{"id":"https://openalex.org/W3031562984","doi":"https://doi.org/10.1109/tase.2020.2995078","title":"An Approximation Algorithm for Unrelated Parallel Machine Scheduling Under TOU Electricity Tariffs","display_name":"An Approximation Algorithm for Unrelated Parallel Machine Scheduling Under TOU Electricity Tariffs","publication_year":2020,"publication_date":"2020-05-30","ids":{"openalex":"https://openalex.org/W3031562984","doi":"https://doi.org/10.1109/tase.2020.2995078","mag":"3031562984"},"language":"en","primary_location":{"id":"doi:10.1109/tase.2020.2995078","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tase.2020.2995078","pdf_url":null,"source":{"id":"https://openalex.org/S34881539","display_name":"IEEE Transactions on Automation Science and Engineering","issn_l":"1545-5955","issn":["1545-5955","1558-3783"],"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 Automation Science and Engineering","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/A5081960668","display_name":"Zhi Pei","orcid":"https://orcid.org/0000-0001-6808-1490"},"institutions":[{"id":"https://openalex.org/I55712492","display_name":"Zhejiang University of Technology","ror":"https://ror.org/02djqfd08","country_code":"CN","type":"education","lineage":["https://openalex.org/I55712492"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Zhi Pei","raw_affiliation_strings":["College of Mechanical Engineering, Zhejiang University of Technology, Hangzhou, China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"College of Mechanical Engineering, Zhejiang University of Technology, Hangzhou, China","institution_ids":["https://openalex.org/I55712492"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5112563802","display_name":"Mingzhong Wan","orcid":null},"institutions":[{"id":"https://openalex.org/I9224756","display_name":"Northeastern University","ror":"https://ror.org/03awzbc87","country_code":"CN","type":"education","lineage":["https://openalex.org/I9224756"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Mingzhong Wan","raw_affiliation_strings":["Institute of Behavioral and Service Operations Management, Northeastern University, Shenyang, China","School of Business Administration, Northeastern University, Shenyang, China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Institute of Behavioral and Service Operations Management, Northeastern University, Shenyang, China","institution_ids":["https://openalex.org/I9224756"]},{"raw_affiliation_string":"School of Business Administration, Northeastern University, Shenyang, China","institution_ids":["https://openalex.org/I9224756"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5048539691","display_name":"Zhong\u2010Zhong Jiang","orcid":"https://orcid.org/0000-0003-0616-9416"},"institutions":[{"id":"https://openalex.org/I9224756","display_name":"Northeastern University","ror":"https://ror.org/03awzbc87","country_code":"CN","type":"education","lineage":["https://openalex.org/I9224756"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Zhong-Zhong Jiang","raw_affiliation_strings":["Institute of Behavioral and Service Operations Management, Northeastern University, Shenyang, China","Key Laboratory of Data Analytics and Optimization for Smart Industry, Ministry of Education, Northeastern University, Shenyang, China","School of Business Administration, Northeastern University, Shenyang, China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Institute of Behavioral and Service Operations Management, Northeastern University, Shenyang, China","institution_ids":["https://openalex.org/I9224756"]},{"raw_affiliation_string":"Key Laboratory of Data Analytics and Optimization for Smart Industry, Ministry of Education, Northeastern University, Shenyang, China","institution_ids":["https://openalex.org/I9224756"]},{"raw_affiliation_string":"School of Business Administration, Northeastern University, Shenyang, China","institution_ids":["https://openalex.org/I9224756"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5040424136","display_name":"Ziteng Wang","orcid":"https://orcid.org/0000-0001-7763-8959"},"institutions":[{"id":"https://openalex.org/I102502594","display_name":"Northern Illinois University","ror":"https://ror.org/012wxa772","country_code":"US","type":"education","lineage":["https://openalex.org/I102502594"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Ziteng Wang","raw_affiliation_strings":["Department of Industrial and Systems Engineering, Northern Illinois