{"id":"https://openalex.org/W4379644805","doi":"https://doi.org/10.1007/s10479-023-05425-z","title":"A generalization of the increasing generalized failure rate unimodality condition","display_name":"A generalization of the increasing generalized failure rate unimodality condition","publication_year":2023,"publication_date":"2023-06-07","ids":{"openalex":"https://openalex.org/W4379644805","doi":"https://doi.org/10.1007/s10479-023-05425-z"},"language":"en","primary_location":{"id":"doi:10.1007/s10479-023-05425-z","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s10479-023-05425-z","pdf_url":"https://link.springer.com/content/pdf/10.1007/s10479-023-05425-z.pdf","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":"cc-by","license_id":"https://openalex.org/licenses/cc-by","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":true,"oa_status":"hybrid","oa_url":"https://link.springer.com/content/pdf/10.1007/s10479-023-05425-z.pdf","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5048295129","display_name":"Stefanos Leonardos","orcid":"https://orcid.org/0000-0002-1498-1490"},"institutions":[{"id":"https://openalex.org/I183935753","display_name":"King's College London","ror":"https://ror.org/0220mzb33","country_code":"GB","type":"education","lineage":["https://openalex.org/I124357947","https://openalex.org/I183935753"]}],"countries":["GB"],"is_corresponding":true,"raw_author_name":"Stefanos Leonardos","raw_affiliation_strings":["Department of Informatics, King\u2019s College London, London, UK","Department of Informatics, King's College London, London, UK"],"raw_orcid":"https://orcid.org/0000-0002-1498-1490","affiliations":[{"raw_affiliation_string":"Department of Informatics, King\u2019s College London, London, UK","institution_ids":["https://openalex.org/I183935753"]},{"raw_affiliation_string":"Department of Informatics, King's College London, London, UK","institution_ids":["https://openalex.org/I183935753"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5045418483","display_name":"Constandina Koki","orcid":"https://orcid.org/0000-0002-3236-8876"},"institutions":[{"id":"https://openalex.org/I39555362","display_name":"University of Warwick","ror":"https://ror.org/01a77tt86","country_code":"GB","type":"education","lineage":["https://openalex.org/I39555362"]}],"countries":["GB"],"is_corresponding":true,"raw_author_name":"Constandina Koki","raw_affiliation_strings":["Mathematics Institute, University of Warwick, Coventry, UK"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Mathematics Institute, University of Warwick, Coventry, UK","institution_ids":["https://openalex.org/I39555362"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5030319932","display_name":"Costis Melolidakis","orcid":"https://orcid.org/0000-0002-2528-5781"},"institutions":[{"id":"https://openalex.org/I200777214","display_name":"National and Kapodistrian University of Athens","ror":"https://ror.org/04gnjpq42","country_code":"GR","type":"education","lineage":["https://openalex.org/I200777214"]}],"countries":["GR"],"is_corresponding":true,"raw_author_name":"Costis Melolidakis","raw_affiliation_strings":["Department of Mathematics, National and Kapodistrian University of Athens, Zografou, Greece"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics, National and Kapodistrian University of Athens, Zografou, Greece","institution_ids":["https://openalex.org/I200777214"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5030319932","https://openalex.org/A5045418483","https://openalex.org/A5048295129"],"corresponding_institution_ids":["https://openalex.org/I183935753","https://openalex.org/I200777214","https://openalex.org/I39555362"],"apc_list":{"value":2990,"currency":"USD","value_usd":2990},"apc_paid":{"value":2990,"currency":"USD","value_usd":2990},"fwci":0.2536,"has_fulltext":true,"cited_by_count":1,"citation_normalized_percentile":{"value":0.57511052,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":91,"max":95},"biblio":{"volume":"336","issue":"3","first_page":"1661","last_page":"1679"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10328","display_name":"Supply Chain and Inventory Management","score":0.9995999932289124,"subfield":{"id":"https://openalex.org/subfields/1404","display_name":"Management Information Systems"},"field":{"id":"https://openalex.org/fields/14","display_name":"Business, Management and Accounting"},"domain":{"id":"https://openalex.org/domains/2","display_name":"Social Sciences"}},"topics":[{"id":"https://openalex.org/T10328","display_name":"Supply Chain and Inventory Management","score":0.9995999932289124,"subfield":{"id":"https://openalex.org/subfields/1404","display_name":"Management Information