{"id":"https://openalex.org/W3023616016","doi":"https://doi.org/10.1016/b978-0-08-016053-5.50008-9","title":"LINEAR PROGRAMMING","display_name":"LINEAR PROGRAMMING","publication_year":1971,"publication_date":"1971-01-01","ids":{"openalex":"https://openalex.org/W3023616016","doi":"https://doi.org/10.1016/b978-0-08-016053-5.50008-9","mag":"3023616016"},"language":"en","primary_location":{"id":"doi:10.1016/b978-0-08-016053-5.50008-9","doi":"https://doi.org/10.1016/b978-0-08-016053-5.50008-9","is_oa":false,"landing_page_url":"https://doi.org/10.1016/b978-0-08-016053-5.50008-9","pdf_url":null,"source":{"id":"https://openalex.org/S4306463230","display_name":"Elsevier eBooks","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/P4310320990","host_organization_name":"Elsevier BV","host_organization_lineage":["https://openalex.org/P4310320990"],"host_organization_lineage_names":["Elsevier BV"],"type":"ebook platform"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Optimal Decisions","raw_type":"book-chapter"},"volume":{"id":"https://openalex.org/W4256145581","display_name":"Optimal Decisions"},"type":"book-chapter","is_traditional":true,"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/A5108366788","display_name":"Oskar Lange","orcid":null,"observed_orcids":[]},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"OSKAR LANGE","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":0,"corresponding_author_ids":["https://openalex.org/A5108366788"],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":false,"cited_by_count":0,"citation_normalized_percentile":{"value":0.0,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":null,"issue":null,"first_page":"84","last_page":"131"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T12709","display_name":"Optimization and Mathematical Programming","score":0.9794999957084656,"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/T12709","display_name":"Optimization and Mathematical Programming","score":0.9794999957084656,"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/T10963","display_name":"Advanced Optimization Algorithms Research","score":0.016100000590085983,"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/T10720","display_name":"Complexity and Algorithms in Graphs","score":0.003000000026077032,"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/linear-programming","display_name":"linear programming","score":1.0},{"id":"https://openalex.org/keywords/simplex-method","display_name":"simplex method","score":0.9860000014305115},{"id":"https://openalex.org/keywords/geometric-interpretation","display_name":"geometric interpretation","score":0.671999990940094},{"id":"https://openalex.org/keywords/economic-optimization","display_name":"economic optimization","score":0.7279999852180481},{"id":"https://openalex.org/keywords/linear-objective-function","display_name":"linear objective function","score":0.6539999842643738},{"id":"https://openalex.org/keywords/linear-constraints","display_name":"linear constraints","score":0.6119999885559082},{"id":"https://openalex.org/keywords/economic-analysis","display_name":"economic analysis","score":0.33899998664855957}],"concepts":[{"id":"https://openalex.org/C41045048","wikidata":"https://www.wikidata.org/wiki/Q202843","display_name":"Linear programming","level":2,"score":0.8454383611679077},{"id":"https://openalex.org/C144521790","wikidata":"https://www.wikidata.org/wiki/Q134164","display_name":"Simplex algorithm","level":3,"score":0.8170826435089111},{"id":"https://openalex.org/C205658194","wikidata":"https://www.wikidata.org/wiki/Q4168281","display_name":"Linear-fractional programming","level":3,"score":0.7475590705871582},{"id":"https://openalex.org/C62438384","wikidata":"https://www.wikidata.org/wiki/Q331350","display_name":"Simplex","level":2,"score":0.49398475885391235},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.4814545512199402},{"id":"https://openalex.org/C191157680","wikidata":"https://www.wikidata.org/wiki/Q17085895","display_name":"Revised simplex method","level":4,"score":0.47842222452163696},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.4676152467727661},{"id":"https://openalex.org/C527412718","wikidata":"https://www.wikidata.org/wiki/Q855395","display_name":"Interpretation (philosophy)","level":2,"score":0.4661024808883667},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.45811668038368225},{"id":"https://openalex.org/C139352143","wikidata":"https://www.wikidata.org/wiki/Q82571","display_name":"Linear algebra","level":2,"score":0.4567923843860626},{"id":"https://openalex.org/C52486349","wikidata":"https://www.wikidata.org/wiki/Q17006040","display_name":"Criss-cross algorithm","level":4,"score":0.44015011191368103},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.43159496784210205},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.35269108414649963},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.34812405705451965},{"id":"https://openalex.org/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","level":1,"score":0.24881836771965027},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.10722783207893372},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1016/b978-0-08-016053-5.50008-9","doi":"https://doi.org/10.1016/b978-0-08-016053-5.50008-9","is_oa":false,"landing_page_url":"https://doi.org/10.1016/b978-0-08-016053-5.50008-9","pdf_url":null,"source":{"id":"https://openalex.org/S4306463230","display_name":"Elsevier eBooks","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/P4310320990","host_organization_name":"Elsevier BV","host_organization_lineage":["https://openalex.org/P4310320990"],"host_organization_lineage_names":["Elsevier BV"],"type":"ebook platform"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Optimal Decisions","raw_type":"book-chapter"}],"best_oa_location":null,"sustainable_development_goals":[],"study_designs":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":0,"referenced_works":[],"related_works":["https://openalex.org/W1507716237","https://openalex.org/W2214462370","https://openalex.org/W3021572409","https://openalex.org/W1582925778","https://openalex.org/W7129334524","https://openalex.org/W600248715","https://openalex.org/W998297107","https://openalex.org/W1604068273","https://openalex.org/W2327284619","https://openalex.org/W3156040042"],"abstract_inverted_index":null,"counts_by_year":[],"updated_date":"2026-10-10T09:11:00.788812","created_date":"2020-05-13T00:00:00"}