{"id":"https://openalex.org/W2943672646","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/W2943672646","doi":"https://doi.org/10.1007/s10951-020-00667-2","mag":"2943672646"},"language":"en","primary_location":{"id":"doi:10.1007/s10951-020-00667-2","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_core":true,"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":"Journal of Scheduling","raw_type":"journal-article"},"type":"article","indexed_in":["arxiv","crossref"],"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":null,"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":"education","lineage":["https://openalex.org/I153267046"]},{"id":"https://openalex.org/I4577782","display_name":"Technische Universit\u00e4t Berlin","ror":"https://ror.org/03v4gjf40","country_code":"DE","type":"education","lineage":["https://openalex.org/I4577782"]}],"countries":["DE"],"is_corresponding":true,"raw_author_name":"Christoph Hertrich","raw_affiliation_strings":["Department of Mathematics, Technische Universit\u00e4t Kaiserslautern, 67663, Kaiserslautern, Germany","Department of Mathematics, Technische Universit\u00e4t Kaiserslautern, Kaiserslautern, Germany","Institute of Mathematics, Technische Universit\u00e4t Berlin, 10623, Berlin, Germany","Institute of Mathematics, Technische Universit\u00e4t Berlin, Berlin, Germany"],"raw_orcid":"https://orcid.org/0000-0001-5646-8567","affiliations":[{"raw_affiliation_string":"Department of Mathematics, Technische Universit\u00e4t Kaiserslautern, 67663, Kaiserslautern, Germany","institution_ids":["https://openalex.org/I153267046"]},{"raw_affiliation_string":"Department of Mathematics, Technische Universit\u00e4t Kaiserslautern, Kaiserslautern, Germany","institution_ids":["https://openalex.org/I153267046"]},{"raw_affiliation_string":"Institute of Mathematics, Technische Universit\u00e4t Berlin, 10623, Berlin, Germany","institution_ids":["https://openalex.org/I4577782"]},{"raw_affiliation_string":"Institute of Mathematics, Technische Universit\u00e4t Berlin, Berlin, Germany","institution_ids":["https://openalex.org/I4577782"]}]},{"author_position":"middle","author":{"id":null,"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":true,"raw_author_name":"Christian Wei\u00df","raw_affiliation_strings":["Department of Optimization, Fraunhofer Institute for Industrial Mathematics ITWM, 67663, Kaiserslautern, Germany","Department of Optimization, Fraunhofer Institute for Industrial Mathematics ITWM, Kaiserslautern, Germany"],"raw_orcid":"https://orcid.org/0000-0003-0577-9933","affiliations":[{"raw_affiliation_string":"Department of Optimization, Fraunhofer Institute for Industrial Mathematics ITWM, 67663, Kaiserslautern, Germany","institution_ids":["https://openalex.org/I3019415892"]},{"raw_affiliation_string":"Department of Optimization, Fraunhofer Institute for Industrial Mathematics ITWM, Kaiserslautern, Germany","institution_ids":["https://openalex.org/I3019415892"]}]},{"author_position":"middle","author":{"id":null,"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":true,"raw_author_name":"Heiner Ackermann","raw_affiliation_strings":["Department of Optimization, Fraunhofer Institute for Industrial Mathematics ITWM, 67663, Kaiserslautern, Germany","Department of Optimization, Fraunhofer Institute for Industrial Mathematics ITWM, Kaiserslautern, Germany"],"raw_orcid":"https://orcid.org/0000-0003-4091-5558","affiliations":[{"raw_affiliation_string":"Department of Optimization, Fraunhofer Institute for Industrial Mathematics ITWM, 67663, Kaiserslautern, Germany","institution_ids":["https://openalex.org/I3019415892"]},{"raw_affiliation_string":"Department of Optimization, Fraunhofer Institute for Industrial Mathematics ITWM, Kaiserslautern, Germany","institution_ids":["https://openalex.org/I3019415892"]}]},{"author_position":"middle","author":{"id":null,"display_name":"Sandy Heydrich","orcid":null},"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":true,"raw_author_name":"Sandy Heydrich","raw_affiliation_strings":["Department of Optimization, Fraunhofer Institute for Industrial Mathematics ITWM, 67663, Kaiserslautern, Germany","Department of Optimization, Fraunhofer Institute for Industrial Mathematics ITWM, Kaiserslautern, Germany"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Optimization, Fraunhofer Institute