{"id":"https://openalex.org/W1974338406","doi":"https://doi.org/10.1007/bf01587077","title":"Marginal values in mixed integer linear programming","display_name":"Marginal values in mixed integer linear programming","publication_year":1989,"publication_date":"1989-05-01","ids":{"openalex":"https://openalex.org/W1974338406","doi":"https://doi.org/10.1007/bf01587077","mag":"1974338406"},"language":"en","primary_location":{"id":"doi:10.1007/bf01587077","is_oa":false,"landing_page_url":"https://doi.org/10.1007/bf01587077","pdf_url":null,"source":{"id":"https://openalex.org/S193920097","display_name":"Mathematical Programming","issn_l":"0025-5610","issn":["0025-5610","1436-4646"],"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":"Mathematical Programming","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/A5072551968","display_name":"Adrian Williams","orcid":"https://orcid.org/0000-0003-2098-808X"},"institutions":[{"id":"https://openalex.org/I102322142","display_name":"Rutgers, The State University of New Jersey","ror":"https://ror.org/05vt9qd57","country_code":"US","type":"education","lineage":["https://openalex.org/I102322142"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"A. C. Williams","raw_affiliation_strings":["RUTCOR, Rutgers \u2014 The State University of New Jersey, 08903, New Brunswick, NJ, USA","The State University of New Jersey , New Brunswick"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"RUTCOR, Rutgers \u2014 The State University of New Jersey, 08903, New Brunswick, NJ, USA","institution_ids":["https://openalex.org/I102322142"]},{"raw_affiliation_string":"The State University of New Jersey , New Brunswick","institution_ids":["https://openalex.org/I102322142"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5072551968"],"corresponding_institution_ids":["https://openalex.org/I102322142"],"apc_list":{"value":2190,"currency":"EUR","value_usd":2890},"apc_paid":null,"fwci":0.52,"has_fulltext":false,"cited_by_count":13,"citation_normalized_percentile":{"value":0.5814978,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":98},"biblio":{"volume":"44","issue":"1-3","first_page":"67","last_page":"75"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10963","display_name":"Advanced Optimization Algorithms Research","score":0.9984999895095825,"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":0.9984999895095825,"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":0.9983999729156494,"subfield":{"id":"https://openalex.org/subfields/2207","display_name":"Control and Systems Engineering"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T10545","display_name":"Optimization and Variational Analysis","score":0.9976999759674072,"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":0.7891128063201904},{"id":"https://openalex.org/keywords/linear-programming","display_name":"Linear programming","score":0.7351162433624268},{"id":"https://openalex.org/keywords/classification-of-discontinuities","display_name":"Classification of discontinuities","score":0.6873697638511658},{"id":"https://openalex.org/keywords/integer-programming","display_name":"Integer programming","score":0.6507453918457031},{"id":"https://openalex.org/keywords/function","display_name":"Function (biology)","score":0.518997311592102},{"id":"https://openalex.org/keywords/value","display_name":"Value (mathematics)","score":0.5071234703063965},{"id":"https://openalex.org/keywords/current","display_name":"Current (fluid)","score":0.49246010184288025},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.4744513928890228},{"id":"https://openalex.org/keywords/work","display_name":"Work (physics)","score":0.4546525776386261},{"id":"https://openalex.org/keywords/bellman-equation","display_name":"Bellman equation","score":0.44781920313835144},{"id":"https://openalex.org/keywords/integer","display_name":"Integer (computer science)","score":0.4128059148788452},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.3903723657131195},{"id":"https://openalex.org/keywords/statistics","display_name":"Statistics","score":0.19039806723594666},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.1669970154762268},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.11702090501785278}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7891128063201904},{"id":"https://openalex.org/C41045048","wikidata":"https://www.wikidata.org/wiki/Q202843","display_name":"Linear