{"id":"https://openalex.org/W1987221073","doi":"https://doi.org/10.1007/s11424-007-9057-7","title":"Approximation Schemes for Scheduling a Batching Machine with Nonidentical Job Size","display_name":"Approximation Schemes for Scheduling a Batching Machine with Nonidentical Job Size","publication_year":2007,"publication_date":"2007-11-05","ids":{"openalex":"https://openalex.org/W1987221073","doi":"https://doi.org/10.1007/s11424-007-9057-7","mag":"1987221073"},"language":"en","primary_location":{"id":"doi:10.1007/s11424-007-9057-7","is_oa":false,"landing_page_url":"https://doi.org/10.1007/s11424-007-9057-7","pdf_url":null,"source":{"id":"https://openalex.org/S45848134","display_name":"Journal of Systems Science and Complexity","issn_l":"1009-6124","issn":["1009-6124","1559-7067"],"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":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Journal of Systems Science and Complexity","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/A5052562833","display_name":"Xianzhao Zhang","orcid":"https://orcid.org/0000-0002-8998-3343"},"institutions":[{"id":"https://openalex.org/I15823474","display_name":"Linyi University","ror":"https://ror.org/01knv0402","country_code":"CN","type":"education","lineage":["https://openalex.org/I15823474"]}],"countries":["CN"],"is_corresponding":true,"raw_author_name":"Xianzhao Zhang","raw_affiliation_strings":["Department of Mathematics, Linyi Normal University, Linyi, 276000, China","Department of Mathematics, Linyi Normal University, Linyi, China"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics, Linyi Normal University, Linyi, 276000, China","institution_ids":["https://openalex.org/I15823474"]},{"raw_affiliation_string":"Department of Mathematics, Linyi Normal University, Linyi, China","institution_ids":["https://openalex.org/I15823474"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5100736149","display_name":"Yu\u2010Zhong Zhang","orcid":"https://orcid.org/0000-0002-2017-1005"},"institutions":[{"id":"https://openalex.org/I202126657","display_name":"Qufu Normal University","ror":"https://ror.org/03ceheh96","country_code":"CN","type":"education","lineage":["https://openalex.org/I202126657"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Yuzhong Zhang","raw_affiliation_strings":["College of Operations Research and Management, Qufu Normal University, Rizhao, 276826, China","College of Operations Research and Management, Qufu Normal University, Rizhao, China"],"affiliations":[{"raw_affiliation_string":"College of Operations Research and Management, Qufu Normal University, Rizhao, 276826, China","institution_ids":["https://openalex.org/I202126657"]},{"raw_affiliation_string":"College of Operations Research and Management, Qufu Normal University, Rizhao, China","institution_ids":["https://openalex.org/I202126657"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5088955310","display_name":"Zhigang Cao","orcid":"https://orcid.org/0000-0001-7106-6734"},"institutions":[{"id":"https://openalex.org/I19820366","display_name":"Chinese Academy of Sciences","ror":"https://ror.org/034t30j35","country_code":"CN","type":"government","lineage":["https://openalex.org/I19820366"]},{"id":"https://openalex.org/I4210120485","display_name":"Academy of Mathematics and Systems Science","ror":"https://ror.org/02jkmyk67","country_code":"CN","type":"facility","lineage":["https://openalex.org/I19820366","https://openalex.org/I4210120485"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Zhigang Cao","raw_affiliation_strings":["Institute of Systems Science, Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing, 100080, China","Institute of Systems Science, Academy of Mathematics and Systems Science Chinese Academy of Sciences, Beijing, China"],"affiliations":[{"raw_affiliation_string":"Institute of Systems Science, Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing, 100080, China","institution_ids":["https://openalex.org/I4210120485","https://openalex.org/I19820366"]},{"raw_affiliation_string":"Institute of Systems Science, Academy of Mathematics and Systems Science Chinese Academy of Sciences, Beijing, China","institution_ids":["https://openalex.org/I19820366"]}]},{"author_position":"last","author":{"id":null,"display_name":"Zengxia Cai","orcid":null},"institutions":[{"id":"https://openalex.org/I15823474","display_name":"Linyi University","ror":"https://ror.org/01knv0402","country_code":"CN","type":"education","lineage":["https://openalex.org/I15823474"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Zengxia Cai","raw_affiliation_strings":["Department of Mathematics, Linyi Normal University, Linyi, 276000, China","Department of Mathematics, Linyi