{"id":"https://openalex.org/W4383908705","doi":"https://doi.org/10.3390/computation11070137","title":"Makespan Minimization for the Two-Stage Hybrid Flow Shop Problem with Dedicated Machines: A Comprehensive Study of Exact and Heuristic Approaches","display_name":"Makespan Minimization for the Two-Stage Hybrid Flow Shop Problem with Dedicated Machines: A Comprehensive Study of Exact and Heuristic Approaches","publication_year":2023,"publication_date":"2023-07-10","ids":{"openalex":"https://openalex.org/W4383908705","doi":"https://doi.org/10.3390/computation11070137"},"language":"en","primary_location":{"id":"doi:10.3390/computation11070137","is_oa":true,"landing_page_url":"https://doi.org/10.3390/computation11070137","pdf_url":"https://www.mdpi.com/2079-3197/11/7/137/pdf?version=1688985007","source":{"id":"https://openalex.org/S2738402919","display_name":"Computation","issn_l":"2079-3197","issn":["2079-3197"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310310987","host_organization_name":"Multidisciplinary Digital Publishing Institute","host_organization_lineage":["https://openalex.org/P4310310987"],"host_organization_lineage_names":["Multidisciplinary Digital Publishing Institute"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Computation","raw_type":"journal-article"},"type":"article","indexed_in":["crossref","doaj"],"open_access":{"is_oa":true,"oa_status":"gold","oa_url":"https://www.mdpi.com/2079-3197/11/7/137/pdf?version=1688985007","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5101951003","display_name":"M. Hajji","orcid":"https://orcid.org/0009-0007-1735-3522"},"institutions":[{"id":"https://openalex.org/I2803079837","display_name":"American University of the Middle East","ror":"https://ror.org/02gqgne03","country_code":"KW","type":"education","lineage":["https://openalex.org/I2803079837"]}],"countries":["KW"],"is_corresponding":true,"raw_author_name":"Mohamed Karim Hajji","raw_affiliation_strings":["College of Engineering and Technology, American University of the Middle East, Egaila 54200, Kuwait"],"affiliations":[{"raw_affiliation_string":"College of Engineering and Technology, American University of the Middle East, Egaila 54200, Kuwait","institution_ids":["https://openalex.org/I2803079837"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5058424456","display_name":"Hatem Hadda","orcid":"https://orcid.org/0000-0002-0010-8885"},"institutions":[{"id":"https://openalex.org/I4210131288","display_name":"National Engineering School of Tunis","ror":"https://ror.org/03b1zjt31","country_code":"TN","type":"education","lineage":["https://openalex.org/I4210131288","https://openalex.org/I63596082"]},{"id":"https://openalex.org/I63596082","display_name":"Tunis El Manar University","ror":"https://ror.org/029cgt552","country_code":"TN","type":"education","lineage":["https://openalex.org/I63596082"]},{"id":"https://openalex.org/I108714496","display_name":"Tunis University","ror":"https://ror.org/02q1spa57","country_code":"TN","type":"education","lineage":["https://openalex.org/I108714496"]}],"countries":["TN"],"is_corresponding":false,"raw_author_name":"Hatem Hadda","raw_affiliation_strings":["Oasis, Ecole Nationale d\u2019Ing\u00e9nieurs de Tunis, Universit\u00e9 de Tunis El Manar, Tunis 1068, Tunisia"],"affiliations":[{"raw_affiliation_string":"Oasis, Ecole Nationale d\u2019Ing\u00e9nieurs de Tunis, Universit\u00e9 de Tunis El Manar, Tunis 1068, Tunisia","institution_ids":["https://openalex.org/I108714496","https://openalex.org/I4210131288","https://openalex.org/I63596082"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5109681698","display_name":"Najoua Dridi","orcid":null},"institutions":[{"id":"https://openalex.org/I108714496","display_name":"Tunis University","ror":"https://ror.org/02q1spa57","country_code":"TN","type":"education","lineage":["https://openalex.org/I108714496"]},{"id":"https://openalex.org/I4210131288","display_name":"National Engineering School of Tunis","ror":"https://ror.org/03b1zjt31","country_code":"TN","type":"education","lineage":["https://openalex.org/I4210131288","https://openalex.org/I63596082"]},{"id":"https://openalex.org/I63596082","display_name":"Tunis El Manar University","ror":"https://ror.org/029cgt552","country_code":"TN","type":"education","lineage":["https://openalex.org/I63596082"]}],"countries":["TN"],"is_corresponding":false,"raw_author_name":"Najoua