University, DeKalb, IL, USA"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Industrial and Systems Engineering, Northern Illinois University, DeKalb, IL, USA","institution_ids":["https://openalex.org/I102502594"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5101530759","display_name":"Xu Dai","orcid":"https://orcid.org/0009-0004-1323-9720"},"institutions":[{"id":"https://openalex.org/I55712492","display_name":"Zhejiang University of Technology","ror":"https://ror.org/02djqfd08","country_code":"CN","type":"education","lineage":["https://openalex.org/I55712492"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Xu Dai","raw_affiliation_strings":["College of Mechanical Engineering, Zhejiang University of Technology, Hangzhou, China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"College of Mechanical Engineering, Zhejiang University of Technology, Hangzhou, China","institution_ids":["https://openalex.org/I55712492"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":3,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":2.181,"has_fulltext":false,"cited_by_count":32,"citation_normalized_percentile":{"value":0.88664998,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":93,"max":99},"biblio":{"volume":"18","issue":"2","first_page":"743","last_page":"756"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10551","display_name":"Scheduling and Optimization Algorithms","score":0.9998000264167786,"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"}},"topics":[{"id":"https://openalex.org/T10551","display_name":"Scheduling and Optimization Algorithms","score":0.9998000264167786,"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/T11814","display_name":"Advanced Manufacturing and Logistics Optimization","score":0.9947999715805054,"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/T11954","display_name":"Energy Efficiency and Management","score":0.9851999878883362,"subfield":{"id":"https://openalex.org/subfields/2105","display_name":"Renewable Energy, Sustainability and the Environment"},"field":{"id":"https://openalex.org/fields/21","display_name":"Energy"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.7186088562011719},{"id":"https://openalex.org/keywords/scheduling","display_name":"Scheduling (production processes)","score":0.6554365754127502},{"id":"https://openalex.org/keywords/electricity","display_name":"Electricity","score":0.6022253632545471},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.5986577868461609},{"id":"https://openalex.org/keywords/job-shop-scheduling","display_name":"Job shop scheduling","score":0.468802273273468},{"id":"https://openalex.org/keywords/electricity-market","display_name":"Electricity market","score":0.46757203340530396},{"id":"https://openalex.org/keywords/single-machine-scheduling","display_name":"Single-machine scheduling","score":0.45312076807022095},{"id":"https://openalex.org/keywords/linear-programming","display_name":"Linear programming","score":0.4403773546218872},{"id":"https://openalex.org/keywords/upper-and-lower-bounds","display_name":"Upper and lower bounds","score":0.4343724846839905},{"id":"https://openalex.org/keywords/rounding","display_name":"Rounding","score":0.42734119296073914},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.34466612339019775},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.2204112708568573},{"id":"https://openalex.org/keywords/routing","display_name":"Routing (electronic design automation)","score":0.1342523992061615},{"id":"https://openalex.org/keywords/engineering","display_name":"Engineering","score":0.11429056525230408}],"concepts":[{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.7186088562011719},{"id":"https://openalex.org/C206729178","wikidata":"https://www.wikidata.org/wiki/Q2271896","display_name":"Scheduling (production processes)","level":2,"score":0.6554365754127502},{"id":"https://openalex.org/C206658404","wikidata":"https://www.wikidata.org/wiki/Q12725","display_name":"Electricity","level":2,"score":0.6022253632545471},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.5986577868461609},{"id":"https://openalex.org/C55416958","wikidata":"https://www.wikidata.org/wiki/Q6206757","display_name":"Job shop scheduling","level":3,"score":0.468802273273468},{"id":"https://openalex.org/C146733006","wikidata":"https://www.wikidata.org/wiki/Q676081","display_name":"Electricity market","level":3,"score":0.46757203340530396},{"id":"https://openalex.org/C2780271269","wikidata":"https://www.wikidata.org/wiki/Q19295956","display_name":"Single-machine