Normal University, Linyi, China"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics, Linyi Normal University, Linyi, 276000, China","institution_ids":["https://openalex.org/I15823474"]},{"raw_affiliation_string":"Department of Mathematics, Linyi Normal University, Linyi, China","institution_ids":["https://openalex.org/I15823474"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":4,"corresponding_author_ids":["https://openalex.org/A5052562833"],"corresponding_institution_ids":["https://openalex.org/I15823474"],"apc_list":{"value":2290,"currency":"EUR","value_usd":2890},"apc_paid":null,"fwci":0.0,"has_fulltext":false,"cited_by_count":1,"citation_normalized_percentile":{"value":0.12536811,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"20","issue":"4","first_page":"592","last_page":"600"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10551","display_name":"Scheduling and Optimization Algorithms","score":0.9997000098228455,"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":0.9997000098228455,"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":0.9997000098228455,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/scheduling","display_name":"Scheduling (production processes)","score":0.6552311182022095},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.6186413764953613},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.526070773601532},{"id":"https://openalex.org/keywords/job-shop-scheduling","display_name":"Job shop scheduling","score":0.4858841300010681},{"id":"https://openalex.org/keywords/approximation-algorithm","display_name":"Approximation algorithm","score":0.4573494791984558},{"id":"https://openalex.org/keywords/job-scheduler","display_name":"Job scheduler","score":0.4465734362602234},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.3323150873184204},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.2248501479625702},{"id":"https://openalex.org/keywords/schedule","display_name":"Schedule","score":0.05821898579597473}],"concepts":[{"id":"https://openalex.org/C206729178","wikidata":"https://www.wikidata.org/wiki/Q2271896","display_name":"Scheduling (production processes)","level":2,"score":0.6552311182022095},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.6186413764953613},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.526070773601532},{"id":"https://openalex.org/C55416958","wikidata":"https://www.wikidata.org/wiki/Q6206757","display_name":"Job shop scheduling","level":3,"score":0.4858841300010681},{"id":"https://openalex.org/C148764684","wikidata":"https://www.wikidata.org/wiki/Q621751","display_name":"Approximation algorithm","level":2,"score":0.4573494791984558},{"id":"https://openalex.org/C111873713","wikidata":"https://www.wikidata.org/wiki/Q1641413","display_name":"Job scheduler","level":3,"score":0.4465734362602234},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.3323150873184204},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.2248501479625702},{"id":"https://openalex.org/C68387754","wikidata":"https://www.wikidata.org/wiki/Q7271585","display_name":"Schedule","level":2,"score":0.05821898579597473},{"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/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","level":1,"score":0.0},{"id":"https://openalex.org/C160403385","wikidata":"https://www.wikidata.org/wiki/Q220543","display_name":"Queue","level":2,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1007/s11424-007-9057-7","is_oa":false,"landing_page_url":"https://doi.org/10.1007/s11424-007-9057-7","pdf_url":null,"source":{"id":"https://openalex.org/S45848134","display_name":"Journal of Systems Science and Complexity","issn_l":"1009-6124","issn":["1009-6124","1559-7067"],"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":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Journal of Systems Science and Complexity","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[{"id":"https://metadata.un.org/sdg/8","score":0.7699999809265137,"display_name":"Decent work and economic growth"}],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":2,"referenced_works":["https://openalex.org/W2048631059","https://openalex.org/W2150171969"],"related_works":["https://openalex.org/W2970302286","https://openalex.org/W2810352541","https://openalex.org/W3204654320","https://openalex.org/W2142195909","https://openalex.org/W2092966558","https://openalex.org/W1956651153","https://openalex.org/W1984267569","https://openalex.org/W2347561926","https://openalex.org/W2327547880","https://openalex.org/W2315766899"],"abstract_inverted_index":null,"counts_by_year":[],"updated_date":"2026-04-16T08:26:57.006410","created_date":"2025-10-10T00:00:00"}