{"id":"https://openalex.org/W4311867966","doi":"https://doi.org/10.1007/s12532-022-00227-z","title":"Mixed integer bilevel optimization with a k-optimal follower: a hierarchy of bounds","display_name":"Mixed integer bilevel optimization with a k-optimal follower: a hierarchy of bounds","publication_year":2022,"publication_date":"2022-12-08","ids":{"openalex":"https://openalex.org/W4311867966","doi":"https://doi.org/10.1007/s12532-022-00227-z"},"language":"en","primary_location":{"id":"doi:10.1007/s12532-022-00227-z","is_oa":false,"landing_page_url":"https://doi.org/10.1007/s12532-022-00227-z","pdf_url":null,"source":{"id":"https://openalex.org/S173077093","display_name":"Mathematical Programming Computation","issn_l":"1867-2949","issn":["1867-2949","1867-2957"],"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 Computation","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/A5088419286","display_name":"Xueyu Shi","orcid":"https://orcid.org/0000-0001-5488-4452"},"institutions":[{"id":"https://openalex.org/I170201317","display_name":"University of Pittsburgh","ror":"https://ror.org/01an3r305","country_code":"US","type":"education","lineage":["https://openalex.org/I170201317"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Xueyu Shi","raw_affiliation_strings":["Department of Industrial Engineering, University of Pittsburgh, Pittsburgh, PA, USA"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Industrial Engineering, University of Pittsburgh, Pittsburgh, PA, USA","institution_ids":["https://openalex.org/I170201317"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5057562290","display_name":"Oleg A. Prokopyev","orcid":"https://orcid.org/0000-0003-2888-8630"},"institutions":[{"id":"https://openalex.org/I170201317","display_name":"University of Pittsburgh","ror":"https://ror.org/01an3r305","country_code":"US","type":"education","lineage":["https://openalex.org/I170201317"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Oleg A. Prokopyev","raw_affiliation_strings":["Department of Industrial Engineering, University of Pittsburgh, Pittsburgh, PA, USA"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Industrial Engineering, University of Pittsburgh, Pittsburgh, PA, USA","institution_ids":["https://openalex.org/I170201317"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5080991298","display_name":"Ted K. Ralphs","orcid":"https://orcid.org/0000-0002-4306-9089"},"institutions":[{"id":"https://openalex.org/I186143895","display_name":"Lehigh University","ror":"https://ror.org/012afjb06","country_code":"US","type":"education","lineage":["https://openalex.org/I186143895"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"Ted K. Ralphs","raw_affiliation_strings":["Department of Industrial and System Engineering, Lehigh University, Bethlehem, PA, USA"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Industrial and System Engineering, Lehigh University, Bethlehem, PA, USA","institution_ids":["https://openalex.org/I186143895"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5080991298"],"corresponding_institution_ids":["https://openalex.org/I186143895"],"apc_list":{"value":2390,"currency":"EUR","value_usd":3090},"apc_paid":null,"fwci":0.7612,"has_fulltext":false,"cited_by_count":8,"citation_normalized_percentile":{"value":0.75367339,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":99},"biblio":{"volume":"15","issue":"1","first_page":"1","last_page":"51"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10545","display_name":"Optimization and Variational Analysis","score":0.9926999807357788,"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/T10545","display_name":"Optimization and Variational Analysis","score":0.9926999807357788,"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/T10567","display_name":"Vehicle Routing Optimization Methods","score":0.9850000143051147,"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"}},{"id":"https://openalex.org/T12709","display_name":"Optimization and Mathematical Programming","score":0.9715999960899353,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/bilevel-optimization","display_name":"Bilevel optimization","score":0.8845862150192261},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.7724233865737915},{"id":"https://openalex.org/keywords/hierarchy","display_name":"Hierarchy","score":0.7274643182754517},{"id":"https://openalex.org/keywords/stackelberg-competition","display_name":"Stackelberg competition","score":0.6967870593070984},{"id":"https://openalex.org/keywords/theory-of-computation","display_name":"Theory of computation","score":0.6210898756980896},{"id":"https://openalex.org/keywords/relaxation","display_name":"Relaxation (psychology)","score":0.5538437366485596},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.5046039819717407},{"id":"https://openalex.org/keywords/integer","display_name":"Integer (computer science)","score":0.4992046356201172},{"id":"https://openalex.org/keywords/integer-programming","display_name":"Integer programming","score":0.4917135536670685},{"id":"https://openalex.org/keywords/optimization-problem","display_name":"Optimization problem","score":0.4576631188392639},{"id":"https://openalex.org/keywords/upper-and-lower-bounds","display_name":"Upper and lower bounds","score":0.43101391196250916},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.4147849678993225},{"id":"https://openalex.org/keywords/mathematical-economics","display_name":"Mathematical economics","score":0.17072027921676636},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.11452800035476685}],"concepts":[{"id":"https://openalex.org/C3309286","wikidata":"https://www.wikidata.org/wiki/Q4907693","display_name":"Bilevel