scheduling","level":4,"score":0.45312076807022095},{"id":"https://openalex.org/C41045048","wikidata":"https://www.wikidata.org/wiki/Q202843","display_name":"Linear programming","level":2,"score":0.4403773546218872},{"id":"https://openalex.org/C77553402","wikidata":"https://www.wikidata.org/wiki/Q13222579","display_name":"Upper and lower bounds","level":2,"score":0.4343724846839905},{"id":"https://openalex.org/C136625980","wikidata":"https://www.wikidata.org/wiki/Q663208","display_name":"Rounding","level":2,"score":0.42734119296073914},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.34466612339019775},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.2204112708568573},{"id":"https://openalex.org/C74172769","wikidata":"https://www.wikidata.org/wiki/Q1446839","display_name":"Routing (electronic design automation)","level":2,"score":0.1342523992061615},{"id":"https://openalex.org/C127413603","wikidata":"https://www.wikidata.org/wiki/Q11023","display_name":"Engineering","level":0,"score":0.11429056525230408},{"id":"https://openalex.org/C119599485","wikidata":"https://www.wikidata.org/wiki/Q43035","display_name":"Electrical engineering","level":1,"score":0.0},{"id":"https://openalex.org/C31258907","wikidata":"https://www.wikidata.org/wiki/Q1301371","display_name":"Computer network","level":1,"score":0.0},{"id":"https://openalex.org/C111919701","wikidata":"https://www.wikidata.org/wiki/Q9135","display_name":"Operating system","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/tase.2020.2995078","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tase.2020.2995078","pdf_url":null,"source":{"id":"https://openalex.org/S34881539","display_name":"IEEE Transactions on Automation Science and Engineering","issn_l":"1545-5955","issn":["1545-5955","1558-3783"],"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 Automation Science and Engineering","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G1461344756","display_name":null,"funder_award_id":"L1924063","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G2311391187","display_name":null,"funder_award_id":"B16009","funder_id":"https://openalex.org/F4320327912","funder_display_name":"Higher Education Discipline Innovation Project"},{"id":"https://openalex.org/G3033548306","display_name":null,"funder_award_id":"LY18G010017","funder_id":"https://openalex.org/F4320338464","funder_display_name":"Natural Science Foundation of Zhejiang Province"},{"id":"https://openalex.org/G3594911729","display_name":null,"funder_award_id":"51305400","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G6058898927","display_name":null,"funder_award_id":"71520107004","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G7435116500","display_name":"\u5171\u4eab\u7ecf\u6d4e\u6a21\u5f0f\u4e0b\u57fa\u4e8e\u4ea7\u6d88\u8005\u6709\u9650\u7406\u6027\u7684\u80fd\u6e90\u5171\u4eab\u4f18\u5316\u5b9a\u4ef7\u7b56\u7565\u7814\u7a76","funder_award_id":"71671033","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G7668491202","display_name":null,"funder_award_id":"N2006006","funder_id":"https://openalex.org/F4320335787","funder_display_name":"Fundamental Research Funds for the Central Universities"},{"id":"https://openalex.org/G8044671957","display_name":"\u793e\u4f1a\u4e92\u52a8\u884c\u4e3a\u89c6\u89d2\u4e0b\u57fa\u4e8e\u4f17\u7b79\u7684\u670d\u52a1\u578b\u5236\u9020\u4f9b\u5e94\u94fe\u5b9a\u4ef7\u7b56\u7565\u7814\u7a76","funder_award_id":"71971052","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G8466990788","display_name":null,"funder_award_id":"71621061","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G978423042","display_name":"\u5171\u4eab\u7ecf\u6d4e\u6a21\u5f0f\u4e0b\u8003\u8651\u4f9b\u9700\u53cc\u65b9\u884c\u4e3a\u7279\u5f81\u7684\u5206\u5e03\u5f0f\u5236\u9020\u7cfb\u7edf\u51b3\u7b56\u673a\u7406\u7814\u7a76","funder_award_id":"71871203","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"}],"funders":[{"id":"https://openalex.org/F4320321001","display_name":"National Natural Science Foundation of China","ror":"https://ror.org/01h0zpd94"},{"id":"https://openalex.org/F4320327912","display_name":"Higher Education Discipline Innovation Project","ror":null},{"id":"https://openalex.org/F4320335787","display_name":"Fundamental Research Funds for the Central Universities","ror":null},{"id":"https://openalex.org/F4320338464","display_name":"Natural Science Foundation of Zhejiang