{"id":"https://openalex.org/W4377091921","doi":"https://doi.org/10.3390/axioms12050498","title":"Mathematical Modeling and Exact Optimizing of University Course Scheduling Considering Preferences of Professors","display_name":"Mathematical Modeling and Exact Optimizing of University Course Scheduling Considering Preferences of Professors","publication_year":2023,"publication_date":"2023-05-19","ids":{"openalex":"https://openalex.org/W4377091921","doi":"https://doi.org/10.3390/axioms12050498"},"language":"en","primary_location":{"id":"doi:10.3390/axioms12050498","is_oa":true,"landing_page_url":"https://doi.org/10.3390/axioms12050498","pdf_url":"https://www.mdpi.com/2075-1680/12/5/498/pdf?version=1685086911","source":{"id":"https://openalex.org/S4210173132","display_name":"Axioms","issn_l":"2075-1680","issn":["2075-1680"],"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":"Axioms","raw_type":"journal-article"},"type":"article","indexed_in":["crossref","doaj"],"open_access":{"is_oa":true,"oa_status":"gold","oa_url":"https://www.mdpi.com/2075-1680/12/5/498/pdf?version=1685086911","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5100387256","display_name":"Mo Chen","orcid":"https://orcid.org/0000-0003-4457-4498"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Mo Chen","raw_affiliation_strings":["Yantai Vocational College, Yantai 264000, China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Yantai Vocational College, Yantai 264000, China","institution_ids":[]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5000420548","display_name":"Frank Werner","orcid":"https://orcid.org/0000-0002-0709-3591"},"institutions":[{"id":"https://openalex.org/I95793202","display_name":"Otto-von-Guericke-Universit\u00e4t Magdeburg","ror":"https://ror.org/00ggpsq73","country_code":"DE","type":"education","lineage":["https://openalex.org/I95793202"]}],"countries":["DE"],"is_corresponding":true,"raw_author_name":"Frank Werner","raw_affiliation_strings":["Faculty of Mathematics, Otto-Von-Guericke-University, 39016 Magdeburg, Germany"],"raw_orcid":"https://orcid.org/0000-0002-0709-3591","affiliations":[{"raw_affiliation_string":"Faculty of Mathematics, Otto-Von-Guericke-University, 39016 Magdeburg, Germany","institution_ids":["https://openalex.org/I95793202"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5048004042","display_name":"Mohammad Shokouhifar","orcid":"https://orcid.org/0000-0001-7370-4760"},"institutions":[{"id":"https://openalex.org/I48379061","display_name":"Shahid Beheshti University","ror":"https://ror.org/0091vmj44","country_code":"IR","type":"education","lineage":["https://openalex.org/I48379061"]}],"countries":["IR"],"is_corresponding":true,"raw_author_name":"Mohammad Shokouhifar","raw_affiliation_strings":["Department of Electrical and Computer Engineering, Shahid Beheshti University, Tehran 1983969411, Iran"],"raw_orcid":"https://orcid.org/0000-0001-7370-4760","affiliations":[{"raw_affiliation_string":"Department of Electrical and Computer Engineering, Shahid Beheshti University, Tehran 1983969411, Iran","institution_ids":["https://openalex.org/I48379061"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5000420548","https://openalex.org/A5048004042"],"corresponding_institution_ids":["https://openalex.org/I48379061","https://openalex.org/I95793202"],"apc_list":{"value":1600,"currency":"CHF","value_usd":1782},"apc_paid":{"value":1600,"currency":"CHF","value_usd":1782},"fwci":1.9743,"has_fulltext":true,"cited_by_count":10,"citation_normalized_percentile":{"value":0.861529,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":98},"biblio":{"volume":"12","issue":"5","first_page":"498","last_page":"498"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T12401","display_name":"Scheduling and Timetabling Solutions","score":0.9998999834060669,"subfield":{"id":"https://openalex.org/subfields/1803","display_name":"Management Science and Operations Research"},"field":{"id":"https://openalex.org/fields/18","display_name":"Decision Sciences"},"domain":{"id":"https://openalex.org/domains/2","display_name":"Social Sciences"}},"topics":[{"id":"https://openalex.org/T12401","display_name":"Scheduling and Timetabling Solutions","score":0.9998999834060669,"subfield":{"id":"https://openalex.org/subfields/1803","display_name":"Management Science and Operations Research"},"field":{"id":"https://openalex.org/fields/18","display_name":"Decision Sciences"},"domain":{"id":"https://openalex.org/domains/2","display_name":"Social Sciences"}},{"id":"https://openalex.org/T11902","display_name":"Intelligent Tutoring