{"id":"https://openalex.org/W3087037340","doi":"https://doi.org/10.1007/s10951-020-00667-2","title":"Scheduling a proportionate flow shop of batching machines","display_name":"Scheduling a proportionate flow shop of batching machines","publication_year":2020,"publication_date":"2020-09-17","ids":{"openalex":"https://openalex.org/W3087037340","doi":"https://doi.org/10.1007/s10951-020-00667-2","mag":"3087037340"},"language":"en","primary_location":{"is_oa":true,"landing_page_url":"https://doi.org/10.1007/s10951-020-00667-2","pdf_url":"https://link.springer.com/content/pdf/10.1007/s10951-020-00667-2.pdf","source":{"id":"https://openalex.org/S91278097","display_name":"Journal of Scheduling","issn_l":"1094-6136","issn":["1094-6136","1099-1425"],"is_oa":false,"is_in_doaj":false,"is_indexed_in_scopus":true,"is_core":true,"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319965","https://openalex.org/P4310319900"],"host_organization_lineage_names":["Springer Nature","Springer Science+Business Media"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true},"type":"article","type_crossref":"journal-article","indexed_in":["arxiv","crossref","datacite"],"open_access":{"is_oa":true,"oa_status":"hybrid","oa_url":"https://link.springer.com/content/pdf/10.1007/s10951-020-00667-2.pdf","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5066485339","display_name":"Christoph Hertrich","orcid":"https://orcid.org/0000-0001-5646-8567"},"institutions":[{"id":"https://openalex.org/I153267046","display_name":"University of Kaiserslautern","ror":"https://ror.org/04zrf7b53","country_code":"DE","type":"funder","lineage":["https://openalex.org/I153267046"]}],"countries":["DE"],"is_corresponding":false,"raw_author_name":"Christoph Hertrich","raw_affiliation_strings":["Department of Mathematics, Technische Universit\u00e4t Kaiserslautern, 67663, Kaiserslautern, Germany"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics, Technische Universit\u00e4t Kaiserslautern, 67663, Kaiserslautern, Germany","institution_ids":["https://openalex.org/I153267046"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5001448799","display_name":"Christian Wei\u00df","orcid":"https://orcid.org/0000-0003-0577-9933"},"institutions":[{"id":"https://openalex.org/I3019415892","display_name":"Fraunhofer Institute for Industrial Mathematics","ror":"https://ror.org/019hjw009","country_code":"DE","type":"facility","lineage":["https://openalex.org/I3019415892","https://openalex.org/I4923324"]}],"countries":["DE"],"is_corresponding":false,"raw_author_name":"Christian Wei\u00df","raw_affiliation_strings":["Department of Optimization, Fraunhofer Institute for Industrial Mathematics ITWM, 67663, Kaiserslautern, Germany"],"affiliations":[{"raw_affiliation_string":"Department of Optimization, Fraunhofer Institute for Industrial Mathematics ITWM, 67663, Kaiserslautern, Germany","institution_ids":["https://openalex.org/I3019415892"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5064316993","display_name":"Heiner Ackermann","orcid":"https://orcid.org/0000-0003-4091-5558"},"institutions":[{"id":"https://openalex.org/I3019415892","display_name":"Fraunhofer Institute for Industrial Mathematics","ror":"https://ror.org/019hjw009","country_code":"DE","type":"facility","lineage":["https://openalex.org/I3019415892","https://openalex.org/I4923324"]}],"countries":["DE"],"is_corresponding":false,"raw_author_name":"Heiner Ackermann","raw_affiliation_strings":["Department of Optimization, Fraunhofer Institute for Industrial Mathematics ITWM, 67663, Kaiserslautern, Germany"],"affiliations":[{"raw_affiliation_string":"Department of Optimization, Fraunhofer Institute for Industrial Mathematics ITWM, 67663, Kaiserslautern, Germany","institution_ids":["https://openalex.org/I3019415892"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5023385398","display_name":"Sandy