{"id":"https://openalex.org/W2039017923","doi":"https://doi.org/10.1155/2014/490297","title":"A New Linearizing Method for Sum of Linear Ratios Problem with Coefficients","display_name":"A New Linearizing Method for Sum of Linear Ratios Problem with Coefficients","publication_year":2014,"publication_date":"2014-01-01","ids":{"openalex":"https://openalex.org/W2039017923","doi":"https://doi.org/10.1155/2014/490297","mag":"2039017923"},"language":"en","primary_location":{"id":"doi:10.1155/2014/490297","is_oa":true,"landing_page_url":"https://doi.org/10.1155/2014/490297","pdf_url":"https://downloads.hindawi.com/journals/jam/2014/490297.pdf","source":{"id":"https://openalex.org/S190082376","display_name":"Journal of Applied Mathematics","issn_l":"1110-757X","issn":["1110-757X","1687-0042"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310319869","host_organization_name":"Hindawi Publishing Corporation","host_organization_lineage":["https://openalex.org/P4310319869"],"host_organization_lineage_names":["Hindawi Publishing Corporation"],"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 Applied Mathematics","raw_type":"journal-article"},"type":"article","indexed_in":["crossref","doaj"],"open_access":{"is_oa":true,"oa_status":"gold","oa_url":"https://downloads.hindawi.com/journals/jam/2014/490297.pdf","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5023541572","display_name":"Hongwei Jiao","orcid":"https://orcid.org/0000-0002-3695-387X"},"institutions":[{"id":"https://openalex.org/I4210163247","display_name":"Henan Institute of Science and Technology","ror":"https://ror.org/0578f1k82","country_code":"CN","type":"education","lineage":["https://openalex.org/I4210163247"]}],"countries":["CN"],"is_corresponding":true,"raw_author_name":"Hongwei Jiao","raw_affiliation_strings":["School of Mathematics, Henan Institute of Science and Technology, Xinxiang 453003, China"],"raw_orcid":"https://orcid.org/0000-0002-3695-387X","affiliations":[{"raw_affiliation_string":"School of Mathematics, Henan Institute of Science and Technology, Xinxiang 453003, China","institution_ids":["https://openalex.org/I4210163247"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5100611592","display_name":"Yongqiang Chen","orcid":"https://orcid.org/0000-0003-2195-1844"},"institutions":[{"id":"https://openalex.org/I21193070","display_name":"Beijing Jiaotong University","ror":"https://ror.org/01yj56c84","country_code":"CN","type":"education","lineage":["https://openalex.org/I21193070"]},{"id":"https://openalex.org/I75955062","display_name":"Henan Normal University","ror":"https://ror.org/00s13br28","country_code":"CN","type":"education","lineage":["https://openalex.org/I75955062"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Yongqiang Chen","raw_affiliation_strings":["Department of Mathematics, Beijing Jiaotong University, Beijing 100044, China","Department of Mathematics, Henan Normal University, Xinxiang 453007, China"],"raw_orcid":"https://orcid.org/0000-0003-2195-1844","affiliations":[{"raw_affiliation_string":"Department of Mathematics, Beijing Jiaotong University, Beijing 100044, China","institution_ids":["https://openalex.org/I21193070"]},{"raw_affiliation_string":"Department of Mathematics, Henan Normal University, Xinxiang 453007, China","institution_ids":["https://openalex.org/I75955062"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5023541572"],"corresponding_institution_ids":["https://openalex.org/I4210163247"],"apc_list":{"value":1025,"currency":"USD","value_usd":1025},"apc_paid":{"value":1025,"currency":"USD","value_usd":1025},"fwci":0.0,"has_fulltext":true,"cited_by_count":1,"citation_normalized_percentile":{"value":0.13062592,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":91,"max":95},"biblio":{"volume":"2014","issue":null,"first_page":"1","last_page":"10"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10963","display_name":"Advanced Optimization Algorithms Research","score":0.9994999766349792,"subfield":{"id":"https://openalex.org/subfields/2612","display_name":"Numerical Analysis"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T10963","display_name":"Advanced Optimization Algorithms Research","score":0.9994999766349792,"subfield":{"id":"https://openalex.org/subfields/2612","display_name":"Numerical Analysis"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T12401","display_name":"Scheduling and