Systems and Adaptive Learning","score":0.9330999851226807,"subfield":{"id":"https://openalex.org/subfields/1702","display_name":"Artificial Intelligence"},"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/T11409","display_name":"Advanced Wireless Network Optimization","score":0.9248999953269958,"subfield":{"id":"https://openalex.org/subfields/2208","display_name":"Electrical and Electronic 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/scheduling","display_name":"Scheduling (production processes)","score":0.6987603902816772},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.6100596785545349},{"id":"https://openalex.org/keywords/curriculum","display_name":"Curriculum","score":0.5611725449562073},{"id":"https://openalex.org/keywords/integer-programming","display_name":"Integer programming","score":0.5017979145050049},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.49501150846481323},{"id":"https://openalex.org/keywords/set","display_name":"Set (abstract data type)","score":0.43392807245254517},{"id":"https://openalex.org/keywords/mathematics-education","display_name":"Mathematics education","score":0.34030020236968994},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.2029968500137329},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.11042267084121704},{"id":"https://openalex.org/keywords/programming-language","display_name":"Programming language","score":0.07948219776153564}],"concepts":[{"id":"https://openalex.org/C206729178","wikidata":"https://www.wikidata.org/wiki/Q2271896","display_name":"Scheduling (production processes)","level":2,"score":0.6987603902816772},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.6100596785545349},{"id":"https://openalex.org/C47177190","wikidata":"https://www.wikidata.org/wiki/Q207137","display_name":"Curriculum","level":2,"score":0.5611725449562073},{"id":"https://openalex.org/C56086750","wikidata":"https://www.wikidata.org/wiki/Q6042592","display_name":"Integer programming","level":2,"score":0.5017979145050049},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.49501150846481323},{"id":"https://openalex.org/C177264268","wikidata":"https://www.wikidata.org/wiki/Q1514741","display_name":"Set (abstract data type)","level":2,"score":0.43392807245254517},{"id":"https://openalex.org/C145420912","wikidata":"https://www.wikidata.org/wiki/Q853077","display_name":"Mathematics education","level":1,"score":0.34030020236968994},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.2029968500137329},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.11042267084121704},{"id":"https://openalex.org/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","level":1,"score":0.07948219776153564},{"id":"https://openalex.org/C15744967","wikidata":"https://www.wikidata.org/wiki/Q9418","display_name":"Psychology","level":0,"score":0.0},{"id":"https://openalex.org/C19417346","wikidata":"https://www.wikidata.org/wiki/Q7922","display_name":"Pedagogy","level":1,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.3390/axioms12050498","is_oa":true,"landing_page_url":"https://doi.org/10.3390/axioms12050498","pdf_url":"https://www.mdpi.com/2075-1680/12/5/498/pdf?version=1685086911","source":{"id":"https://openalex.org/S4210173132","display_name":"Axioms","issn_l":"2075-1680","issn":["2075-1680"],"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":"Axioms","raw_type":"journal-article"},{"id":"pmh:oai:doaj.org/article:89452900146a4acfba71aa8e322639a4","is_oa":true,"landing_page_url":"https://doaj.org/article/89452900146a4acfba71aa8e322639a4","pdf_url":null,"source":{"id":"https://openalex.org/S4306401280","display_name":"DOAJ (DOAJ: Directory of Open Access Journals)","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-sa","license_id":"https://openalex.org/licenses/cc-by-sa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Axioms, Vol 12, Iss 5, p 498 (2023)","raw_type":"article"}],"best_oa_location":{"id":"doi:10.3390/axioms12050498","is_oa":true,"landing_page_url":"https://doi.org/10.3390/axioms12050498","pdf_url":"https://www.mdpi.com/2075-1680/12/5/498/pdf?version=1685086911","source":{"id":"https://openalex.org/S4210173132","display_name":"Axioms","issn_l":"2075-1680","issn":["2075-1680"],"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":"Axioms","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":true,"grobid_xml":false},"content_urls":{"pdf":"https://content.openalex.org/works/W4377091921.pdf"},"referenced_works_count":34,"referenced_works":["https://openalex.org/W842791523","https://openalex.org/W1997071828","https://openalex.org/