{"id":"https://openalex.org/W1942810166","doi":"https://doi.org/10.3233/inf-2000-11406","title":"Computing True Shadow Prices in Linear Programming.","display_name":"Computing True Shadow Prices in Linear Programming.","publication_year":2000,"publication_date":"2000-01-01","ids":{"openalex":"https://openalex.org/W1942810166","doi":"https://doi.org/10.3233/inf-2000-11406","mag":"1942810166"},"language":"en","primary_location":{"id":"pmh:oai:CiteSeerX.psu:10.1.1.515.8712","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.515.8712","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://www.mii.lt/Informatica/pdf/INFO219.pdf","raw_type":"text"},"type":"article","indexed_in":[],"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/A5108295916","display_name":"James K. Ho","orcid":null},"institutions":[{"id":"https://openalex.org/I39422238","display_name":"University of Illinois Chicago","ror":"https://ror.org/02mpq6x41","country_code":"US","type":"education","lineage":["https://openalex.org/I39422238"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"James K. Ho","raw_affiliation_strings":["University of Illinois at Chicago"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"University of Illinois at Chicago","institution_ids":["https://openalex.org/I39422238"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5108295916"],"corresponding_institution_ids":["https://openalex.org/I39422238"],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":false,"cited_by_count":19,"citation_normalized_percentile":{"value":0.08071444,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":88,"max":98},"biblio":{"volume":"11","issue":"4","first_page":"421","last_page":"434"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T12709","display_name":"Optimization and Mathematical Programming","score":0.754800021648407,"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"}},"topics":[{"id":"https://openalex.org/T12709","display_name":"Optimization and Mathematical Programming","score":0.754800021648407,"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/T10551","display_name":"Scheduling and Optimization Algorithms","score":0.7282000184059143,"subfield":{"id":"https://openalex.org/subfields/2209","display_name":"Industrial and Manufacturing Engineering"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/shadow-price","display_name":"Shadow price","score":0.9338216781616211},{"id":"https://openalex.org/keywords/linear-programming","display_name":"Linear programming","score":0.677685022354126},{"id":"https://openalex.org/keywords/shadow","display_name":"Shadow (psychology)","score":0.6770214438438416},{"id":"https://openalex.org/keywords/software","display_name":"Software","score":0.64483642578125},{"id":"https://openalex.org/keywords/dual","display_name":"Dual (grammatical number)","score":0.5503189563751221},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.5379022359848022},{"id":"https://openalex.org/keywords/degenerate-energy-levels","display_name":"Degenerate energy levels","score":0.5173099040985107},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.49191951751708984},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.3584010899066925},{"id":"https://openalex.org/keywords/programming-language","display_name":"Programming language","score":0.12467050552368164}],"concepts":[{"id":"https://openalex.org/C139748260","wikidata":"https://www.wikidata.org/wiki/Q3308839","display_name":"Shadow price","level":2,"score":0.9338216781616211},{"id":"https://openalex.org/C41045048","wikidata":"https://www.wikidata.org/wiki/Q202843","display_name":"Linear programming","level":2,"score":0.677685022354126},{"id":"https://openalex.org/C117797892","wikidata":"https://www.wikidata.org/wiki/Q286363","display_name":"Shadow (psychology)","level":2,"score":0.6770214438438416},{"id":"https://openalex.org/C2777904410","wikidata":"https://www.wikidata.org/wiki/Q7397","display_name":"Software","level":2,"score":0.64483642578125},{"id":"https://openalex.org/C2780980858","wikidata":"https://www.wikidata.org/wiki/Q110022","display_name":"Dual (grammatical number)","level":2,"score":0.5503189563751221},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.5379022359848022},{"id":"https://openalex.org/C72319582","wikidata":"https://www.wikidata.org/wiki/Q584304","display_name":"Degenerate