for Industrial Mathematics ITWM, 67663, Kaiserslautern, Germany","institution_ids":["https://openalex.org/I3019415892"]},{"raw_affiliation_string":"Department of Optimization, Fraunhofer Institute for Industrial Mathematics ITWM, Kaiserslautern, Germany","institution_ids":["https://openalex.org/I3019415892"]}]},{"author_position":"last","author":{"id":null,"display_name":"Sven O. Krumke","orcid":null},"institutions":[{"id":"https://openalex.org/I153267046","display_name":"University of Kaiserslautern","ror":"https://ror.org/04zrf7b53","country_code":"DE","type":"education","lineage":["https://openalex.org/I153267046"]}],"countries":["DE"],"is_corresponding":true,"raw_author_name":"Sven O. Krumke","raw_affiliation_strings":["Department of Mathematics, Technische Universit\u00e4t Kaiserslautern, 67663, Kaiserslautern, Germany","Department of Mathematics, Technische Universit\u00e4t Kaiserslautern, Kaiserslautern, Germany"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics, Technische Universit\u00e4t Kaiserslautern, 67663, Kaiserslautern, Germany","institution_ids":["https://openalex.org/I153267046"]},{"raw_affiliation_string":"Department of Mathematics, Technische Universit\u00e4t Kaiserslautern, Kaiserslautern, Germany","institution_ids":["https://openalex.org/I153267046"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":3,"corresponding_author_ids":[],"corresponding_institution_ids":["https://openalex.org/I153267046","https://openalex.org/I3019415892","https://openalex.org/I4577782"],"apc_list":{"value":2290,"currency":"EUR","value_usd":2890},"apc_paid":{"value":2290,"currency":"EUR","value_usd":2890},"fwci":0.3512,"has_fulltext":true,"cited_by_count":6,"citation_normalized_percentile":{"value":0.65412994,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":97},"biblio":{"volume":"23","issue":"5","first_page":"575","last_page":"593"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10551","display_name":"Scheduling and Optimization Algorithms","score":0.9545000195503235,"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":0.9545000195503235,"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/T10328","display_name":"Supply Chain and Inventory Management","score":0.007499999832361937,"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/T12288","display_name":"Optimization and Search Problems","score":0.007199999876320362,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/tardiness","display_name":"Tardiness","score":0.9218000173568726},{"id":"https://openalex.org/keywords/job-shop-scheduling","display_name":"Job shop scheduling","score":0.7566999793052673},{"id":"https://openalex.org/keywords/flow-shop-scheduling","display_name":"Flow shop scheduling","score":0.6679999828338623},{"id":"https://openalex.org/keywords/scheduling","display_name":"Scheduling (production processes)","score":0.6327999830245972},{"id":"https://openalex.org/keywords/time-complexity","display_name":"Time complexity","score":0.5511999726295471},{"id":"https://openalex.org/keywords/due-date","display_name":"Due date","score":0.4237000048160553},{"id":"https://openalex.org/keywords/polynomial","display_name":"Polynomial","score":0.3653999865055084}],"concepts":[{"id":"https://openalex.org/C2778047078","wikidata":"https://www.wikidata.org/wiki/Q82299449","display_name":"Tardiness","level":4,"score":0.9218000173568726},{"id":"https://openalex.org/C55416958","wikidata":"https://www.wikidata.org/wiki/Q6206757","display_name":"Job shop scheduling","level":3,"score":0.7566999793052673},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.689300000667572},{"id":"https://openalex.org/C158336966","wikidata":"https://www.wikidata.org/wiki/Q3074426","display_name":"Flow shop scheduling","level":4,"score":0.6679999828338623},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.6478000283241272},{"id":"https://openalex.org/C206729178","wikidata":"https://www.wikidata.org/wiki/Q2271896","display_name":"Scheduling (production processes)","level":2,"score":0.6327999830245972},{"id":"https://openalex.org/C311688","wikidata":"https://www.wikidata.org/wiki/Q2393193","display_name":"Time complexity","level":2,"score":0.5511999726295471},{"id":"https://openalex.org/C3019208289","wikidata":"https://www.wikidata.org/wiki/Q56612115","display_name":"Due