Systems"},"field":{"id":"https://openalex.org/fields/14","display_name":"Business, Management and Accounting"},"domain":{"id":"https://openalex.org/domains/2","display_name":"Social Sciences"}},{"id":"https://openalex.org/T11161","display_name":"Consumer Market Behavior and Pricing","score":0.986299991607666,"subfield":{"id":"https://openalex.org/subfields/1406","display_name":"Marketing"},"field":{"id":"https://openalex.org/fields/14","display_name":"Business, Management and Accounting"},"domain":{"id":"https://openalex.org/domains/2","display_name":"Social Sciences"}},{"id":"https://openalex.org/T10539","display_name":"Sustainable Supply Chain Management","score":0.9805999994277954,"subfield":{"id":"https://openalex.org/subfields/1408","display_name":"Strategy and Management"},"field":{"id":"https://openalex.org/fields/14","display_name":"Business, Management and Accounting"},"domain":{"id":"https://openalex.org/domains/2","display_name":"Social Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/unimodality","display_name":"Unimodality","score":0.7099691033363342},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.5791366100311279},{"id":"https://openalex.org/keywords/cournot-competition","display_name":"Cournot competition","score":0.5505648851394653},{"id":"https://openalex.org/keywords/price-elasticity-of-demand","display_name":"Price elasticity of demand","score":0.5453275442123413},{"id":"https://openalex.org/keywords/mathematical-economics","display_name":"Mathematical economics","score":0.5351942777633667},{"id":"https://openalex.org/keywords/economics","display_name":"Economics","score":0.48673275113105774},{"id":"https://openalex.org/keywords/elasticity","display_name":"Elasticity (physics)","score":0.4298507273197174},{"id":"https://openalex.org/keywords/inverse-demand-function","display_name":"Inverse demand function","score":0.4188956320285797},{"id":"https://openalex.org/keywords/demand-curve","display_name":"Demand curve","score":0.34780144691467285},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.3335025906562805},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.1415596604347229},{"id":"https://openalex.org/keywords/microeconomics","display_name":"Microeconomics","score":0.13944855332374573}],"concepts":[{"id":"https://openalex.org/C21596040","wikidata":"https://www.wikidata.org/wiki/Q2896771","display_name":"Unimodality","level":2,"score":0.7099691033363342},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5791366100311279},{"id":"https://openalex.org/C16520705","wikidata":"https://www.wikidata.org/wiki/Q601799","display_name":"Cournot competition","level":2,"score":0.5505648851394653},{"id":"https://openalex.org/C51355593","wikidata":"https://www.wikidata.org/wiki/Q3194154","display_name":"Price elasticity of demand","level":2,"score":0.5453275442123413},{"id":"https://openalex.org/C144237770","wikidata":"https://www.wikidata.org/wiki/Q747534","display_name":"Mathematical economics","level":1,"score":0.5351942777633667},{"id":"https://openalex.org/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","level":0,"score":0.48673275113105774},{"id":"https://openalex.org/C121854251","wikidata":"https://www.wikidata.org/wiki/Q62932","display_name":"Elasticity (physics)","level":2,"score":0.4298507273197174},{"id":"https://openalex.org/C143685982","wikidata":"https://www.wikidata.org/wiki/Q1376545","display_name":"Inverse demand function","level":3,"score":0.4188956320285797},{"id":"https://openalex.org/C176398731","wikidata":"https://www.wikidata.org/wiki/Q8981416","display_name":"Demand curve","level":2,"score":0.34780144691467285},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.3335025906562805},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.1415596604347229},{"id":"https://openalex.org/C175444787","wikidata":"https://www.wikidata.org/wiki/Q39072","display_name":"Microeconomics","level":1,"score":0.13944855332374573},{"id":"https://openalex.org/C159985019","wikidata":"https://www.wikidata.org/wiki/Q181790","display_name":"Composite material","level":1,"score":0.0},{"id":"https://openalex.org/C192562407","wikidata":"https://www.wikidata.org/wiki/Q228736","display_name":"Materials science","level":0,"score":0.0}],"mesh":[],"locations_count":6,"locations":[{"id":"doi:10.1007/s10479-023-05425-z","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s10479-023-05425-z","pdf_url":"https://link.springer.com/content/pdf/10.1007/s10479-023-05425-z.pdf","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":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Annals of Operations