Timetabling Solutions","score":0.9860000014305115,"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/T10792","display_name":"Matrix Theory and Algorithms","score":0.9707000255584717,"subfield":{"id":"https://openalex.org/subfields/1703","display_name":"Computational Theory and Mathematics"},"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/mathematics","display_name":"Mathematics","score":0.7522088289260864},{"id":"https://openalex.org/keywords/relaxation","display_name":"Relaxation (psychology)","score":0.68549644947052},{"id":"https://openalex.org/keywords/linear-programming","display_name":"Linear programming","score":0.648496150970459},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.5364376306533813},{"id":"https://openalex.org/keywords/linear-programming-relaxation","display_name":"Linear programming relaxation","score":0.5165209174156189},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.5079887509346008},{"id":"https://openalex.org/keywords/upper-and-lower-bounds","display_name":"Upper and lower bounds","score":0.5026144981384277},{"id":"https://openalex.org/keywords/linear-system","display_name":"Linear system","score":0.4679374098777771},{"id":"https://openalex.org/keywords/branch-and-bound","display_name":"Branch and bound","score":0.4531058669090271},{"id":"https://openalex.org/keywords/value","display_name":"Value (mathematics)","score":0.4148273169994354},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.15050160884857178},{"id":"https://openalex.org/keywords/statistics","display_name":"Statistics","score":0.07212430238723755}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7522088289260864},{"id":"https://openalex.org/C2776029896","wikidata":"https://www.wikidata.org/wiki/Q3935810","display_name":"Relaxation (psychology)","level":2,"score":0.68549644947052},{"id":"https://openalex.org/C41045048","wikidata":"https://www.wikidata.org/wiki/Q202843","display_name":"Linear programming","level":2,"score":0.648496150970459},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.5364376306533813},{"id":"https://openalex.org/C25360446","wikidata":"https://www.wikidata.org/wiki/Q1512771","display_name":"Linear programming relaxation","level":3,"score":0.5165209174156189},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.5079887509346008},{"id":"https://openalex.org/C77553402","wikidata":"https://www.wikidata.org/wiki/Q13222579","display_name":"Upper and lower bounds","level":2,"score":0.5026144981384277},{"id":"https://openalex.org/C6802819","wikidata":"https://www.wikidata.org/wiki/Q1072174","display_name":"Linear system","level":2,"score":0.4679374098777771},{"id":"https://openalex.org/C93693863","wikidata":"https://www.wikidata.org/wiki/Q897659","display_name":"Branch and bound","level":2,"score":0.4531058669090271},{"id":"https://openalex.org/C2776291640","wikidata":"https://www.wikidata.org/wiki/Q2912517","display_name":"Value (mathematics)","level":2,"score":0.4148273169994354},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.15050160884857178},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.07212430238723755},{"id":"https://openalex.org/C77805123","wikidata":"https://www.wikidata.org/wiki/Q161272","display_name":"Social psychology","level":1,"score":0.0},{"id":"https://openalex.org/C15744967","wikidata":"https://www.wikidata.org/wiki/Q9418","display_name":"Psychology","level":0,"score":0.0}],"mesh":[],"locations_count":4,"locations":[{"id":"doi:10.1155/2014/490297","is_oa":true,"landing_page_url":"https://doi.org/10.1155/2014/490297","pdf_url":"https://downloads.hindawi.com/journals/jam/2014/490297.pdf","source":{"id":"https://openalex.org/S190082376","display_name":"Journal of Applied Mathematics","issn_l":"1110-757X","issn":["1110-757X","1687-0042"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310319869","host_organization_name":"Hindawi Publishing Corporation","host_organization_lineage":["https://openalex.org/P4310319869"],"host_organization_lineage_names":["Hindawi Publishing Corporation"],"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 Applied Mathematics","raw_type":"journal-article"},{"id":"pmh:oai:CULeuclid:euclid.jam/1425305637","is_oa":false,"landing_page_url":"https://projecteuclid.org/euclid.jam/1425305637","pdf_url":null,"source":{"id":"https://openalex.org/S4306400787","display_name":"Project Euclid (Cornell