{"id":"https://openalex.org/W2898780166","doi":"https://doi.org/10.1051/ro/2018097","title":"A PTAS for single-machine scheduling with release dates and job delivery to minimize makespan","display_name":"A PTAS for single-machine scheduling with release dates and job delivery to minimize makespan","publication_year":2018,"publication_date":"2018-10-30","ids":{"openalex":"https://openalex.org/W2898780166","doi":"https://doi.org/10.1051/ro/2018097","mag":"2898780166"},"language":"en","primary_location":{"id":"doi:10.1051/ro/2018097","is_oa":false,"landing_page_url":"https://doi.org/10.1051/ro/2018097","pdf_url":null,"source":{"id":"https://openalex.org/S20631277","display_name":"RAIRO - Operations Research","issn_l":"0399-0559","issn":["0399-0559","1290-3868"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319748","host_organization_name":"EDP Sciences","host_organization_lineage":["https://openalex.org/P4310319748"],"host_organization_lineage_names":["EDP Sciences"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"RAIRO - Operations Research","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":false,"oa_status":"closed","oa_url":null,"any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5081699183","display_name":"Lingfa Lu","orcid":"https://orcid.org/0000-0002-2561-5613"},"institutions":[{"id":"https://openalex.org/I38877650","display_name":"Zhengzhou University","ror":"https://ror.org/04ypx8c21","country_code":"CN","type":"education","lineage":["https://openalex.org/I38877650"]}],"countries":["CN"],"is_corresponding":true,"raw_author_name":"Lingfa Lu","raw_affiliation_strings":["School of Mathematics and Statistics, Zhengzhou University, 450001 Zhengzhou, Henan, PR China"],"raw_orcid":"https://orcid.org/0000-0002-2561-5613","affiliations":[{"raw_affiliation_string":"School of Mathematics and Statistics, Zhengzhou University, 450001 Zhengzhou, Henan, PR China","institution_ids":["https://openalex.org/I38877650"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5085082654","display_name":"Liqi Zhang","orcid":"https://orcid.org/0000-0002-6421-680X"},"institutions":[{"id":"https://openalex.org/I4750791","display_name":"Henan Agricultural University","ror":"https://ror.org/04eq83d71","country_code":"CN","type":"education","lineage":["https://openalex.org/I4750791"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Liqi Zhang","raw_affiliation_strings":["College of Information and Management Science, Henan Agricultural University, 450003 Zhengzhou, Henan, PR China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"College of Information and Management Science, Henan Agricultural University, 450003 Zhengzhou, Henan, PR China","institution_ids":["https://openalex.org/I4750791"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5081699183"],"corresponding_institution_ids":["https://openalex.org/I38877650"],"apc_list":null,"apc_paid":null,"fwci":0.2522,"has_fulltext":false,"cited_by_count":4,"citation_normalized_percentile":{"value":0.65465165,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":96},"biblio":{"volume":"53","issue":"4","first_page":"1261","last_page":"1266"},"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/T11814","display_name":"Advanced Manufacturing and Logistics Optimization","score":0.9987999796867371,"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/T12176","display_name":"Optimization and Packing Problems","score":0.996999979019165,"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/job-shop-scheduling","display_name":"Job shop scheduling","score":0.8505452871322632},{"id":"https://openalex.org/keywords/preemption","display_name":"Preemption","score":0.7920000553131104},{"id":"https://openalex.org/keywords/polynomial-time-approximation-scheme","display_name":"Polynomial-time approximation scheme","score":0.6811692714691162},{"id":"https://openalex.org/keywords/single-machine-scheduling","display_name":"Single-machine scheduling","score":0.67755526304245},{"id":"https://openalex.org/keywords/scheduling","display_name":"Scheduling (production processes)","score":0.6334545612335205},{"id":"https://openalex.org/keywords/approximation-algorithm","display_name":"Approximation algorithm","score":0.5744742751121521},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.561188280582428},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.4992852210998535},{"id":"https://openalex.org/keywords/time-complexity","display_name":"Time complexity","score":0.4413793087005615},{"id":"https://openalex.org/keywords/real-time-computing","display_name":"Real-time computing","score":0.33092883229255676},{"id":"https://openalex.org/keywords/computer-network","display_name":"Computer network","score":0.21574047207832336},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.21101894974708557},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.20594564080238342},{"id":"https://openalex.org/keywords/operating-system","display_name":"Operating system","score":0.14146950840950012},{"id":"https://openalex.org/keywords/routing","display_name":"Routing (electronic design automation)","score":0.05775228142738342}],"concepts":[{"id":"https://openalex.org/C55416958","wikidata":"https://www.wikidata.org/wiki/Q6206757","display_name":"Job shop scheduling","level":3,"score":0.8505452871322632},{"id":"https://openalex.org/C206952183","wikidata":"https://www.wikidata.org/wiki/Q1193100","display_name":"Preemption","level":2,"score":0.7920000553131104},{"id":"https://openalex.org/C99140742","wikidata":"https://www.wikidata.org/wiki/Q843550","display_name":"Polynomial-time approximation scheme","level":3,"score":0.6811692714691162},{"id":"https://openalex.org/C2780271269","wikidata":"https://www.wikidata.org/wiki/Q19295956","display_name":"Single-machine