Dridi","raw_affiliation_strings":["Oasis, Ecole Nationale d\u2019Ing\u00e9nieurs de Tunis, Universit\u00e9 de Tunis El Manar, Tunis 1068, Tunisia"],"affiliations":[{"raw_affiliation_string":"Oasis, Ecole Nationale d\u2019Ing\u00e9nieurs de Tunis, Universit\u00e9 de Tunis El Manar, Tunis 1068, Tunisia","institution_ids":["https://openalex.org/I108714496","https://openalex.org/I4210131288","https://openalex.org/I63596082"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5101951003"],"corresponding_institution_ids":["https://openalex.org/I2803079837"],"apc_list":{"value":1400,"currency":"CHF","value_usd":1515},"apc_paid":{"value":1400,"currency":"CHF","value_usd":1515},"fwci":1.4508,"has_fulltext":true,"cited_by_count":7,"citation_normalized_percentile":{"value":0.84004015,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":96,"max":98},"biblio":{"volume":"11","issue":"7","first_page":"137","last_page":"137"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10551","display_name":"Scheduling and Optimization Algorithms","score":0.9998999834060669,"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":0.9998999834060669,"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/T12782","display_name":"Assembly Line Balancing Optimization","score":0.996399998664856,"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":0.9937999844551086,"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/tabu-search","display_name":"Tabu search","score":0.8357787728309631},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.7326943874359131},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.6752160787582397},{"id":"https://openalex.org/keywords/job-shop-scheduling","display_name":"Job shop scheduling","score":0.6067228317260742},{"id":"https://openalex.org/keywords/solver","display_name":"Solver","score":0.5553714036941528},{"id":"https://openalex.org/keywords/heuristic","display_name":"Heuristic","score":0.5371907353401184},{"id":"https://openalex.org/keywords/incremental-heuristic-search","display_name":"Incremental heuristic search","score":0.49012288451194763},{"id":"https://openalex.org/keywords/constraint-programming","display_name":"Constraint programming","score":0.4871663749217987},{"id":"https://openalex.org/keywords/scheduling","display_name":"Scheduling (production processes)","score":0.4562495946884155},{"id":"https://openalex.org/keywords/constraint","display_name":"Constraint (computer-aided design)","score":0.45090287923812866},{"id":"https://openalex.org/keywords/beam-search","display_name":"Beam search","score":0.43039727210998535},{"id":"https://openalex.org/keywords/search-algorithm","display_name":"Search algorithm","score":0.30046868324279785},{"id":"https://openalex.org/keywords/schedule","display_name":"Schedule","score":0.22510987520217896},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.1843683421611786},{"id":"https://openalex.org/keywords/stochastic-programming","display_name":"Stochastic programming","score":0.1148657500743866}],"concepts":[{"id":"https://openalex.org/C123370116","wikidata":"https://www.wikidata.org/wiki/Q1424540","display_name":"Tabu search","level":2,"score":0.8357787728309631},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.7326943874359131},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.6752160787582397},{"id":"https://openalex.org/C55416958","wikidata":"https://www.wikidata.org/wiki/Q6206757","display_name":"Job shop scheduling","level":3,"score":0.6067228317260742},{"id":"https://openalex.org/C2778770139","wikidata":"https://www.wikidata.org/wiki/Q1966904","display_name":"Solver","level":2,"score":0.5553714036941528},{"id":"https://openalex.org/C173801870","wikidata":"https://www.wikidata.org/wiki/Q201413","display_name":"Heuristic","level":2,"score":0.5371907353401184},{"id":"https://openalex.org/C139979381","wikidata":"https://www.wikidata.org/wiki/Q17056021","display_name":"Incremental heuristic search","level":4,"score":0.49012288451194763},{"id":"https://openalex.org/C173404611","wikidata":"https://www.wikidata.org/wiki/Q528588","display_name":"Constraint programming","level":3,"score":0.4871663749217987},{"id":"https://openalex.org/C206729178","wikidata":"https://www.wikidata.org/wiki/Q2271896","display_name":"Scheduling (production processes)","level":2,"score":0.4562495946884155},{"id":"https://openalex.org/C2776036281","wikidata":"https://www.wikidata.org/wiki/Q48769818","display_name":"Constraint (computer-aided design)","level":2,"score":0.45090287923812866},{"id":"https://openalex.org/C19889080","wikidata":"https://www.wikidata.org/wiki/Q2835852","display_name":"Beam search","level":3,"score":0.43039727210998535},{"id":"https://openalex.org/C125583679","wikidata":"https://www.wikidata.org/wiki/Q755673","display_name":"Search algorithm","level":2,"score":0.30046868324279785},{"id":"https://openalex.org/C68387754","wikidata":"https://www.wikidata.org/wiki/Q7271585","display_name":"Schedule","level":2,"score":0.22510987520217896},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.1843683421611786},{"id":"https://openalex.org/C137631369","wikidata":"https://www.wikidata.org/wiki/Q7617831","display_name":"Stochastic programming","level":2,"score":0.1148657500743866},{"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/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.0}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.3390/computation11070137","is_oa":true,"landing_page_url":"https://doi.org/10.3390/computation11070137","pdf_url":"https://www.mdpi.com/2079-3197/11/7/137/pdf?version=1688985007","source":{"id":"https://openalex.org/S2738402919","display_name":"Computation","issn_l":"2079-3197","issn":["2079-3197"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310310987","host_organization_name":"Multidisciplinary Digital Publishing Institute","host_organization_lineage":["https://openalex.org/P4310310987"],"host_organization_lineage_names":["Multidisciplinary Digital Publishing Institute"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Computation","raw_type":"journal-article"},{"id":"pmh:oai:doaj.org/article:cf9c4f21ff474c508deefa849dca2e59","is_oa":true,"landing_page_url":"https://doaj.org/article/cf9c4f21ff474c508deefa849dca2e59","pdf_url":null,"source":{"id":"https://openalex.org/S112646816","display_name":"SHILAP Revista de lepidopterolog\u00eda","issn_l":"0300-5267","issn":["0300-5267","2340-4078"],"is_oa":true,"is_in_doaj":true,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Computation, Vol 11, Iss 7, p 137 (2023)","raw_type":"article"},{"id":"pmh:oai:mdpi.com:/2079-3197/11/7/137/","is_oa":true,"landing_page_url":"https://dx.doi.org/10.3390/computation11070137","pdf_url":null,"source":{"id":"https://openalex.org/S4306400947","display_name":"MDPI (MDPI AG)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I4210097602","host_organization_name":"Multidisciplinary Digital Publishing Institute (Switzerland)","host_organization_lineage":["https://openalex.org/I4210097602"],"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":"Computation; Volume 11; Issue 7; Pages: 137","raw_type":"Text"}],"best_oa_location":{"id":"doi:10.3390/computation11070137","is_oa":true,"landing_page_url":"https://doi.org/10.3390/computation11070137","pdf_url":"https://www.mdpi.com/2079-3197/11/7/137/pdf?version=1688985007","source":{"id":"https://openalex.org/S2738402919","display_name":"Computation","issn_l":"2079-3197","issn":["2079-3197"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310310987","host_organization_name":"Multidisciplinary Digital Publishing Institute","host_organization_lineage":["https://openalex.org/P4310310987"],"host_organization_lineage_names":["Multidisciplinary Digital Publishing Institute"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Computation","raw_type":"journal-article"},"sustainable_development_goals":[{"id":"https://metadata.un.org/sdg/9","score":0.5400000214576721,"display_name":"Industry, innovation and