Heydrich","orcid":"https://orcid.org/0000-0002-7724-2644"},"institutions":[{"id":"https://openalex.org/I3019415892","display_name":"Fraunhofer Institute for Industrial Mathematics","ror":"https://ror.org/019hjw009","country_code":"DE","type":"facility","lineage":["https://openalex.org/I3019415892","https://openalex.org/I4923324"]}],"countries":["DE"],"is_corresponding":false,"raw_author_name":"Sandy Heydrich","raw_affiliation_strings":["Department of Optimization, Fraunhofer Institute for Industrial Mathematics ITWM, 67663, Kaiserslautern, Germany"],"affiliations":[{"raw_affiliation_string":"Department of Optimization, Fraunhofer Institute for Industrial Mathematics ITWM, 67663, Kaiserslautern, Germany","institution_ids":["https://openalex.org/I3019415892"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5069280526","display_name":"Sven O. Krumke","orcid":"https://orcid.org/0000-0002-8726-9963"},"institutions":[{"id":"https://openalex.org/I153267046","display_name":"University of Kaiserslautern","ror":"https://ror.org/04zrf7b53","country_code":"DE","type":"funder","lineage":["https://openalex.org/I153267046"]}],"countries":["DE"],"is_corresponding":false,"raw_author_name":"Sven O. Krumke","raw_affiliation_strings":["Department of Mathematics, Technische Universit\u00e4t Kaiserslautern, 67663, Kaiserslautern, Germany"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics, Technische Universit\u00e4t Kaiserslautern, 67663, Kaiserslautern, Germany","institution_ids":["https://openalex.org/I153267046"]}]}],"institution_assertions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":{"value":2290,"currency":"EUR","value_usd":2890},"apc_paid":{"value":2290,"currency":"EUR","value_usd":2890},"fwci":0.802,"has_fulltext":true,"fulltext_origin":"pdf","cited_by_count":4,"citation_normalized_percentile":{"value":0.909858,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":76,"max":78},"biblio":{"volume":"23","issue":"5","first_page":"575","last_page":"593"},"is_retracted":false,"is_paratext":false,"primary_topic":{"id":"https://openalex.org/T10551","display_name":"Scheduling and Optimization Algorithms","score":1.0,"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":1.0,"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/T12288","display_name":"Optimization and Search Problems","score":0.9977,"subfield":{"id":"https://openalex.org/subfields/1705","display_name":"Computer Networks and Communications"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T12176","display_name":"Optimization and Packing Problems","score":0.9957,"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/tardiness","display_name":"Tardiness","score":0.95193934}],"concepts":[{"id":"https://openalex.org/C2778047078","wikidata":"https://www.wikidata.org/wiki/Q82299449","display_name":"Tardiness","level":4,"score":0.95193934},{"id":"https://openalex.org/C55416958","wikidata":"https://www.wikidata.org/wiki/Q6206757","display_name":"Job shop scheduling","level":3,"score":0.7506647},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.6479701},{"id":"https://openalex.org/C206729178","wikidata":"https://www.wikidata.org/wiki/Q2271896","display_name":"Scheduling (production processes)","level":2,"score":0.62347984},{"id":"https://openalex.org/C311688","wikidata":"https://www.wikidata.org/wiki/Q2393193","display_name":"Time complexity","level":2,"score":0.519577},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.51951444},{"id":"https://openalex.org/C158336966","wikidata":"https://www.wikidata.org/wiki/Q3074426","display_name":"Flow shop scheduling","level":4,"score":0.4839185},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.41876006},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.28566146},{"id":"https://openalex.org/C68387754","wikidata":"https://www.wikidata.org/wiki/Q7271585","display_name":"Schedule","level":2,"score":0.0},{"id":"https://openalex.org/C111919701","wikidata":"https://www.wikidata.org/wiki/Q9135","display_name":"Operating