org/W3032916910","https://openalex.org/W4312837919","https://openalex.org/W1510357621","https://openalex.org/W2981882443","https://openalex.org/W2899851694","https://openalex.org/W3143161784"],"abstract_inverted_index":{"Optimizing":[0],"production":[1,10,22,90,162,215],"planning":[2,16,37,216],"has":[3],"tremendous":[4],"economic":[5],"impact":[6],"for":[7,154,212],"many":[8],"industrial":[9],"systems.":[11],"In":[12],"this":[13,69],"paper,":[14],"the":[15,46,51,73,78,88,102,148,156,192,205,218],"problem":[17,42,132],"of":[18,21,34,96,101,124,150],"a":[19,107,122,129,165,178],"class":[20],"systems":[23],"with":[24,31,50,80,106,169,217],"hybrid":[25,81,220],"dynamics":[26,82,221],"and":[27,38,55,83,128,147,158,210,222],"constraints":[28,58,84],"is":[29,43,66,111,118,141,152,187,208],"considered":[30],"practical":[32],"background":[33],"power":[35],"generation":[36],"other":[39],"applications.":[40],"The":[41,161,184],"solved":[44],"within":[45],"Lagrangian":[47],"relaxation":[48],"framework,":[49],"system":[52],"wide":[53],"demand":[54],"resource":[56],"limit":[57],"relaxed":[59],"by":[60],"Lagrange":[61],"multipliers.":[62],"A":[63,98],"new":[64,206],"method":[65,140,186,207],"developed":[67,142],"in":[68,164,177],"paper":[70],"to":[71,77,143,190],"obtain":[72],"exact":[74],"optimal":[75,193],"solutions":[76],"subproblems":[79,146],"efficiently":[85],"without":[86,182],"discretizing":[87],"continuous":[89,125,157],"levels":[91,95,163],"or":[92],"introducing":[93],"intermediate":[94],"relaxation.":[97],"novel":[99],"definition":[100],"discrete":[103,130,159,194],"state":[104],"associated":[105],"consecutive":[108,166],"time":[109,198],"span":[110,168],"introduced":[112],"so":[113],"that":[114,204],"solving":[115,121],"each":[116],"subproblem":[117],"converted":[119],"into":[120],"number":[123],"optimization":[126,131,213],"problems":[127],"separately.":[133],"An":[134],"efficient":[135,209],"double":[136],"dynamic":[137],"programming":[138],"(DP)":[139],"solve":[144],"these":[145],"principle":[149],"optimality":[151],"guaranteed":[153],"both":[155],"problem.":[160],"running":[167],"non-convex":[170],"piecewise":[171],"linear":[172],"cost":[173],"functions":[174],"are":[175],"determined":[176],"DP":[179,185],"forward":[180],"sweep":[181],"discretization.":[183],"then":[188],"applied":[189],"determine":[191],"operating":[195],"states":[196],"across":[197],"efficiently.":[199],"Numerical":[200],"testing":[201],"results":[202],"demonstrate":[203],"effective":[211],"based":[214],"complex":[219],"constraints.":[223]},"counts_by_year":[{"year":2025,"cited_by_count":1},{"year":2023,"cited_by_count":3},{"year":2021,"cited_by_count":2},{"year":2020,"cited_by_count":2},{"year":2016,"cited_by_count":1},{"year":2013,"cited_by_count":1},{"year":2012,"cited_by_count":2}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}