infrastructure"}],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W4383908705.pdf"},"referenced_works_count":38,"referenced_works":["https://openalex.org/W56091958","https://openalex.org/W1488422606","https://openalex.org/W2011198146","https://openalex.org/W2017539352","https://openalex.org/W2017708827","https://openalex.org/W2019704988","https://openalex.org/W2023170315","https://openalex.org/W2024085737","https://openalex.org/W2034282101","https://openalex.org/W2034290282","https://openalex.org/W2036768904","https://openalex.org/W2049790232","https://openalex.org/W2052542866","https://openalex.org/W2060880823","https://openalex.org/W2095150268","https://openalex.org/W2097701129","https://openalex.org/W2115299891","https://openalex.org/W2136420381","https://openalex.org/W2167813355","https://openalex.org/W2326242208","https://openalex.org/W2331901840","https://openalex.org/W2562149778","https://openalex.org/W2756755406","https://openalex.org/W2957456999","https://openalex.org/W2968482180","https://openalex.org/W3032628781","https://openalex.org/W3131203918","https://openalex.org/W3155065624","https://openalex.org/W3196402541","https://openalex.org/W4226210625","https://openalex.org/W4226479876","https://openalex.org/W4298153554","https://openalex.org/W4318604517","https://openalex.org/W4321019937","https://openalex.org/W6701651223","https://openalex.org/W6744311641","https://openalex.org/W6765680834","https://openalex.org/W6801245042"],"related_works":["https://openalex.org/W2081821176","https://openalex.org/W2358427436","https://openalex.org/W1994919150","https://openalex.org/W4386269615","https://openalex.org/W2064794194","https://openalex.org/W2402589461","https://openalex.org/W3022707108","https://openalex.org/W4200104947","https://openalex.org/W2494989913","https://openalex.org/W1605808593"],"abstract_inverted_index":{"This":[0,25,99,192,247],"paper":[1],"presents":[2,101],"a":[3,18,28,32,37,55,133,141,165],"comprehensive":[4,142],"approach":[5,128,193,216],"for":[6,112,224],"minimizing":[7],"makespan":[8],"in":[9,89,122,220],"the":[10,60,65,80,84,90,110,123,156,173,176,184,189,195,208,211,232,261,266],"challenging":[11],"two-stage":[12,93],"hybrid":[13,94],"flowshop":[14,95],"with":[15,96,242],"dedicated":[16,97],"machines,":[17],"problem":[19,100],"known":[20],"to":[21,44,82,105,139,201,244,252],"be":[22],"strongly":[23],"NP-hard.":[24],"study":[26,120],"proposed":[27,147,212,267],"constraint":[29,50,131,148,233],"programming":[30,51,149,234],"approach,":[31],"novel":[33,134],"heuristic":[34,66,157,215],"based":[35],"on":[36],"priority":[38],"rule,":[39],"and":[40,67,109,136,143,158,169,187,199,263],"Tabu":[41,68,137,159],"search":[42,69,138,160,174,185,190],"procedures":[43],"tackle":[45],"this":[46,77,119],"optimization":[47,114,197],"problem.":[48],"The":[49,74,116,146,205,214],"model,":[52],"implemented":[53],"using":[54],"commercial":[56],"solver,":[57],"serves":[58],"as":[59],"exact":[61,152,257],"resolution":[62,153],"method,":[63],"while":[64,155],"explore":[70],"approximate":[71,162],"solutions":[72],"simultaneously.":[73],"motivation":[75],"behind":[76],"research":[78,177],"is":[79,249],"need":[81,111],"address":[83],"complexities":[85],"of":[86,92,118,125,210,265],"scheduling":[87],"problems":[88,241],"context":[91],"machines.":[98],"significant":[102],"challenges":[103],"due":[104],"its":[106,228],"NP-hard":[107],"nature":[108],"efficient":[113,144],"techniques.":[115],"contribution":[117],"lies":[121],"development":[124],"an":[126],"integrated":[127],"that":[129],"combines":[130],"programming,":[132],"heuristic,":[135],"provide":[140,161],"solution.":[145],"model":[150,235],"offers":[151],"capabilities,":[154],"solutions,":[163],"offering":[164],"balance":[166],"between":[167],"accuracy":[168],"efficiency.":[170],"To":[171],"enhance":[172],"process,":[175],"introduces":[178],"effective":[179],"elimination":[180],"rules,":[181],"which":[182],"reduce":[183],"space":[186],"simplify":[188],"effort.":[191],"improves":[194],"overall":[196],"performance":[198],"contributes":[200],"finding":[202],"high-quality":[203],"solutions.":[204],"results":[206],"demonstrate":[207],"effectiveness":[209,264],"approach.":[213],"achieves":[217],"complete":[218],"success":[219],"solving":[221,240],"all":[222],"instances":[223,253],"specific":[225],"classes,":[226],"showcasing":[227],"practical":[229],"applicability.":[230],"Furthermore,":[231],"exhibits":[236],"exceptional":[237],"efficiency,":[238],"successfully":[239],"up":[243],"n=500":[245],"jobs.":[246],"efficiency":[248],"noteworthy":[250],"compared":[251],"solved":[254],"by":[255],"other":[256],"solution":[258],"approaches,":[259],"indicating":[260],"scalability":[262],"method.":[268]},"counts_by_year":[{"year":2025,"cited_by_count":4},{"year":2024,"cited_by_count":3}],"updated_date":"2026-02-28T09:26:25.869077","created_date":"2023-07-12T00:00:00"}