energy levels","level":2,"score":0.5173099040985107},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.49191951751708984},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.3584010899066925},{"id":"https://openalex.org/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","level":1,"score":0.12467050552368164},{"id":"https://openalex.org/C124952713","wikidata":"https://www.wikidata.org/wiki/Q8242","display_name":"Literature","level":1,"score":0.0},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.0},{"id":"https://openalex.org/C542102704","wikidata":"https://www.wikidata.org/wiki/Q183257","display_name":"Psychotherapist","level":1,"score":0.0},{"id":"https://openalex.org/C15744967","wikidata":"https://www.wikidata.org/wiki/Q9418","display_name":"Psychology","level":0,"score":0.0},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.0},{"id":"https://openalex.org/C142362112","wikidata":"https://www.wikidata.org/wiki/Q735","display_name":"Art","level":0,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"pmh:oai:CiteSeerX.psu:10.1.1.515.8712","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.515.8712","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://www.mii.lt/Informatica/pdf/INFO219.pdf","raw_type":"text"},{"id":"mag:1942810166","is_oa":false,"landing_page_url":"https://www.mii.lt/Informatica/pdf/INFO219.pdf","pdf_url":null,"source":null,"license":null,"license_id":null,"version":null,"is_accepted":false,"is_published":null,"raw_source_name":"Informatica","raw_type":null}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":15,"referenced_works":["https://openalex.org/W32221055","https://openalex.org/W1590736488","https://openalex.org/W1973520969","https://openalex.org/W1974142055","https://openalex.org/W2009005114","https://openalex.org/W2033925391","https://openalex.org/W2051209971","https://openalex.org/W2056634284","https://openalex.org/W2064837119","https://openalex.org/W2066656703","https://openalex.org/W2124163050","https://openalex.org/W2127470768","https://openalex.org/W2166016858","https://openalex.org/W2404372381","https://openalex.org/W2507373415"],"related_works":["https://openalex.org/W2067903272","https://openalex.org/W1974142055","https://openalex.org/W2376011943","https://openalex.org/W2381267709","https://openalex.org/W1983348597","https://openalex.org/W2087923334","https://openalex.org/W2361916906","https://openalex.org/W1991000959","https://openalex.org/W189031407","https://openalex.org/W2133755802","https://openalex.org/W2009979822","https://openalex.org/W2531278276","https://openalex.org/W1582677233","https://openalex.org/W1555207426","https://openalex.org/W2047774784","https://openalex.org/W2949469051","https://openalex.org/W2191038799","https://openalex.org/W2082028133","https://openalex.org/W2396224275","https://openalex.org/W2088021388"],"abstract_inverted_index":{"Abstract.":[0],"It":[1],"is":[2,31],"well":[3],"known":[4,61],"that":[5],"in":[6,63],"linear":[7,84],"programming,":[8,85],"the":[9,13,25,43],"optimal":[10],"values":[11],"of":[12,24],"dual":[14],"variables":[15],"can":[16,53,72],"be":[17,54,73],"interpreted":[18],"as":[19],"shadow":[20,70,86],"prices":[21,71],"(marginal":[22],"values)":[23],"right-hand":[26],"side":[27],"coefficients.":[28],"However,":[29],"this":[30,64],"true":[32,69],"only":[33],"under":[34],"nondegeneracy":[35],"assumptions.":[36],"Since":[37],"real":[38],"problems":[39],"are":[40],"often":[41],"degenerate,":[42],"output":[44],"from":[45],"conventional":[46],"LP":[47],"software":[48],"regarding":[49],"such":[50],"marginal":[51],"information":[52],"misleading.":[55],"This":[56],"paper":[57],"surveys":[58],"and":[59,66],"generalizes":[60],"results":[62],"topic":[65],"demonstrates":[67],"how":[68],"computed":[74],"with":[75],"or":[76],"without":[77],"modification":[78],"to":[79],"existing":[80],"software.":[81,89],"Key":[82],"words:":[83],"prices,":[87],"optimization":[88],"1.":[90]},"counts_by_year":[{"year":2024,"cited_by_count":1},{"year":2023,"cited_by_count":1},{"year":2021,"cited_by_count":1},{"year":2018,"cited_by_count":2},{"year":2017,"cited_by_count":1},{"year":2016,"cited_by_count":2},{"year":2014,"cited_by_count":4}],"updated_date":"2026-08-26T07:47:46.906454","created_date":"2025-10-10T00:00:00"}