W2017385842","https://openalex.org/W2038611897","https://openalex.org/W2047317516","https://openalex.org/W2048957381","https://openalex.org/W2055579305","https://openalex.org/W2068449902","https://openalex.org/W2070313595","https://openalex.org/W2073634948","https://openalex.org/W2080707386","https://openalex.org/W2111019697","https://openalex.org/W2145087005","https://openalex.org/W2182253609","https://openalex.org/W2202502706","https://openalex.org/W2338390895","https://openalex.org/W2468108119","https://openalex.org/W2605907435","https://openalex.org/W2740351043","https://openalex.org/W2750824817","https://openalex.org/W2765712836","https://openalex.org/W2889006844","https://openalex.org/W2925514807","https://openalex.org/W2962959752","https://openalex.org/W3035476882","https://openalex.org/W3134223240","https://openalex.org/W3183091616","https://openalex.org/W4200070828","https://openalex.org/W4210408109","https://openalex.org/W4308343254","https://openalex.org/W4317438851","https://openalex.org/W4321105319","https://openalex.org/W4366822811","https://openalex.org/W6851945145"],"related_works":["https://openalex.org/W2348562106","https://openalex.org/W2370820329","https://openalex.org/W2370554813","https://openalex.org/W4362576712","https://openalex.org/W2387560707","https://openalex.org/W2363525455","https://openalex.org/W4312355418","https://openalex.org/W2314810092","https://openalex.org/W4295916115","https://openalex.org/W2350876336"],"abstract_inverted_index":{"University":[0],"course":[1,61],"scheduling":[2,62],"(UCS)":[3],"is":[4,74,118,144,154,197],"one":[5],"of":[6,20,38,89,92,97,124,244,255,264],"the":[7,21,60,78,84,87,102,109,114,121,139,147,151,173,177,186,193,217,220,232,236,240,245,253,256],"most":[8],"important":[9],"and":[10,26,41,95,104,108,170,190,216,259,267],"time-consuming":[11],"issues":[12],"that":[13,184],"all":[14,135],"educational":[15,221],"institutions":[16],"face":[17],"yearly.":[18],"Most":[19],"existing":[22],"techniques":[23],"to":[24,48,54,59,76,113,119,128,204],"model":[25,73,153,234,258],"solve":[27,77],"UCS":[28],"problems":[29],"have":[30],"applied":[31],"approximate":[32],"methods,":[33],"which":[34],"differ":[35],"in":[36,67,134,156,168,176,213,219,262],"terms":[37,263],"efficiency,":[39],"performance,":[40],"optimization":[42,52,265],"speed.":[43],"Accordingly,":[44],"this":[45,68,82],"research":[46],"aims":[47],"apply":[49],"an":[50,56,70],"exact":[51],"method":[53,261],"provide":[55],"optimal":[57],"solution":[58,260,268],"problem.":[63,80],"In":[64,81],"other":[65],"words,":[66],"research,":[69],"integer":[71],"programming":[72],"presented":[75,140,152],"USC":[79],"model,":[83],"constraints":[85,189],"include":[86],"facilities":[88],"classrooms,":[90],"courses":[91,100,210,218],"different":[93],"levels":[94],"compression":[96],"students\u2019":[98],"curriculum,":[99],"outside":[101],"faculty":[103,194],"planning":[105],"for":[106,235],"them,":[107],"limited":[110],"time":[111],"allocated":[112],"professors.":[115],"The":[116,180,250],"objective":[117,191],"maximize":[120],"weighted":[122],"sum":[123],"allocating":[125],"available":[126],"times":[127],"professors":[129,246],"based":[130],"on":[131],"their":[132],"preferences":[133],"periods.":[136],"To":[137],"evaluate":[138],"model\u2019s":[141,188],"feasibility,":[142],"it":[143],"implemented":[145],"using":[146,160],"GAMS":[148],"software.":[149],"Finally,":[150],"solved":[155],"a":[157,161,166,202],"larger":[158],"dimension":[159],"real":[162,237],"data":[163],"set":[164],"from":[165,199],"college":[167],"China":[169],"compared":[171],"with":[172,226],"current":[174],"program":[175],"same":[178],"college.":[179],"obtained":[181],"results":[182,251],"show":[183],"considering":[185],"mathematical":[187],"function,":[192],"courses\u2019":[195],"timetable":[196],"reduced":[198],"4":[200],"days":[201],"week":[203],"3":[205],"working":[206],"days.":[207],"Moreover,":[208],"master":[209],"are":[211,247],"planned":[212],"two":[214],"days,":[215],"groups":[222],"do":[223],"not":[224],"interfere":[225],"each":[227],"other.":[228],"Furthermore,":[229],"by":[230],"implementing":[231],"proposed":[233,257],"case":[238],"study,":[239],"maximum":[241],"teaching":[242],"hours":[243],"significantly":[248],"reduced.":[249],"demonstrate":[252],"efficiency":[254],"speed":[266],"accuracy.":[269]},"counts_by_year":[{"year":2026,"cited_by_count":2},{"year":2025,"cited_by_count":5},{"year":2024,"cited_by_count":2},{"year":2023,"cited_by_count":1}],"updated_date":"2026-07-23T08:03:31.855105","created_date":"2025-10-10T00:00:00"}