Research","raw_type":"journal-article"},{"id":"pmh:oai:kclpure.kcl.ac.uk:openaire/7da134e6-b58b-4996-8ad2-cd10fe7a1650","is_oa":true,"landing_page_url":"https://kclpure.kcl.ac.uk/portal/en/publications/7da134e6-b58b-4996-8ad2-cd10fe7a1650","pdf_url":"https://kclpure.kcl.ac.uk/ws/files/216273501/ANOR_distributions_final.pdf","source":{"id":"https://openalex.org/S4306400216","display_name":"Research Portal (King's College London)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I183935753","host_organization_name":"King's College London","host_organization_lineage":["https://openalex.org/I183935753"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Leonardos, S, Koki, C & Melolidakis, C 2023, 'A Generalization of the Increasing Generalized Failure Rate Unimodality Condition', Annals of Operations Research. https://doi.org/10.1007/s10479-023-05425-z","raw_type":"info:eu-repo/semantics/publishedVersion"},{"id":"pmh:oai:kclpure.kcl.ac.uk:publications/7da134e6-b58b-4996-8ad2-cd10fe7a1650","is_oa":true,"landing_page_url":"http://www.scopus.com/inward/record.url?scp=85161344840&partnerID=8YFLogxK","pdf_url":"https://kclpure.kcl.ac.uk/ws/files/220914553/s10479_023_05425_z.pdf","source":{"id":"https://openalex.org/S4306400216","display_name":"Research Portal (King's College London)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I183935753","host_organization_name":"King's College London","host_organization_lineage":["https://openalex.org/I183935753"],"host_organization_lineage_names":[],"type":"repository"},"license":"other-oa","license_id":"https://openalex.org/licenses/other-oa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Leonardos , S , Koki , C &amp; Melolidakis , C 2023 , ' A Generalization of the Increasing Generalized Failure Rate Unimodality Condition ' , Annals of Operations Research . https://doi.org/10.1007/s10479-023-05425-z","raw_type":"article"},{"id":"pmh:oai:kclpure.kcl.ac.uk:publications/7da134e6-b58b-4996-8ad2-cd10fe7a1650","is_oa":true,"landing_page_url":"https://kclpure.kcl.ac.uk/portal/files/216273501/ANOR_distributions_final.pdf","pdf_url":"https://kclpure.kcl.ac.uk/ws/files/216273501/ANOR_distributions_final.pdf","source":{"id":"https://openalex.org/S4306400216","display_name":"Research Portal (King's College London)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I183935753","host_organization_name":"King's College London","host_organization_lineage":["https://openalex.org/I183935753"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Leonardos, S, Koki, C & Melolidakis, C 2023, 'A Generalization of the Increasing Generalized Failure Rate Unimodality Condition', Annals of Operations Research. https://doi.org/10.1007/s10479-023-05425-z","raw_type":"info:eu-repo/semantics/publishedVersion"},{"id":"pmh:oai:wrap.warwick.ac.uk:177817","is_oa":true,"landing_page_url":"https://wrap.warwick.ac.uk/177817/1/s10479-023-05425-z.pdf","pdf_url":"https://wrap.warwick.ac.uk/177817/1/s10479-023-05425-z.pdf","source":{"id":"https://openalex.org/S4306400665","display_name":"Warwick Research Archive Portal (University of Warwick)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I39555362","host_organization_name":"University of Warwick","host_organization_lineage":["https://openalex.org/I39555362"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"Journal Article"},{"id":"pmh:oai:RePEc:spr:annopr:v:336:y:2024:i:3:d:10.1007_s10479-023-05425-z","is_oa":false,"landing_page_url":"http://link.springer.com/10.1007/s10479-023-05425-z","pdf_url":null,"source":{"id":"https://openalex.org/S4306401271","display_name":"RePEc: Research Papers in Economics","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I77793887","host_organization_name":"Federal Reserve Bank of St. Louis","host_organization_lineage":["https://openalex.org/I77793887"],"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":"article"}],"best_oa_location":{"id":"doi:10.1007/s10479-023-05425-z","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s10479-023-05425-z","pdf_url":"https://link.springer.com/content/pdf/10.1007/s10479-023-05425-z.pdf","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":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Annals of Operations Research","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[],"funders":[{"id":"https://openalex.org/F4320323220","display_name":"Alexander S. Onassis Public Benefit