{"id":"https://openalex.org/W3021817659","doi":"https://doi.org/10.1007/s10951-022-00732-y","title":"Online algorithms to schedule a proportionate flexible flow shop of batching machines","display_name":"Online algorithms to schedule a proportionate flexible flow shop of batching machines","publication_year":2022,"publication_date":"2022-04-11","ids":{"openalex":"https://openalex.org/W3021817659","doi":"https://doi.org/10.1007/s10951-022-00732-y","mag":"3021817659"},"language":"en","primary_location":{"id":"doi:10.1007/s10951-022-00732-y","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s10951-022-00732-y","pdf_url":"https://link.springer.com/content/pdf/10.1007/s10951-022-00732-y.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/s10951-022-00732-y.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":"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":false,"raw_author_name":"Christoph Hertrich","raw_affiliation_strings":["Department of Mathematics, Technische Universit\u00e4t Kaiserslautern, 67663, Kaiserslautern, Germany","Institute of Mathematics, Technische Universit\u00e4t Berlin, 10623, 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":"Institute of Mathematics, Technische Universit\u00e4t Berlin, 10623, Berlin, Germany","institution_ids":["https://openalex.org/I4577782"]}]},{"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":true,"raw_author_name":"Christian Wei\u00df","raw_affiliation_strings":["Department of Optimization, Fraunhofer Institute for Industrial Mathematics ITWM, 67663, 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"]}]},{"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"],"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"]}]},{"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"],"raw_orcid":"https://orcid.org/0000-0002-7724-2644","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":"education","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"],"raw_orcid":"https://orcid.org/0000-0002-8726-9963","affiliations":[{"raw_affiliation_string":"Department of Mathematics, Technische Universit\u00e4t Kaiserslautern, 67663, Kaiserslautern, Germany","institution_ids":["https://openalex.org/I153267046"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":5,"corresponding_author_ids":["https://openalex.org/A5001448799"],"corresponding_institution_ids":["https://openalex.org/I3019415892"],"apc_list":{"value":2290,"currency":"EUR","value_usd":2890},"apc_paid":{"value":2290,"currency":"EUR","value_usd":2890},"fwci":0.4066,"has_fulltext":true,"cited_by_count":3,"citation_normalized_percentile":{"value":0.65541865,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":96},"biblio":{"volume":"25","issue":"6","first_page":"643","last_page":"657"},"is_retracted":false,"is_paratext":false,"is_xpac":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":0.9994000196456909,"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/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"}}],"keywords":[{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.8055610656738281},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.707737386226654},{"id":"https://openalex.org/keywords/job-shop-scheduling","display_name":"Job shop scheduling","score":0.6001139879226685},{"id":"https://openalex.org/keywords/scheduling","display_name":"Scheduling (production processes)","score":0.5578897595405579},{"id":"https://openalex.org/keywords/competitive-analysis","display_name":"Competitive analysis","score":0.5123196840286255},{"id":"https://openalex.org/keywords/schedule","display_name":"Schedule","score":0.42136022448539734},{"id":"https://openalex.org/keywords/online-algorithm","display_name":"Online algorithm","score":0.41716018319129944},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.33813220262527466},{"id":"https://openalex.org/keywords/machine-learning","display_name":"Machine learning","score":0.33631277084350586},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.2051633894443512},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.20010533928871155},{"id":"https://openalex.org/keywords/upper-and-lower-bounds","display_name":"Upper and lower bounds","score":0.1322576403617859}],"concepts":[{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.8055610656738281},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.707737386226654},{"id":"https://openalex.org/C55416958","wikidata":"https://www.wikidata.org/wiki/Q6206757","display_name":"Job shop scheduling","level":3,"score":0.6001139879226685},{"id":"https://openalex.org/C206729178","wikidata":"https://www.wikidata.org/wiki/Q2271896","display_name":"Scheduling (production processes)","level":2,"score":0.5578897595405579},{"id":"https://openalex.org/C102408133","wikidata":"https://www.wikidata.org/wiki/Q5156350","display_name":"Competitive analysis","level":3,"score":0.5123196840286255},{"id":"https://openalex.org/C68387754","wikidata":"https://www.wikidata.org/wiki/Q7271585","display_name":"Schedule","level":2,"score":0.42136022448539734},{"id":"https://openalex.org/C196921405","wikidata":"https://www.wikidata.org/wiki/Q786431","display_name":"Online algorithm","level":2,"score":0.41716018319129944},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.33813220262527466},{"id":"https://openalex.org/C119857082","wikidata":"https://www.wikidata.org/wiki/Q2539","display_name":"Machine learning","level":1,"score":0.33631277084350586},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.2051633894443512},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.20010533928871155},{"id":"https://openalex.org/C77553402","wikidata":"https://www.wikidata.org/wiki/Q13222579","display_name":"Upper and lower bounds","level":2,"score":0.1322576403617859},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","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}],"mesh":[],"locations_count":5,"locations":[{"id":"doi:10.1007/s10951-022-00732-y","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s10951-022-00732-y","pdf_url":"https://link.springer.com/content/pdf/10.1007/s10951-022-00732-y.