scheduling","level":4,"score":0.67755526304245},{"id":"https://openalex.org/C206729178","wikidata":"https://www.wikidata.org/wiki/Q2271896","display_name":"Scheduling (production processes)","level":2,"score":0.6334545612335205},{"id":"https://openalex.org/C148764684","wikidata":"https://www.wikidata.org/wiki/Q621751","display_name":"Approximation algorithm","level":2,"score":0.5744742751121521},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.561188280582428},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.4992852210998535},{"id":"https://openalex.org/C311688","wikidata":"https://www.wikidata.org/wiki/Q2393193","display_name":"Time complexity","level":2,"score":0.4413793087005615},{"id":"https://openalex.org/C79403827","wikidata":"https://www.wikidata.org/wiki/Q3988","display_name":"Real-time computing","level":1,"score":0.33092883229255676},{"id":"https://openalex.org/C31258907","wikidata":"https://www.wikidata.org/wiki/Q1301371","display_name":"Computer network","level":1,"score":0.21574047207832336},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.21101894974708557},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.20594564080238342},{"id":"https://openalex.org/C111919701","wikidata":"https://www.wikidata.org/wiki/Q9135","display_name":"Operating system","level":1,"score":0.14146950840950012},{"id":"https://openalex.org/C74172769","wikidata":"https://www.wikidata.org/wiki/Q1446839","display_name":"Routing (electronic design automation)","level":2,"score":0.05775228142738342}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1051/ro/2018097","is_oa":false,"landing_page_url":"https://doi.org/10.1051/ro/2018097","pdf_url":null,"source":{"id":"https://openalex.org/S20631277","display_name":"RAIRO - Operations Research","issn_l":"0399-0559","issn":["0399-0559","1290-3868"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319748","host_organization_name":"EDP Sciences","host_organization_lineage":["https://openalex.org/P4310319748"],"host_organization_lineage_names":["EDP Sciences"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"RAIRO - Operations Research","raw_type":"journal-article"},{"id":"pmh:oai:numdam.org:RO_2019__53_4_1261_0","is_oa":false,"landing_page_url":"https://www.numdam.org/articles/10.1051/ro/2018097/","pdf_url":null,"source":{"id":"https://openalex.org/S4306402264","display_name":"French digital mathematics library (Numdam)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I70900168","host_organization_name":"Universit\u00e9 Savoie Mont Blanc","host_organization_lineage":["https://openalex.org/I70900168"],"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":"Text"}],"best_oa_location":null,"sustainable_development_goals":[{"score":0.5199999809265137,"display_name":"Decent work and economic growth","id":"https://metadata.un.org/sdg/8"}],"awards":[{"id":"https://openalex.org/G2439628550","display_name":null,"funder_award_id":"11771406","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G4305356474","display_name":null,"funder_award_id":"11571321","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G5901811429","display_name":null,"funder_award_id":"U1504103","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"}],"funders":[{"id":"https://openalex.org/F4320321001","display_name":"National Natural Science Foundation of China","ror":"https://ror.org/01h0zpd94"}],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":18,"referenced_works":["https://openalex.org/W81942118","https://openalex.org/W1484610295","https://openalex.org/W1989494422","https://openalex.org/W1991617064","https://openalex.org/W2027466232","https://openalex.org/W2029006621","https://openalex.org/W2034279788","https://openalex.org/W2043712566","https://openalex.org/W2047821474","https://openalex.org/W2057960110","https://openalex.org/W2079870327","https://openalex.org/W2079884080","https://openalex.org/W2086012697","https://openalex.org/W2086256122","https://openalex.org/W2095831266","https://openalex.org/W2103404729","https://openalex.org/W2108648237","https://openalex.org/W2117782865"],"related_works":["https://openalex.org/W1977040436","https://openalex.org/W2529680039","https://openalex.org/W2040050870","https://openalex.org/W3089811425","https://openalex.org/W2801279942","https://openalex.org/W1815446007","https://openalex.org/W2783992526","https://openalex.org/W4380884924","https://openalex.org/W2962917430","https://openalex.org/W1903284337"],"abstract_inverted_index":{"We":[0],"consider":[1],"the":[2,20,23,63,88,101],"single-machine":[3],"scheduling":[4],"problem":[5,74],"with":[6],"release":[7],"dates":[8],"and":[9,34,65,81],"job":[10],"delivery":[11],"to":[12,41,77],"minimize":[13],"makespan.":[14],"Preemption":[15],"is":[16,67],"not":[17],"allowed":[18],"in":[19,55,87],"processing":[21],"of":[22],"jobs.":[24],"All":[25],"jobs":[26,54],"are":[27],"first":[28],"processed":[29],"on":[30],"a":[31,38,42,68,82,95],"single":[32,43],"machine":[33,64],"then":[35],"delivered":[36],"by":[37],"capacitated":[39],"vehicle":[40,46],"customer.":[44],"The":[45,58,73],"can":[47],"deliver":[48],"at":[49],"most":[50],"c":[51],"\u2265":[52],"1":[53],"each":[56],"shipment.":[57],"round-trip":[59],"transportation":[60],"time":[61],"between":[62],"customer":[66],"constant":[69],"T":[70],">":[71],"0.":[72],"was":[75,85],"proved":[76],"be":[78],"strongly":[79],"NP-hard":[80],"3/2-approximation":[83],"algorithm":[84],"presented":[86],"literature.":[89],"In":[90],"this":[91],"paper":[92],"we":[93],"provide":[94],"polynomial-time":[96],"approximation":[97],"scheme":[98],"(PTAS)":[99],"for":[100],"problem.":[102]},"counts_by_year":[{"year":2025,"cited_by_count":2},{"year":2022,"cited_by_count":1},{"year":2020,"cited_by_count":1}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}