{"id":"https://openalex.org/W115224644","doi":"https://doi.org/10.1007/978-3-7091-6957-5_4","title":"A Self-Validating Method for Solving Linear Programming Problems with Interval Input Data","display_name":"A Self-Validating Method for Solving Linear Programming Problems with Interval Input Data","publication_year":1988,"publication_date":"1988-01-01","ids":{"openalex":"https://openalex.org/W115224644","doi":"https://doi.org/10.1007/978-3-7091-6957-5_4","mag":"115224644"},"language":"en","primary_location":{"id":"doi:10.1007/978-3-7091-6957-5_4","doi":"https://doi.org/10.1007/978-3-7091-6957-5_4","is_oa":false,"landing_page_url":"https://doi.org/10.1007/978-3-7091-6957-5_4","pdf_url":null,"source":{"id":"https://openalex.org/S4210201491","display_name":"Computing. Supplementum","issn_l":"0344-8029","issn":["0344-8029"],"is_oa":false,"is_in_doaj":false,"is_core":true,"listed_in":["cwts-core"],"host_organization":"https://openalex.org/P4310321666","host_organization_name":"Springer Vienna","host_organization_lineage":["https://openalex.org/P4310321666","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Vienna","Springer Nature"],"type":"book series"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Computing Supplementum","raw_type":"book-chapter"},"volume":{"id":"https://openalex.org/W2379095230","display_name":"Scientific Computation with Automatic Result Verification"},"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/A5010637941","display_name":"Christian Jansson","orcid":null,"observed_orcids":[]},"institutions":[{"id":"https://openalex.org/I884043246","display_name":"Hamburg University of Technology","ror":"https://ror.org/04bs1pb34","country_code":"DE","type":"education","lineage":["https://openalex.org/I884043246"]}],"countries":["DE"],"is_corresponding":true,"raw_author_name":"Christian Jansson","raw_affiliation_strings":["Informatik III, Technische Universit\u00e4t Hamburg, Hamburg 90, Federal Republic of Germany","TECHNISCHE UNIVERSITAT HAMBURG"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Informatik III, Technische Universit\u00e4t Hamburg, Hamburg 90, Federal Republic of Germany","institution_ids":["https://openalex.org/I884043246"]},{"raw_affiliation_string":"TECHNISCHE UNIVERSITAT HAMBURG","institution_ids":["https://openalex.org/I884043246"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5010637941"],"corresponding_institution_ids":["https://openalex.org/I884043246"],"apc_list":null,"apc_paid":null,"fwci":3.4,"has_fulltext":false,"cited_by_count":52,"citation_normalized_percentile":{"value":0.86816269,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":88,"max":98},"biblio":{"volume":null,"issue":null,"first_page":"33","last_page":"45"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11697","display_name":"Numerical Methods and Algorithms","score":0.9682999849319458,"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"}},"topics":[{"id":"https://openalex.org/T11697","display_name":"Numerical Methods and Algorithms","score":0.9682999849319458,"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"}},{"id":"https://openalex.org/T10963","display_name":"Advanced Optimization Algorithms Research","score":0.013700000010430813,"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/T12709","display_name":"Optimization and Mathematical Programming","score":0.01080000028014183,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/linear-programming","display_name":"linear programming","score":0.8740000128746033},{"id":"https://openalex.org/keywords/guaranteed-bounds","display_name":"guaranteed bounds","score":0.6909999847412109},{"id":"https://openalex.org/keywords/sensitivity-analysis","display_name":"sensitivity analysis","score":0.8019999861717224},{"id":"https://openalex.org/keywords/post-optimality-analysis","display_name":"post-optimality analysis","score":0.9259999990463257},{"id":"https://openalex.org/keywords/round-off-error","display_name":"rounding errors","score":0.6980000138282776},{"id":"https://openalex.org/keywords/cancellation-error","display_name":"cancellation error","score":0.5809999704360962},{"id":"https://openalex.org/keywords/tolerance-intervals","display_name":"tolerance intervals","score":0.41600000858306885},{"id":"https://openalex.org/keywords/diet-problem","display_name":"diet problem","score":0.8989999890327454}],"concepts":[{"id":"https://openalex.org/C41045048","wikidata":"https://www.wikidata.org/wiki/Q202843","display_name":"Linear programming","level":2,"score":0.7800893783569336},{"id":"https://openalex.org/C144521790","wikidata":"https://www.wikidata.org/wiki/Q134164","display_name":"Simplex