date","level":3,"score":0.4237000048160553},{"id":"https://openalex.org/C90119067","wikidata":"https://www.wikidata.org/wiki/Q43260","display_name":"Polynomial","level":2,"score":0.3653999865055084},{"id":"https://openalex.org/C99844830","wikidata":"https://www.wikidata.org/wiki/Q102441924","display_name":"Scaling","level":2,"score":0.3540000021457672},{"id":"https://openalex.org/C2778348673","wikidata":"https://www.wikidata.org/wiki/Q739302","display_name":"Production (economics)","level":2,"score":0.32120001316070557},{"id":"https://openalex.org/C38349280","wikidata":"https://www.wikidata.org/wiki/Q1434290","display_name":"Flow (mathematics)","level":2,"score":0.3188999891281128},{"id":"https://openalex.org/C44104985","wikidata":"https://www.wikidata.org/wiki/Q492886","display_name":"Supply chain management","level":3,"score":0.29679998755455017},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.2768000066280365},{"id":"https://openalex.org/C157469704","wikidata":"https://www.wikidata.org/wiki/Q2585642","display_name":"Maximum flow problem","level":2,"score":0.2718999981880188},{"id":"https://openalex.org/C2780271269","wikidata":"https://www.wikidata.org/wiki/Q19295956","display_name":"Single-machine scheduling","level":4,"score":0.25690001249313354}],"mesh":[],"locations_count":5,"locations":[{"id":"doi:10.1007/s10951-020-00667-2","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_core":true,"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":"Journal of Scheduling","raw_type":"journal-article"},{"id":"pmh:oai:arXiv.org:2006.09872","is_oa":true,"landing_page_url":"http://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_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"acceptedVersion","is_accepted":true,"is_published":false,"raw_source_name":null,"raw_type":"text"},{"id":"pmh:oai:RePEc:spr:jsched:v:23:y:2020:i:5:d:10.1007_s10951-020-00667-2","is_oa":false,"landing_page_url":"http://link.springer.com/10.1007/s10951-020-00667-2","pdf_url":null,"source":{"id":"https://openalex.org/S4306401271","display_name":"RePEc: Research Papers in Economics","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I77793887","host_organization_name":"Federal Reserve Bank of St. Louis","host_organization_lineage":["https://openalex.org/I77793887"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"article"},{"id":"pmh:oai:econstor.eu:10419/288444","is_oa":true,"landing_page_url":"https://hdl.handle.net/10419/288444","pdf_url":null,"source":{"id":"https://openalex.org/S4306401696","display_name":"Econstor (Econstor)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"doc-type:article"},{"id":"pmh:oai:publica.fraunhofer.de:publica/265727","is_oa":false,"landing_page_url":"https://publica.fraunhofer.de/handle/publica/265727","pdf_url":null,"source":{"id":"https://openalex.org/S4306400318","display_name":"Fraunhofer-Publica (Fraunhofer-Gesellschaft)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I4923324","host_organization_name":"Fraunhofer-Gesellschaft","host_organization_lineage":["https://openalex.org/I4923324"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"journal article"}],"best_oa_location":{"id":"doi:10.1007/s10951-020-00667-2","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_core":true,"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":"Journal of Scheduling","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W2943672646.pdf","grobid_xml":"https://content.openalex.org/works/W2943672646.grobid-xml"},"referenced_works_count":31,"referenced_works":["https://openalex.org/W1488422606","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/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/W2344946706","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/W6638028154"],"related_works":[],"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],"<mml:math":[23],"xmlns:mml=\"http://www.w3.org/1998/Math/MathML\">":[24],"<mml:mrow>":[25],"<mml:mi>m</mml:mi>":[26],"<mml:mo>\u2265</mml:mo>":[27],"<mml:mn>2</mml:mn>":[28],"</mml:mrow>":[29],"</mml:math>":[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]},"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2025,"cited_by_count":1},{"year":2024,"cited_by_count":2},{"year":2022,"cited_by_count":1},{"year":2021,"cited_by_count":1}],"updated_date":"2026-07-03T08:13:44.112507","created_date":"2019-05-09T00:00:00"}