programming","level":2,"score":0.7351162433624268},{"id":"https://openalex.org/C15627037","wikidata":"https://www.wikidata.org/wiki/Q541961","display_name":"Classification of discontinuities","level":2,"score":0.6873697638511658},{"id":"https://openalex.org/C56086750","wikidata":"https://www.wikidata.org/wiki/Q6042592","display_name":"Integer programming","level":2,"score":0.6507453918457031},{"id":"https://openalex.org/C14036430","wikidata":"https://www.wikidata.org/wiki/Q3736076","display_name":"Function (biology)","level":2,"score":0.518997311592102},{"id":"https://openalex.org/C2776291640","wikidata":"https://www.wikidata.org/wiki/Q2912517","display_name":"Value (mathematics)","level":2,"score":0.5071234703063965},{"id":"https://openalex.org/C148043351","wikidata":"https://www.wikidata.org/wiki/Q4456944","display_name":"Current (fluid)","level":2,"score":0.49246010184288025},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.4744513928890228},{"id":"https://openalex.org/C18762648","wikidata":"https://www.wikidata.org/wiki/Q42213","display_name":"Work (physics)","level":2,"score":0.4546525776386261},{"id":"https://openalex.org/C14646407","wikidata":"https://www.wikidata.org/wiki/Q1430750","display_name":"Bellman equation","level":2,"score":0.44781920313835144},{"id":"https://openalex.org/C97137487","wikidata":"https://www.wikidata.org/wiki/Q729138","display_name":"Integer (computer science)","level":2,"score":0.4128059148788452},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.3903723657131195},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.19039806723594666},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.1669970154762268},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.11702090501785278},{"id":"https://openalex.org/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","level":1,"score":0.0},{"id":"https://openalex.org/C119599485","wikidata":"https://www.wikidata.org/wiki/Q43035","display_name":"Electrical engineering","level":1,"score":0.0},{"id":"https://openalex.org/C78458016","wikidata":"https://www.wikidata.org/wiki/Q840400","display_name":"Evolutionary biology","level":1,"score":0.0},{"id":"https://openalex.org/C86803240","wikidata":"https://www.wikidata.org/wiki/Q420","display_name":"Biology","level":0,"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/C78519656","wikidata":"https://www.wikidata.org/wiki/Q101333","display_name":"Mechanical engineering","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1007/bf01587077","is_oa":false,"landing_page_url":"https://doi.org/10.1007/bf01587077","pdf_url":null,"source":{"id":"https://openalex.org/S193920097","display_name":"Mathematical Programming","issn_l":"0025-5610","issn":["0025-5610","1436-4646"],"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":"Mathematical Programming","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":21,"referenced_works":["https://openalex.org/W36169824","https://openalex.org/W306515463","https://openalex.org/W1496039454","https://openalex.org/W1550762362","https://openalex.org/W1994325510","https://openalex.org/W2008131758","https://openalex.org/W2026073821","https://openalex.org/W2033151347","https://openalex.org/W2044609813","https://openalex.org/W2066656703","https://openalex.org/W2068913356","https://openalex.org/W2090839948","https://openalex.org/W2223181934","https://openalex.org/W2252863398","https://openalex.org/W2336259629","https://openalex.org/W2561873886","https://openalex.org/W2795674018","https://openalex.org/W4245545442","https://openalex.org/W4249667877","https://openalex.org/W6667210788","https://openalex.org/W6730551242"],"related_works":["https://openalex.org/W1925942709","https://openalex.org/W2047683846","https://openalex.org/W2044902158","https://openalex.org/W2109912052","https://openalex.org/W1711527768","https://openalex.org/W4285278887","https://openalex.org/W2365237642","https://openalex.org/W2995925505","https://openalex.org/W3116484972","https://openalex.org/W2941986668"],"abstract_inverted_index":null,"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2019,"cited_by_count":1},{"year":2016,"cited_by_count":1},{"year":2012,"cited_by_count":2}],"updated_date":"2026-04-26T08:31:28.666265","created_date":"2025-10-10T00:00:00"}