{"id":"https://openalex.org/W2018040383","doi":"https://doi.org/10.1007/bf02187296","title":"Chapter 4 The lack of invariance of optimal dual solutions under translation","display_name":"Chapter 4 The lack of invariance of optimal dual solutions under translation","publication_year":1996,"publication_date":"1996-04-01","ids":{"openalex":"https://openalex.org/W2018040383","doi":"https://doi.org/10.1007/bf02187296","mag":"2018040383"},"language":"en","primary_location":{"id":"doi:10.1007/bf02187296","is_oa":false,"landing_page_url":"https://doi.org/10.1007/bf02187296","pdf_url":null,"source":{"id":"https://openalex.org/S57667410","display_name":"Annals of Operations Research","issn_l":"0254-5330","issn":["0254-5330","1572-9338"],"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":"Annals of 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/A5060684119","display_name":"Robert Thrall","orcid":null},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Robert M. Thrall","raw_affiliation_strings":["12003 Pebble Hill Drive, 77024, Houston, TX, USA","Houston, USA"],"affiliations":[{"raw_affiliation_string":"12003 Pebble Hill Drive, 77024, Houston, TX, USA","institution_ids":[]},{"raw_affiliation_string":"Houston, USA","institution_ids":[]}]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5060684119"],"corresponding_institution_ids":[],"apc_list":{"value":2390,"currency":"EUR","value_usd":2990},"apc_paid":null,"fwci":1.8509,"has_fulltext":false,"cited_by_count":31,"citation_normalized_percentile":{"value":0.84697337,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":96},"biblio":{"volume":"66","issue":"2","first_page":"103","last_page":"108"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10357","display_name":"Efficiency Analysis Using DEA","score":0.9998000264167786,"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/T10357","display_name":"Efficiency Analysis Using DEA","score":0.9998000264167786,"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/T10007","display_name":"Monetary Policy and Economic Impact","score":0.9878000020980835,"subfield":{"id":"https://openalex.org/subfields/2000","display_name":"General Economics, Econometrics and Finance"},"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/T11770","display_name":"Fiscal Policy and Economic Growth","score":0.9878000020980835,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/theory-of-computation","display_name":"Theory of computation","score":0.8383209109306335},{"id":"https://openalex.org/keywords/invariant","display_name":"Invariant (physics)","score":0.7293016314506531},{"id":"https://openalex.org/keywords/translation","display_name":"Translation (biology)","score":0.6897108554840088},{"id":"https://openalex.org/keywords/dual","display_name":"Dual (grammatical number)","score":0.6877630949020386},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.6120970845222473},{"id":"https://openalex.org/keywords/zero","display_name":"Zero (linguistics)","score":0.5541130304336548},{"id":"https://openalex.org/keywords/data-envelopment-analysis","display_name":"Data envelopment analysis","score":0.5108284950256348},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.4440472424030304},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.42566561698913574},{"id":"https://openalex.org/keywords/mathematical-economics","display_name":"Mathematical economics","score":0.3959678113460541},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.3388533294200897},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.32556307315826416},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.17019328474998474},{"id":"https://openalex.org/keywords/philosophy","display_name":"Philosophy","score":0.043315231800079346}],"concepts":[{"id":"https://openalex.org/C24858836","wikidata":"https://www.wikidata.org/wiki/Q844718","display_name":"Theory of computation","level":2,"score":0.8383209109306335},{"id":"https://openalex.org/C190470478","wikidata":"https://www.wikidata.org/wiki/Q2370229","display_name":"Invariant (physics)","level":2,"score":0.7293016314506531},{"id":"https://openalex.org/C149364088","wikidata":"https://www.wikidata.org/wiki/Q185917","display_name":"Translation (biology)","level":4,"score":0.6897108554840088},{"id":"https://openalex.org/C2780980858","wikidata":"https://www.wikidata.org/wiki/Q110022","display_name":"Dual (grammatical number)","level":2,"score":0.6877630949020386},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6120970845222473},{"id":"https://openalex.org/C2780813799","wikidata":"https://www.wikidata.org/wiki/Q3274237","display_name":"Zero (linguistics)","level":2,"score":0.5541130304336548},{"id":"https://openalex.org/C22088475","wikidata":"https://www.wikidata.org/wiki/Q647974","display_name":"Data envelopment analysis","level":2,"score":0.5108284950256348},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.4440472424030304},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.42566561698913574},{"id":"https://openalex.org/C144237770","wikidata":"https://www.wikidata.org/wiki/Q747534","display_name":"Mathematical economics","level":1,"score":0.3959678113460541},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.3388533294200897},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.32556307315826416},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.17019328474998474},{"id":"https://openalex.org/C138885662","wikidata":"https://www.wikidata.org/wiki/Q5891","display_name":"Philosophy","level":0,"score":0.043315231800079346},{"id":"https://openalex.org/C105580179","wikidata":"https://www.wikidata.org/wiki/Q188928","display_name":"Messenger RNA","level":3,"score":0.0},{"id":"https://openalex.org/C185592680","wikidata":"https://www.wikidata.org/wiki/Q2329","display_name":"Chemistry","level":0,"score":0.0},{"id":"https://openalex.org/C104317684","wikidata":"https://www.wikidata.org/wiki/Q7187","display_name":"Gene","level":2,"score":0.0},{"id":"https://openalex.org/C41895202","wikidata":"https://www.wikidata.org/wiki/Q8162","display_name":"Linguistics","level":1,"score":0.0},{"id":"https://openalex.org/C55493867","wikidata":"https://www.wikidata.org/wiki/Q7094","display_name":"Biochemistry","level":1,"score":0.0},{"id":"https://openalex.org/C37914503","wikidata":"https://www.wikidata.org/wiki/Q156495","display_name":"Mathematical physics","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1007/bf02187296","is_oa":false,"landing_page_url":"https://doi.org/10.1007/bf02187296","pdf_url":null,"source":{"id":"https://openalex.org/S57667410","display_name":"Annals of Operations Research","issn_l":"0254-5330","issn":["0254-5330","1572-9338"],"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":"Annals of Operations Research","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":5,"referenced_works":["https://openalex.org/W1967711861","https://openalex.org/W2052927476","https://openalex.org/W2095723131","https://openalex.org/W2127324006","https://openalex.org/W2129763896"],"related_works":["https://openalex.org/W2801360836","https://openalex.org/W2120745168","https://openalex.org/W2736559621","https://openalex.org/W2352291457","https://openalex.org/W2360317231","https://openalex.org/W2126538897","https://openalex.org/W4378625608","https://openalex.org/W2277194173","https://openalex.org/W2958550830","https://openalex.org/W3168886930"],"abstract_inverted_index":null,"counts_by_year":[{"year":2024,"cited_by_count":2},{"year":2022,"cited_by_count":1},{"year":2021,"cited_by_count":1},{"year":2020,"cited_by_count":1},{"year":2019,"cited_by_count":1},{"year":2018,"cited_by_count":1},{"year":2014,"cited_by_count":2},{"year":2013,"cited_by_count":2},{"year":2012,"cited_by_count":1}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}