system","level":1,"score":0.0}],"mesh":[],"locations_count":5,"locations":[{"is_oa":true,"landing_page_url":"https://doi.org/10.1007/s10951-020-00667-2","pdf_url":"https://link.springer.com/content/pdf/10.1007/s10951-020-00667-2.pdf","source":{"id":"https://openalex.org/S91278097","display_name":"Journal of Scheduling","issn_l":"1094-6136","issn":["1094-6136","1099-1425"],"is_oa":false,"is_in_doaj":false,"is_indexed_in_scopus":true,"is_core":true,"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319965","https://openalex.org/P4310319900"],"host_organization_lineage_names":["Springer Nature","Springer Science+Business Media"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true},{"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2006.09872","pdf_url":"https://arxiv.org/pdf/2006.09872","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_indexed_in_scopus":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":["Cornell University"],"type":"repository"},"license":null,"license_id":null,"version":"acceptedVersion","is_accepted":true,"is_published":false},{"is_oa":true,"landing_page_url":"https://kluedo.ub.uni-kl.de/frontdoor/index/index/docId/5496","pdf_url":"https://kluedo.ub.rptu.de/files/5496/masterThesis.pdf","source":{"id":"https://openalex.org/S4306402046","display_name":"Publication Server of Kaiserslautern University of Technology (Kaiserslautern University of Technology)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_indexed_in_scopus":false,"is_core":false,"host_organization":"https://openalex.org/I153267046","host_organization_name":"University of Kaiserslautern","host_organization_lineage":["https://openalex.org/I153267046"],"host_organization_lineage_names":["University of Kaiserslautern"],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"submittedVersion","is_accepted":false,"is_published":false},{"is_oa":true,"landing_page_url":"https://kluedo.ub.uni-kl.de/files/5496/masterThesis.pdf","pdf_url":"https://kluedo.ub.uni-kl.de/files/5496/masterThesis.pdf","source":{"id":"https://openalex.org/S4306402046","display_name":"Publication Server of Kaiserslautern University of Technology (Kaiserslautern University of Technology)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_indexed_in_scopus":false,"is_core":false,"host_organization":"https://openalex.org/I153267046","host_organization_name":"University of Kaiserslautern","host_organization_lineage":["https://openalex.org/I153267046"],"host_organization_lineage_names":["University of Kaiserslautern"],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"submittedVersion","is_accepted":false,"is_published":false},{"is_oa":false,"landing_page_url":"https://api.datacite.org/dois/10.48550/arxiv.2006.09872","pdf_url":null,"source":{"id":"https://openalex.org/S4393179698","display_name":"DataCite API","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_indexed_in_scopus":false,"is_core":false,"host_organization":"https://openalex.org/I4210145204","host_organization_name":"DataCite","host_organization_lineage":["https://openalex.org/I4210145204"],"host_organization_lineage_names":["DataCite"],"type":"metadata"},"license":null,"license_id":null,"version":null}],"best_oa_location":{"is_oa":true,"landing_page_url":"https://doi.org/10.1007/s10951-020-00667-2","pdf_url":"https://link.springer.com/content/pdf/10.1007/s10951-020-00667-2.pdf","source":{"id":"https://openalex.org/S91278097","display_name":"Journal of Scheduling","issn_l":"1094-6136","issn":["1094-6136","1099-1425"],"is_oa":false,"is_in_doaj":false,"is_indexed_in_scopus":true,"is_core":true,"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319965","https://openalex.org/P4310319900"],"host_organization_lineage_names":["Springer