Province","ror":"https://ror.org/01h0zpd94"}],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":22,"referenced_works":["https://openalex.org/W1977643613","https://openalex.org/W2056831785","https://openalex.org/W2161148179","https://openalex.org/W2329354063","https://openalex.org/W2339929657","https://openalex.org/W2483412501","https://openalex.org/W2484855292","https://openalex.org/W2570770292","https://openalex.org/W2604573531","https://openalex.org/W2606846577","https://openalex.org/W2606878445","https://openalex.org/W2738498247","https://openalex.org/W2748298211","https://openalex.org/W2768736937","https://openalex.org/W2770625762","https://openalex.org/W2799418757","https://openalex.org/W2800828338","https://openalex.org/W2896325524","https://openalex.org/W2901569208","https://openalex.org/W2931544713","https://openalex.org/W2966192810","https://openalex.org/W3014616321"],"related_works":["https://openalex.org/W4220780102","https://openalex.org/W2410881844","https://openalex.org/W3196334750","https://openalex.org/W1502401885","https://openalex.org/W2004257129","https://openalex.org/W2162001022","https://openalex.org/W2092240563","https://openalex.org/W2074319831","https://openalex.org/W2094800167","https://openalex.org/W2020576236"],"abstract_inverted_index":{"In":[0,27,214],"an":[1,30,43,142,180,204],"era":[2],"of":[3,66,93,138,190,207,231],"sustainable":[4],"development,":[5],"considerable":[6],"emphasis":[7,234],"has":[8],"been":[9],"put":[10],"onto":[11],"energy":[12],"saving,":[13],"environment":[14],"friendly,":[15],"and":[16,50,80,121,179,237,240,259,265],"social":[17],"welfare":[18],"as":[19,21,76,116,131],"well":[20],"productivity":[22,52,236],"in":[23,162],"the":[24,47,63,67,71,90,94,97,135,139,158,176,187,191,208,215,219,252,255,266],"manufacturing":[25,33],"sector.":[26],"this":[28],"work,":[29],"unrelated":[31,159],"parallel":[32,160],"setting":[34],"with":[35,42,108,211],"time-of-use":[36],"(TOU)":[37],"electricity":[38,48,110,238,245],"price":[39],"is":[40,59,101,145,152,172,183,200,223,249,261],"explored,":[41],"aim":[44],"to":[45,61,87,154,157,185,202],"reduce":[46],"cost":[49],"increase":[51],"simultaneously.":[53],"A":[54],"nonlinear":[55],"mathematical":[56],"programming":[57,119],"model":[58,171],"formulated":[60],"exploit":[62],"special":[64,149],"structure":[65],"scheduling":[68,99,106,209],"problem,":[69,120,141],"where":[70,147],"quadratic":[72],"constraints":[73],"are":[74,85],"reformulated":[75],"second-order-cone":[77],"(SOC)":[78],"constraints,":[79],"several":[81,104],"tailored":[82],"cutting":[83],"planes":[84],"introduced":[86],"further":[88],"tighten":[89],"feasible":[91],"region":[92],"problem.":[95,194],"Then,":[96],"original":[98],"problem":[100,210],"transformed":[102],"into":[103],"single-machine":[105],"problems":[107],"TOU":[109,212,244],"price,":[111,239],"which":[112],"could":[113,123,270],"be":[114,124],"relaxed":[115,140],"a":[117,148,163,168,196,272],"single-objective":[118],"it":[122],"solved":[125],"rapidly":[126],"via":[127],"commercial":[128],"solvers,":[129],"such":[130],"CPLEX.":[132],"Based":[133],"on":[134,228,235],"optimal":[136,188],"solution":[137,189,274],"approximate":[143,221,257],"algorithm":[144,182,222,258],"proposed,":[146],"rounding":[150],"technique":[151],"employed":[153],"assign":[155],"jobs":[156],"machines":[161],"local":[164],"search":[165],"manner.":[166],"Furthermore,":[167],"lower":[169,192],"bound":[170,193,206,268],"constructed":[173],"by":[174],"eliminating":[175],"nonpreemption":[177],"constraint,":[178],"iteration-based":[181],"devised":[184],"obtain":[186,271],"Meanwhile,":[195],"dispatch":[197],"rule-based":[198],"approach":[199],"proposed":[201,220,256],"provide":[203],"upper":[205],"constraint.":[213],"numerical":[216],"analysis":[217],"section,":[218],"validated":[224],"through":[225],"extensive":[226],"testing":[227],"various":[229],"scales":[230],"instances,":[232],"different":[233],"under":[241],"two":[242],"typical":[243],"pricing":[246],"policies.":[247],"It":[248],"observed":[250],"that":[251],"gap":[253],"between":[254],"CPLEX":[260],"mostly":[262],"within":[263,275],"4%,":[264],"lower/upper":[267],"methods":[269],"relaxed/feasible":[273],"0.01":[276],"s.":[277]},"counts_by_year":[{"year":2026,"cited_by_count":5},{"year":2025,"cited_by_count":6},{"year":2024,"cited_by_count":7},{"year":2023,"cited_by_count":7},{"year":2022,"cited_by_count":5},{"year":2021,"cited_by_count":2}],"updated_date":"2026-07-17T09:13:05.818461","created_date":"2025-10-10T00:00:00"}