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:2005.03552","is_oa":true,"landing_page_url":"http://arxiv.org/abs/2005.03552","pdf_url":"https://arxiv.org/pdf/2005.03552","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:25:y:2022:i:6:d:10.1007_s10951-022-00732-y","is_oa":false,"landing_page_url":"http://link.springer.com/10.1007/s10951-022-00732-y","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:10419/312241","is_oa":true,"landing_page_url":"https://hdl.handle.net/10419/312241","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":null,"raw_type":"doc-type:article"},{"id":"pmh:oai:publica.fraunhofer.de:publica/427399","is_oa":false,"landing_page_url":"https://publica.fraunhofer.de/handle/publica/427399","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/s10951-022-00732-y","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s10951-022-00732-y","pdf_url":"https://link.springer.com/content/pdf/10.1007/s10951-022-00732-y.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":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W3021817659.pdf","grobid_xml":"https://content.openalex.org/works/W3021817659.grobid-xml"},"referenced_works_count":25,"referenced_works":["https://openalex.org/W238776573","https://openalex.org/W1488422606","https://openalex.org/W1966303191","https://openalex.org/W1970915793","https://openalex.org/W1972609089","https://openalex.org/W1979867954","https://openalex.org/W2004572055","https://openalex.org/W2011912841","https://openalex.org/W2015117320","https://openalex.org/W2060749288","https://openalex.org/W2063824228","https://openalex.org/W2064961370","https://openalex.org/W2066466881","https://openalex.org/W2073731934","https://openalex.org/W2076671014","https://openalex.org/W2077168140","https://openalex.org/W2124860803","https://openalex.org/W2169465249","https://openalex.org/W2626058839","https://openalex.org/W2766772614","https://openalex.org/W2937649430","https://openalex.org/W2943672646","https://openalex.org/W2968713904","https://openalex.org/W3089206849","https://openalex.org/W4255654664"],"related_works":["https://openalex.org/W4213299358","https://openalex.org/W2564742953","https://openalex.org/W2793095688","https://openalex.org/W1623410360","https://openalex.org/W3115340459","https://openalex.org/W2950803469","https://openalex.org/W4390203503","https://openalex.org/W2797898895","https://openalex.org/W2131569046","https://openalex.org/W2045215405"],"abstract_inverted_index":{"Abstract":[0],"This":[1],"paper":[2,176],"is":[3,24,65,73,172],"the":[4,54,106,113,127,152,174],"first":[5,63,175],"to":[6,10,38,57,177],"consider":[7],"online":[8,47,179],"algorithms":[9],"schedule":[11],"a":[12],"proportionate":[13,161],"flexible":[14],"flow":[15,95,163],"shop":[16],"of":[17,29,81,165],"batching":[18,166],"machines":[19,167],"(PFFB).":[20],"The":[21,62],"scheduling":[22,70,87],"model":[23],"motivated":[25],"by":[26],"manufacturing":[27],"processes":[28],"individualized":[30],"medicaments,":[31],"which":[32,170],"are":[33],"used":[34],"in":[35],"modern":[36],"medicine":[37],"treat":[39],"some":[40],"serious":[41],"illnesses.":[42],"We":[43,89],"provide":[44],"two":[45,110],"different":[46],"algorithms,":[48],"proving":[49],"also":[50,90,158,173],"lower":[51],"bounds":[52],"for":[53,75,84,93,160,169],"offline":[55],"problem":[56],"compute":[58],"their":[59],"competitive":[60,102,130],"ratios.":[61],"algorithm":[64,99,124],"an":[66,78,122],"easy-to-implement,":[67],"general":[68],"local":[69],"heuristic.":[71],"It":[72],"2-competitive":[74],"PFFBs":[76],"with":[77,100,109],"arbitrary":[79],"number":[80],"stages":[82,111],"and":[83,112],"several":[85],"natural":[86],"objectives.":[88],"show":[91],"that":[92,125],"total/average":[94],"time,":[96],"no":[97],"deterministic":[98],"better":[101],"ratio":[103,131],"exists.":[104],"For":[105],"special":[107],"case":[108],"makespan":[114],"or":[115],"total":[116],"completion":[117],"time":[118],"objective,":[119],"we":[120],"describe":[121],"improved":[123],"achieves":[126],"best":[128],"possible":[129],"$$\\varphi":[132],"=\\frac{1+\\sqrt{5}}{2}$$":[133],"<mml:math":[134],"xmlns:mml=\"http://www.w3.org/1998/Math/MathML\">":[135],"<mml:mrow>":[136,140],"<mml:mi>\u03c6</mml:mi>":[137],"<mml:mo>=</mml:mo>":[138],"<mml:mfrac>":[139],"<mml:mn>1</mml:mn>":[141],"<mml:mo>+</mml:mo>":[142],"<mml:msqrt>":[143],"<mml:mn>5</mml:mn>":[144],"</mml:msqrt>":[145],"</mml:mrow>":[146,149],"<mml:mn>2</mml:mn>":[147],"</mml:mfrac>":[148],"</mml:math>":[150],",":[151],"golden":[153],"ratio.":[154],"All":[155],"our":[156],"results":[157],"hold":[159],"(non-flexible)":[162],"shops":[164],"(PFB)":[168],"this":[171],"study":[178],"algorithms.":[180]},"counts_by_year":[{"year":2024,"cited_by_count":2},{"year":2023,"cited_by_count":1}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}