Nature","Springer Science+Business Media"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true},"sustainable_development_goals":[{"display_name":"Industry, innovation and infrastructure","score":0.53,"id":"https://metadata.un.org/sdg/9"}],"grants":[],"datasets":[],"versions":["https://openalex.org/W2943672646","https://openalex.org/W3087037340"],"referenced_works_count":37,"referenced_works":["https://openalex.org/W1488422606","https://openalex.org/W1791475283","https://openalex.org/W1966303191","https://openalex.org/W1975678202","https://openalex.org/W1979867954","https://openalex.org/W1986284055","https://openalex.org/W2011912841","https://openalex.org/W2022012895","https://openalex.org/W2024085737","https://openalex.org/W2034279788","https://openalex.org/W2064961370","https://openalex.org/W2066466881","https://openalex.org/W2076671014","https://openalex.org/W2077168140","https://openalex.org/W2077214869","https://openalex.org/W2081195398","https://openalex.org/W2092288295","https://openalex.org/W2107481047","https://openalex.org/W2111001493","https://openalex.org/W2136186989","https://openalex.org/W2157846217","https://openalex.org/W2160283566","https://openalex.org/W2168633992","https://openalex.org/W2301104033","https://openalex.org/W2341350247","https://openalex.org/W2344946706","https://openalex.org/W238776573","https://openalex.org/W2588704993","https://openalex.org/W2626058839","https://openalex.org/W2751935900","https://openalex.org/W2939739936","https://openalex.org/W2941444704","https://openalex.org/W2972216804","https://openalex.org/W3087037340","https://openalex.org/W3089206849","https://openalex.org/W3090498441","https://openalex.org/W4239337465"],"related_works":["https://openalex.org/W3216729967","https://openalex.org/W3097192092","https://openalex.org/W3029619930","https://openalex.org/W2967782293","https://openalex.org/W2955323683","https://openalex.org/W2902517208","https://openalex.org/W2185192838","https://openalex.org/W2113526966","https://openalex.org/W2061005265","https://openalex.org/W1980879778"],"abstract_inverted_index":{"Abstract":[0],"In":[1],"this":[2],"paper":[3],"we":[4,89],"study":[5],"a":[6,17],"proportionate":[7],"flow":[8],"shop":[9],"of":[10,31,60,72,79,113],"batching":[11],"machines":[12],"with":[13],"release":[14,121],"dates":[15,122],"and":[16,76,110],"fixed":[18,70],"number":[19,71,112],"$$m":[20],"\\ge":[21],"2$$":[22],"":[24],"":[25],"m":[26],"\u2265":[27],"2":[28],"":[29],"":[30],"machines.":[32,135],"The":[33],"scheduling":[34],"problem":[35],"has":[36,50],"so":[37],"far":[38],"barely":[39],"received":[40],"any":[41,69],"attention":[42],"in":[43,56,85,116],"the":[44,57,74,77,92,101],"literature,":[45],"but":[46],"recently":[47],"its":[48],"importance":[49],"increased":[51],"significantly,":[52],"due":[53],"to":[54,99],"applications":[55],"industrial":[58],"scaling":[59],"modern":[61],"bio-medicine":[62],"production":[63],"processes.":[64],"We":[65],"show":[66,90],"that":[67,91],"for":[68,133],"machines,":[73],"makespan":[75],"sum":[78],"completion":[80,104],"times":[81],"can":[82,95],"be":[83,97],"minimized":[84],"polynomial":[86,117,126],"time.":[87],"Furthermore,":[88],"obtained":[93],"algorithm":[94],"also":[96],"used":[98],"minimize":[100],"weighted":[102],"total":[103,108],"time,":[105],"maximum":[106],"lateness,":[107],"tardiness":[109],"(weighted)":[111],"late":[114],"jobs":[115],"time":[118,127],"if":[119],"all":[120],"are":[123],"0.":[124],"Previously,":[125],"algorithms":[128],"have":[129],"only":[130],"been":[131],"known":[132],"two":[134]},"abstract_inverted_index_v3":null,"cited_by_api_url":"https://api.openalex.org/works?filter=cites:W3087037340","counts_by_year":[{"year":2021,"cited_by_count":2},{"year":2020,"cited_by_count":2}],"updated_date":"2025-04-26T17:56:17.972226","created_date":"2020-09-25"}