Foundation","ror":"https://ror.org/017nq0d63"}],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W4379644805.pdf","grobid_xml":"https://content.openalex.org/works/W4379644805.grobid-xml"},"referenced_works_count":61,"referenced_works":["https://openalex.org/W1599465408","https://openalex.org/W1756643235","https://openalex.org/W1965069249","https://openalex.org/W1968204503","https://openalex.org/W1968539380","https://openalex.org/W1970081679","https://openalex.org/W1991567646","https://openalex.org/W1996675930","https://openalex.org/W2001745000","https://openalex.org/W2005176259","https://openalex.org/W2008924865","https://openalex.org/W2009084832","https://openalex.org/W2009381794","https://openalex.org/W2023048877","https://openalex.org/W2038625227","https://openalex.org/W2084629560","https://openalex.org/W2092912220","https://openalex.org/W2106258759","https://openalex.org/W2106796631","https://openalex.org/W2127125266","https://openalex.org/W2127275253","https://openalex.org/W2131642659","https://openalex.org/W2134690646","https://openalex.org/W2143346627","https://openalex.org/W2146156512","https://openalex.org/W2149035559","https://openalex.org/W2157672420","https://openalex.org/W2160416232","https://openalex.org/W2163539713","https://openalex.org/W2168612340","https://openalex.org/W2324074576","https://openalex.org/W2492297833","https://openalex.org/W2493504759","https://openalex.org/W2517152090","https://openalex.org/W2518722952","https://openalex.org/W2587926013","https://openalex.org/W2620623683","https://openalex.org/W2787119534","https://openalex.org/W2788428977","https://openalex.org/W2793570447","https://openalex.org/W2887316738","https://openalex.org/W2887780636","https://openalex.org/W2890482463","https://openalex.org/W2896166264","https://openalex.org/W2912604055","https://openalex.org/W2948325399","https://openalex.org/W2994051799","https://openalex.org/W3005161457","https://openalex.org/W3042648110","https://openalex.org/W3121701465","https://openalex.org/W3124124207","https://openalex.org/W3125872315","https://openalex.org/W3157138105","https://openalex.org/W4230900674","https://openalex.org/W4245777296","https://openalex.org/W4292070112","https://openalex.org/W4297974475","https://openalex.org/W4299432846","https://openalex.org/W4302114916","https://openalex.org/W4376999555","https://openalex.org/W6632414946"],"related_works":["https://openalex.org/W1578423955","https://openalex.org/W1993446692","https://openalex.org/W3122277563","https://openalex.org/W1975948686","https://openalex.org/W2621908726","https://openalex.org/W1509440366","https://openalex.org/W3124065407","https://openalex.org/W3143857428","https://openalex.org/W2035913161","https://openalex.org/W2110160345"],"abstract_inverted_index":{"Abstract":[0],"In":[1],"this":[2],"paper,":[3],"we":[4],"study":[5],"unimodality":[6,169],"conditions":[7,17,80],"for":[8],"distributions":[9,111,124,160],"that":[10,96,105,161,183],"describe":[11],"markets":[12,97],"with":[13,98,112],"stochastic":[14],"demand.":[15],"Such":[16],"naturally":[18],"emerge":[19],"in":[20,45,164,173,181],"the":[21,39,48,55,72,82,127,140,143,174,188,200],"analysis":[22,175],"of":[23,26,42,47,54,65,71,102,142,158,176,196],"game-theoretic":[24],"models":[25],"market":[27],"competition":[28],"(Cournot":[29],"games)":[30],"and":[31,58,91,119,152,155,202],"supply":[32],"chain":[33],"coordination":[34],"(Stackelberg":[35],"games).":[36],"We":[37,94,136],"express":[38],"price":[40,100],"elasticity":[41,101],"expected":[43,103],"demand":[44,56,83,104],"terms":[46],"mean":[49,115],"residual":[50,116],"life":[51,117],"(MRL)":[52],"function":[53],"distribution":[57,84],"characterize":[59],"optimal":[60,177],"prices":[61],"or":[62],"equivalently,":[63],"points":[64,70,89],"unitary":[66],"elasticity,":[67],"as":[68],"fixed":[69,88],"MRL":[73],"function.":[74],"This":[75],"leads":[76],"to":[77,110,199],"economic":[78,165],"interpretable":[79],"on":[81,139],"under":[85,179],"which":[86],"such":[87],"exist":[90],"are":[92,162,184],"unique.":[93],"find":[95],"increasing":[99,130],"eventually":[106],"become":[107],"elastic":[108],"correspond":[109],"decreasing":[113],"generalized":[114,131],"(DGMRL)":[118],"finite":[120],"second":[121],"moment.":[122],"DGMRL":[123,159,168],"strictly":[125],"generalize":[126],"widely":[128],"used":[129],"failure":[132],"rate":[133],"(IGFR)":[134],"distributions.":[135],"further":[137],"elaborate":[138],"relationship":[141],"two":[144],"classes,":[145],"link":[146],"their":[147],"limiting":[148],"behavior":[149],"at":[150],"infinity":[151],"examine":[153],"moment":[154],"closure":[156],"properties":[157],"important":[163],"applications.":[166],"The":[167],"condition":[170],"is":[171],"useful":[172],"decisions":[178],"uncertainty":[180],"settings":[182],"not":[185],"covered":[186],"by":[187],"widely-used":[189],"IGFR":[190],"condition;":[191],"thus,":[192],"it":[193],"can":[194],"be":[195],"broader":[197],"interest":[198],"game-theory":[201],"operations":[203],"research":[204],"literature.":[205]},"counts_by_year":[{"year":2025,"cited_by_count":1}],"updated_date":"2026-08-18T07:49:30.821534","created_date":"2025-10-10T00:00:00"}