optimization","level":3,"score":0.8845862150192261},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.7724233865737915},{"id":"https://openalex.org/C31170391","wikidata":"https://www.wikidata.org/wiki/Q188619","display_name":"Hierarchy","level":2,"score":0.7274643182754517},{"id":"https://openalex.org/C199510392","wikidata":"https://www.wikidata.org/wiki/Q1184602","display_name":"Stackelberg competition","level":2,"score":0.6967870593070984},{"id":"https://openalex.org/C24858836","wikidata":"https://www.wikidata.org/wiki/Q844718","display_name":"Theory of computation","level":2,"score":0.6210898756980896},{"id":"https://openalex.org/C2776029896","wikidata":"https://www.wikidata.org/wiki/Q3935810","display_name":"Relaxation (psychology)","level":2,"score":0.5538437366485596},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5046039819717407},{"id":"https://openalex.org/C97137487","wikidata":"https://www.wikidata.org/wiki/Q729138","display_name":"Integer (computer science)","level":2,"score":0.4992046356201172},{"id":"https://openalex.org/C56086750","wikidata":"https://www.wikidata.org/wiki/Q6042592","display_name":"Integer programming","level":2,"score":0.4917135536670685},{"id":"https://openalex.org/C137836250","wikidata":"https://www.wikidata.org/wiki/Q984063","display_name":"Optimization problem","level":2,"score":0.4576631188392639},{"id":"https://openalex.org/C77553402","wikidata":"https://www.wikidata.org/wiki/Q13222579","display_name":"Upper and lower bounds","level":2,"score":0.43101391196250916},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.4147849678993225},{"id":"https://openalex.org/C144237770","wikidata":"https://www.wikidata.org/wiki/Q747534","display_name":"Mathematical economics","level":1,"score":0.17072027921676636},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.11452800035476685},{"id":"https://openalex.org/C77805123","wikidata":"https://www.wikidata.org/wiki/Q161272","display_name":"Social psychology","level":1,"score":0.0},{"id":"https://openalex.org/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","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/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","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/C34447519","wikidata":"https://www.wikidata.org/wiki/Q179522","display_name":"Market economy","level":1,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1007/s12532-022-00227-z","is_oa":false,"landing_page_url":"https://doi.org/10.1007/s12532-022-00227-z","pdf_url":null,"source":{"id":"https://openalex.org/S173077093","display_name":"Mathematical Programming Computation","issn_l":"1867-2949","issn":["1867-2949","1867-2957"],"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 Computation","raw_type":"journal-article"},{"id":"pmh:doi:10.5167/uzh-265791","is_oa":false,"landing_page_url":null,"pdf_url":null,"source":{"id":"https://openalex.org/S4406922384","display_name":"Open MIND","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"Text"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":54,"referenced_works":["https://openalex.org/W121843079","https://openalex.org/W124060458","https://openalex.org/W1486993561","https://openalex.org/W1503428021","https://openalex.org/W1533818411","https://openalex.org/W1588628884","https://openalex.org/W1989755892","https://openalex.org/W2011039300","https://openalex.org/W2018714454","https://openalex.org/W2023858465","https://openalex.org/W2035893651","https://openalex.org/W2037935057","https://openalex.org/W2039564621","https://openalex.org/W2039766013","https://openalex.org/W2046432398","https://openalex.org/W2047684506","https://openalex.org/W2062459871","https://openalex.org/W2062530151","https://openalex.org/W2066086285","https://openalex.org/W2074987215","https://openalex.org/W2079868147","https://openalex.org/W2105935934","https://openalex.org/W2106371135","https://openalex.org/W2107022409","https://openalex.org/W2108455025","https://openalex.org/W2111240209","https://openalex.org/W2117235989","https://openalex.org/W2117708188","https://openalex.org/W2124659975","https://openalex.org/W2125690626","https://openalex.org/W2141594462","https://openalex.org/W2156293131","https://openalex.org/W2161455936","https://openalex.org/W2162467101","https://openalex.org/W2241389707","https://openalex.org/W2301746362","https://openalex.org/W2319807324","https://openalex.org/W2469279958","https://openalex.org/W2565581500","https://openalex.org/W2605397371","https://openalex.org/W2614367549","https://openalex.org/W2739297732","https://openalex.org/W2754261171","https://openalex.org/W2770478654","https://openalex.org/W2912474513","https://openalex.org/W2928408202","https://openalex.org/W2940477744","https://openalex.org/W2943117283","https://openalex.org/W3006959147","https://openalex.org/W3027865947","https://openalex.org/W3038086788","https://openalex.org/W4239098620","https://openalex.org/W4324345069","https://openalex.org/W6600376255"],"related_works":["https://openalex.org/W2026907359","https://openalex.org/W1981800580","https://openalex.org/W2994124117","https://openalex.org/W2618752689","https://openalex.org/W3025389440","https://openalex.org/W2971526008","https://openalex.org/W4289422123","https://openalex.org/W2991761232","https://openalex.org/W2168616681","https://openalex.org/W4292703869"],"abstract_inverted_index":null,"counts_by_year":[{"year":2026,"cited_by_count":3},{"year":2025,"cited_by_count":3},{"year":2023,"cited_by_count":1},{"year":2022,"cited_by_count":1}],"updated_date":"2026-06-26T08:34:08.712188","created_date":"2025-10-10T00:00:00"}