University)","issn_l":null,"issn":null,"is_oa":false,"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":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"Text"},{"id":"pmh:oai:RePEc:hin:jnljam:490297","is_oa":false,"landing_page_url":"http://downloads.hindawi.com/journals/JAM/2014/490297.xml","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:doaj.org/article:1527ffcf662a4316a6d4c4b69a6f3f08","is_oa":true,"landing_page_url":"https://doaj.org/article/1527ffcf662a4316a6d4c4b69a6f3f08","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":"Journal of Applied Mathematics, Vol 2014 (2014)","raw_type":"article"}],"best_oa_location":{"id":"doi:10.1155/2014/490297","is_oa":true,"landing_page_url":"https://doi.org/10.1155/2014/490297","pdf_url":"https://downloads.hindawi.com/journals/jam/2014/490297.pdf","source":{"id":"https://openalex.org/S190082376","display_name":"Journal of Applied Mathematics","issn_l":"1110-757X","issn":["1110-757X","1687-0042"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310319869","host_organization_name":"Hindawi Publishing Corporation","host_organization_lineage":["https://openalex.org/P4310319869"],"host_organization_lineage_names":["Hindawi Publishing Corporation"],"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 Applied Mathematics","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G1683744605","display_name":null,"funder_award_id":"14A110024","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G7142685729","display_name":"\u6bd4\u5f0f\u548c\u5206\u5f0f\u89c4\u5212\u95ee\u9898\u7684\u7a33\u5065\u89e3\u65b9\u6cd5\u7814\u7a76","funder_award_id":"11171094","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G7281756016","display_name":null,"funder_award_id":"14A110024","funder_id":"https://openalex.org/F4320325625","funder_display_name":"Education Department of Henan Province"}],"funders":[{"id":"https://openalex.org/F4320321001","display_name":"National Natural Science Foundation of China","ror":"https://ror.org/01h0zpd94"},{"id":"https://openalex.org/F4320325625","display_name":"Education Department of Henan Province","ror":null}],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W2039017923.pdf","grobid_xml":"https://content.openalex.org/works/W2039017923.grobid-xml"},"referenced_works_count":11,"referenced_works":["https://openalex.org/W1499399028","https://openalex.org/W1968104480","https://openalex.org/W1975552235","https://openalex.org/W2034713829","https://openalex.org/W2040181397","https://openalex.org/W2041570321","https://openalex.org/W2042046882","https://openalex.org/W2055002919","https://openalex.org/W2079186480","https://openalex.org/W2138417090","https://openalex.org/W2610216665"],"related_works":["https://openalex.org/W2009796757","https://openalex.org/W2389899617","https://openalex.org/W2055782437","https://openalex.org/W2568448495","https://openalex.org/W1931020284","https://openalex.org/W4319942994","https://openalex.org/W2107689258","https://openalex.org/W405521126","https://openalex.org/W4205854323","https://openalex.org/W2115855742"],"abstract_inverted_index":{"A":[0],"new":[1],"linearizing":[2,19],"method":[3,113],"is":[4,34,67,90],"presented":[5],"for":[6,57],"globally":[7],"solving":[8,58,81],"sum":[9,27,60,126],"of":[10,25,28,43,47,61,76,84,97,124,127],"linear":[11,21,29,62,74,128],"ratios":[12,30,63,129],"problem":[13,31,64,130],"with":[14,32,65,102,131],"coefficients.":[15,132],"By":[16,70],"using":[17],"the":[18,26,39,44,48,59,73,77,85,87,93,98,103,111,115,121,125],"method,":[20],"relaxation":[22,75],"programming":[23],"(LRP)":[24],"coefficients":[33,66],"established,":[35],"which":[36],"can":[37],"provide":[38],"reliable":[40],"lower":[41],"bound":[42,55],"optimal":[45,95],"value":[46],"initial":[49,99],"problem.":[50,100],"Thus,":[51],"a":[52,82],"branch":[53],"and":[54,80],"algorithm":[56,89],"put":[68],"forward.":[69],"successively":[71],"partitioning":[72],"feasible":[78],"region":[79],"series":[83],"LRP,":[86],"proposed":[88,112],"convergent":[91],"to":[92],"global":[94,122],"solution":[96],"Compared":[101],"known":[104],"methods,":[105],"numerical":[106],"experimental":[107],"results":[108],"show":[109],"that":[110],"has":[114],"higher":[116],"computational":[117],"efficiency":[118],"in":[119],"finding":[120],"optimum":[123]},"counts_by_year":[{"year":2025,"cited_by_count":1}],"updated_date":"2026-06-06T09:05:17.133730","created_date":"2025-10-10T00:00:00"}