{"id":"https://openalex.org/W1898673259","doi":"https://doi.org/10.1017/cbo9780511559914.019","title":"Linear programming","display_name":"Linear programming","publication_year":1980,"publication_date":"1980-02-07","ids":{"openalex":"https://openalex.org/W1898673259","doi":"https://doi.org/10.1017/cbo9780511559914.019","mag":"1898673259"},"language":"en","primary_location":{"id":"doi:10.1017/cbo9780511559914.019","doi":"https://doi.org/10.1017/cbo9780511559914.019","is_oa":false,"landing_page_url":"https://doi.org/10.1017/cbo9780511559914.019","pdf_url":null,"source":{"id":"https://openalex.org/S4306462995","display_name":"Cambridge University Press eBooks","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/P4310311721","host_organization_name":"Cambridge University Press","host_organization_lineage":["https://openalex.org/P4310311721","https://openalex.org/P4310311702"],"host_organization_lineage_names":["Cambridge University Press","University of Cambridge"],"type":"ebook platform"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Farm Planning and Control","raw_type":"book-chapter"},"volume":{"id":"https://openalex.org/W2039410212","display_name":"Farm Planning and Control"},"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/A5006463295","display_name":"Catherine Barnard","orcid":"https://orcid.org/0000-0001-8786-9240","observed_orcids":["https://orcid.org/0000-0001-8786-9240"]},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"C. S. Barnard","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5004801619","display_name":"J. S. Nix","orcid":null,"observed_orcids":[]},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"J. S. Nix","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":0,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":false,"cited_by_count":0,"citation_normalized_percentile":{"value":0.28085106,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":null,"issue":null,"first_page":"353","last_page":"381"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T12709","display_name":"Optimization and Mathematical Programming","score":0.7627000212669373,"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":0.7627000212669373,"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/T11805","display_name":"Agricultural economics and policies","score":0.23240000009536743,"subfield":{"id":"https://openalex.org/subfields/2002","display_name":"Economics and Econometrics"},"field":{"id":"https://openalex.org/fields/20","display_name":"Economics, Econometrics and Finance"},"domain":{"id":"https://openalex.org/domains/2","display_name":"Social Sciences"}},{"id":"https://openalex.org/T10963","display_name":"Advanced Optimization Algorithms Research","score":0.0008999999845400453,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/linear-programming","display_name":"linear programming","score":1.0},{"id":"https://openalex.org/keywords/farm-planning","display_name":"farm planning","score":0.9909999966621399},{"id":"https://openalex.org/keywords/resource-allocation","display_name":"resource allocation","score":0.7979999780654907},{"id":"https://openalex.org/keywords/matrix-algebra","display_name":"matrix algebra","score":0.6050000190734863},{"id":"https://openalex.org/keywords/programming","display_name":"programming","score":0.5580000281333923},{"id":"https://openalex.org/keywords/farm-decision-making","display_name":"agricultural decision-making","score":0.3610000014305115}],"concepts":[{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.45928215980529785}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1017/cbo9780511559914.019","doi":"https://doi.org/10.1017/cbo9780511559914.019","is_oa":false,"landing_page_url":"https://doi.org/10.1017/cbo9780511559914.019","pdf_url":null,"source":{"id":"https://openalex.org/S4306462995","display_name":"Cambridge University Press eBooks","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/P4310311721","host_organization_name":"Cambridge University Press","host_organization_lineage":["https://openalex.org/P4310311721","https://openalex.org/P4310311702"],"host_organization_lineage_names":["Cambridge University Press","University of Cambridge"],"type":"ebook platform"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Farm Planning and Control","raw_type":"book-chapter"}],"best_oa_location":null,"sustainable_development_goals":[],"study_designs":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":0,"referenced_works":[],"related_works":["https://openalex.org/W2549223336","https://openalex.org/W1119519071","https://openalex.org/W4241554216","https://openalex.org/W7097380583","https://openalex.org/W2157281287","https://openalex.org/W276744294","https://openalex.org/W1975070152","https://openalex.org/W4240249396","https://openalex.org/W2617601576","https://openalex.org/W2033922149"],"abstract_inverted_index":{"Linear":[0],"programming":[1,100],"is":[2,17,120,158,185,239],"a":[3,58,70,85,104,121,138,161,196],"technique":[4],"based":[5],"on":[6,180],"the":[7,44,47,55,80,90,144,151,154,169,175,181,186,189,203,211,215,222,225,229,233,236],"processes":[8],"of":[9,19,27,30,46,49,61,83,92,124,131,153,172,188],"matrix":[10],"algebra,":[11],"which":[12,214,228],"given":[13],"suitably":[14],"formulated":[15],"data,":[16],"capable":[18],"producing":[20,84],"optimal,":[21],"mathematical":[22],"solutions":[23],"in":[24,40,89,160,193,213,227],"terms":[25],"either":[26],"maximising":[28],"or":[29,163],"minimising":[31],"some":[32],"stated":[33,86],"objective.":[34],"It":[35],"thus":[36,148],"lends":[37],"itself":[38,146],"readily":[39],"farm":[41],"planning":[42,216],"to":[43,57,78,103,136,177,221,235],"determination":[45],"combination":[48],"enterprises":[50],"and":[51,118,157,191,224],"techniques":[52],"that":[53,199],"maximises":[54],"returns":[56],"particular":[59],"set":[60],"fixed":[62],"resources.":[63],"Similarly,":[64],"though":[65],"less":[66],"commonly":[67],"so":[68],"as":[69,88,208],"direct":[71],"farming":[72],"application,":[73],"it":[74,209],"can":[75,109],"be":[76,110,178,219],"used":[77],"discover":[79],"least-cost":[81],"way":[82,212],"output,":[87],"computation":[91],"minimum-cost":[93],"rations.":[94],"For":[95],"all":[96],"practical":[97],"purposes,":[98],"linear":[99],"requires":[101],"access":[102],"computer,":[105],"for":[106],"although":[107],"computations":[108],"performed":[111,179],"by":[112,140],"hand":[113],"they":[114],"become":[115],"very":[116],"time-consuming":[117],"there":[119],"considerable":[122],"risk":[123],"cumulative":[125],"errors":[126],"arising.":[127],"Two":[128],"basic":[129],"sets":[130],"input":[132],"data":[133,217],"are":[134],"required":[135],"solve":[137],"problem":[139,145,237],"computer.":[141],"One":[142],"concerns":[143],"\u2013":[147,156,168,232,238],"falling":[149],"within":[150],"province":[152],"planner":[155],"contained":[159],"\u2018matrix\u2019":[162],"two-way":[164],"table.":[165],"The":[166,183],"other":[167],"program":[170],"\u2013consists":[171],"instructions":[173],"about":[174],"manipulations":[176],"matrix.":[182],"latter":[184],"responsibility":[187],"specialist":[190],"is,":[192],"any":[194],"case,":[195],"once-and-for-all":[197],"task":[198],"need":[200],"not":[201],"concern":[202],"computer":[204,223,230],"user,":[205],"except":[206],"insofar":[207],"affects":[210],"must":[218],"presented":[220],"form":[226],"output":[231],"solution":[234],"obtained.":[240]},"counts_by_year":[],"updated_date":"2026-10-10T09:11:00.788812","created_date":"2016-06-24T00:00:00"}