algorithm","level":3,"score":0.714893639087677},{"id":"https://openalex.org/C2778067643","wikidata":"https://www.wikidata.org/wiki/Q166507","display_name":"Interval (graph theory)","level":2,"score":0.6691418886184692},{"id":"https://openalex.org/C191252586","wikidata":"https://www.wikidata.org/wiki/Q1671453","display_name":"Interval arithmetic","level":3,"score":0.5849450826644897},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.5057182312011719},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.4735521376132965},{"id":"https://openalex.org/C21200559","wikidata":"https://www.wikidata.org/wiki/Q7451068","display_name":"Sensitivity (control systems)","level":2,"score":0.4545901417732239},{"id":"https://openalex.org/C205658194","wikidata":"https://www.wikidata.org/wiki/Q4168281","display_name":"Linear-fractional programming","level":3,"score":0.4376413822174072},{"id":"https://openalex.org/C62438384","wikidata":"https://www.wikidata.org/wiki/Q331350","display_name":"Simplex","level":2,"score":0.4284239411354065},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.42619356513023376},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.42405465245246887},{"id":"https://openalex.org/C24326235","wikidata":"https://www.wikidata.org/wiki/Q126095","display_name":"Electronic engineering","level":1,"score":0.0},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.0},{"id":"https://openalex.org/C127413603","wikidata":"https://www.wikidata.org/wiki/Q11023","display_name":"Engineering","level":0,"score":0.0},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.0},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.0},{"id":"https://openalex.org/C34388435","wikidata":"https://www.wikidata.org/wiki/Q2267362","display_name":"Bounded function","level":2,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1007/978-3-7091-6957-5_4","doi":"https://doi.org/10.1007/978-3-7091-6957-5_4","is_oa":false,"landing_page_url":"https://doi.org/10.1007/978-3-7091-6957-5_4","pdf_url":null,"source":{"id":"https://openalex.org/S4210201491","display_name":"Computing. Supplementum","issn_l":"0344-8029","issn":["0344-8029"],"is_oa":false,"is_in_doaj":false,"is_core":true,"listed_in":["cwts-core"],"host_organization":"https://openalex.org/P4310321666","host_organization_name":"Springer Vienna","host_organization_lineage":["https://openalex.org/P4310321666","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Vienna","Springer Nature"],"type":"book series"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Computing Supplementum","raw_type":"book-chapter"},{"id":"pmh:oai:tore.tuhh.de:11420/9505","doi":null,"is_oa":false,"landing_page_url":"http://hdl.handle.net/11420/9505","pdf_url":null,"source":{"id":"https://openalex.org/S4306401751","display_name":"tub.dok (Hamburg University of Technology)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I884043246","host_organization_name":"Hamburg University of Technology","host_organization_lineage":["https://openalex.org/I884043246"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"Book Part"}],"best_oa_location":null,"sustainable_development_goals":[],"study_designs":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":15,"referenced_works":["https://openalex.org/W2189508","https://openalex.org/W16654297","https://openalex.org/W87418472","https://openalex.org/W165390027","https://openalex.org/W317335566","https://openalex.org/W1571045421","https://openalex.org/W1580809199","https://openalex.org/W1588259836","https://openalex.org/W1605702526","https://openalex.org/W1846057234","https://openalex.org/W1968258418","https://openalex.org/W2081355284","https://openalex.org/W2084623031","https://openalex.org/W2101224575","https://openalex.org/W2313814435"],"related_works":["https://openalex.org/W2102857183","https://openalex.org/W2028244093","https://openalex.org/W2033891812","https://openalex.org/W2005325280","https://openalex.org/W151502846","https://openalex.org/W412199253","https://openalex.org/W2481306512","https://openalex.org/W4366705080","https://openalex.org/W2538595016","https://openalex.org/W4255686500"],"abstract_inverted_index":null,"counts_by_year":[{"year":2025,"cited_by_count":4},{"year":2023,"cited_by_count":1},{"year":2022,"cited_by_count":3},{"year":2020,"cited_by_count":1},{"year":2018,"cited_by_count":3},{"year":2016,"cited_by_count":1},{"year":2015,"cited_by_count":4},{"year":2014,"cited_by_count":1},{"year":2012,"cited_by_count":5}],"updated_date":"2026-10-10T09:11:00.788812","created_date":"2016-06-24T00:00:00"}