{"id":"https://openalex.org/W4200103884","doi":"https://doi.org/10.1051/ro/2021185","title":"A bilevel game model for ascertaining competitive target prices for a buyer in negotiation with multiple suppliers","display_name":"A bilevel game model for ascertaining competitive target prices for a buyer in negotiation with multiple suppliers","publication_year":2021,"publication_date":"2021-12-20","ids":{"openalex":"https://openalex.org/W4200103884","doi":"https://doi.org/10.1051/ro/2021185"},"language":"en","primary_location":{"id":"doi:10.1051/ro/2021185","is_oa":true,"landing_page_url":"https://doi.org/10.1051/ro/2021185","pdf_url":"https://www.rairo-ro.org/articles/ro/pdf/2022/01/ro210042.pdf","source":{"id":"https://openalex.org/S20631277","display_name":"RAIRO - Operations Research","issn_l":"0399-0559","issn":["0399-0559","1290-3868","2804-7303"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319748","host_organization_name":"EDP Sciences","host_organization_lineage":["https://openalex.org/P4310319748"],"host_organization_lineage_names":["EDP Sciences"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"RAIRO - Operations Research","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"hybrid","oa_url":"https://www.rairo-ro.org/articles/ro/pdf/2022/01/ro210042.pdf","any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5026684659","display_name":"Akhilesh Kumar","orcid":"https://orcid.org/0000-0001-8914-928X"},"institutions":[{"id":"https://openalex.org/I863896202","display_name":"Delhi Technological University","ror":"https://ror.org/01ztcvt22","country_code":"IN","type":"education","lineage":["https://openalex.org/I863896202"]}],"countries":["IN"],"is_corresponding":false,"raw_author_name":"Akhilesh Kumar","raw_affiliation_strings":["Department of Applied Mathematics, Delhi Technological University, Bawana Road, Rohini, Delhi 110042, India","Department of Mathematics, Arignar Anna Government Arts & Science College, Karaikal, Puducherry 609602, India"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Applied Mathematics, Delhi Technological University, Bawana Road, Rohini, Delhi 110042, India","institution_ids":["https://openalex.org/I863896202"]},{"raw_affiliation_string":"Department of Mathematics, Arignar Anna Government Arts & Science College, Karaikal, Puducherry 609602, India","institution_ids":[]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5067640234","display_name":"Anjana Gupta","orcid":"https://orcid.org/0000-0002-6514-0851"},"institutions":[{"id":"https://openalex.org/I863896202","display_name":"Delhi Technological University","ror":"https://ror.org/01ztcvt22","country_code":"IN","type":"education","lineage":["https://openalex.org/I863896202"]}],"countries":["IN"],"is_corresponding":false,"raw_author_name":"Anjana Gupta","raw_affiliation_strings":["Department of Applied Mathematics, Delhi Technological University, Bawana Road, Rohini, Delhi 110042, India"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Applied Mathematics, Delhi Technological University, Bawana Road, Rohini, Delhi 110042, India","institution_ids":["https://openalex.org/I863896202"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5108661639","display_name":"Aparna Mehra","orcid":null},"institutions":[{"id":"https://openalex.org/I68891433","display_name":"Indian Institute of Technology Delhi","ror":"https://ror.org/049tgcd06","country_code":"IN","type":"education","lineage":["https://openalex.org/I68891433"]}],"countries":["IN"],"is_corresponding":false,"raw_author_name":"Aparna Mehra","raw_affiliation_strings":["Department of Mathematics, Indian Institute of Technology Delhi, Hauz Khas, New Delhi 110016, India"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics, Indian Institute of Technology Delhi, Hauz Khas, New Delhi 110016, India","institution_ids":["https://openalex.org/I68891433"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":1.6929,"has_fulltext":true,"cited_by_count":10,"citation_normalized_percentile":{"value":0.86726205,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":97},"biblio":{"volume":"56","issue":"1","first_page":"293","last_page":"330"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10328","display_name":"Supply Chain and Inventory Management","score":0.9980999827384949,"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":0.9980999827384949,"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/T10545","display_name":"Optimization and Variational Analysis","score":0.9944000244140625,"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/T10539","display_name":"Sustainable Supply Chain Management","score":0.9911999702453613,"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/bilevel-optimization","display_name":"Bilevel optimization","score":0.6752216815948486},{"id":"https://openalex.org/keywords/procurement","display_name":"Procurement","score":0.6361867189407349},{"id":"https://openalex.org/keywords/negotiation","display_name":"Negotiation","score":0.6235673427581787},{"id":"https://openalex.org/keywords/profit","display_name":"Profit (economics)","score":0.6072977185249329},{"id":"https://openalex.org/keywords/stackelberg-competition","display_name":"Stackelberg competition","score":0.4940638840198517},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.48450514674186707},{"id":"https://openalex.org/keywords/microeconomics","display_name":"Microeconomics","score":0.4710792303085327},{"id":"https://openalex.org/keywords/game-theory","display_name":"Game theory","score":0.44878366589546204},{"id":"https://openalex.org/keywords/industrial-organization","display_name":"Industrial organization","score":0.41714510321617126},{"id":"https://openalex.org/keywords/operations-research","display_name":"Operations research","score":0.4078054428100586},{"id":"https://openalex.org/keywords/business","display_name":"Business","score":0.37418729066848755},{"id":"https://openalex.org/keywords/economics","display_name":"Economics","score":0.34555870294570923},{"id":"https://openalex.org/keywords/optimization-problem","display_name":"Optimization problem","score":0.2550027370452881},{"id":"https://openalex.org/keywords/marketing","display_name":"Marketing","score":0.17237338423728943}],"concepts":[{"id":"https://openalex.org/C3309286","wikidata":"https://www.wikidata.org/wiki/Q4907693","display_name":"Bilevel optimization","level":3,"score":0.6752216815948486},{"id":"https://openalex.org/C201650216","wikidata":"https://www.wikidata.org/wiki/Q829492","display_name":"Procurement","level":2,"score":0.6361867189407349},{"id":"https://openalex.org/C199776023","wikidata":"https://www.wikidata.org/wiki/Q202875","display_name":"Negotiation","level":2,"score":0.6235673427581787},{"id":"https://openalex.org/C181622380","wikidata":"https://www.wikidata.org/wiki/Q26911","display_name":"Profit (economics)","level":2,"score":0.6072977185249329},{"id":"https://openalex.org/C199510392","wikidata":"https://www.wikidata.org/wiki/Q1184602","display_name":"Stackelberg competition","level":2,"score":0.4940638840198517},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.48450514674186707},{"id":"https://openalex.org/C175444787","wikidata":"https://www.wikidata.org/wiki/Q39072","display_name":"Microeconomics","level":1,"score":0.4710792303085327},{"id":"https://openalex.org/C177142836","wikidata":"https://www.wikidata.org/wiki/Q44455","display_name":"Game theory","level":2,"score":0.44878366589546204},{"id":"https://openalex.org/C40700","wikidata":"https://www.wikidata.org/wiki/Q1411783","display_name":"Industrial organization","level":1,"score":0.41714510321617126},{"id":"https://openalex.org/C42475967","wikidata":"https://www.wikidata.org/wiki/Q194292","display_name":"Operations research","level":1,"score":0.4078054428100586},{"id":"https://openalex.org/C144133560","wikidata":"https://www.wikidata.org/wiki/Q4830453","display_name":"Business","level":0,"score":0.37418729066848755},{"id":"https://openalex.org/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","level":0,"score":0.34555870294570923},{"id":"https://openalex.org/C137836250","wikidata":"https://www.wikidata.org/wiki/Q984063","display_name":"Optimization problem","level":2,"score":0.2550027370452881},{"id":"https://openalex.org/C162853370","wikidata":"https://www.wikidata.org/wiki/Q39809","display_name":"Marketing","level":1,"score":0.17237338423728943},{"id":"https://openalex.org/C199539241","wikidata":"https://www.wikidata.org/wiki/Q7748","display_name":"Law","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/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.0},{"id":"https://openalex.org/C17744445","wikidata":"https://www.wikidata.org/wiki/Q36442","display_name":"Political science","level":0,"score":0.0}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.1051/ro/2021185","is_oa":true,"landing_page_url":"https://doi.org/10.1051/ro/2021185","pdf_url":"https://www.rairo-ro.org/articles/ro/pdf/2022/01/ro210042.pdf","source":{"id":"https://openalex.org/S20631277","display_name":"RAIRO - Operations Research","issn_l":"0399-0559","issn":["0399-0559","1290-3868","2804-7303"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319748","host_organization_name":"EDP Sciences","host_organization_lineage":["https://openalex.org/P4310319748"],"host_organization_lineage_names":["EDP Sciences"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"RAIRO - Operations Research","raw_type":"journal-article"},{"id":"pmh:oai:edpsciences.org:dkey/10.1051/ro/2021185","is_oa":false,"landing_page_url":"https://www.rairo-ro.org/10.1051/ro/2021185/pdf","pdf_url":null,"source":{"id":"https://openalex.org/S4306400744","display_name":"Springer Link (Chiba Institute of Technology)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I8488066","host_organization_name":"Chiba Institute of Technology","host_organization_lineage":["https://openalex.org/I8488066"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"https://doi.org/10.1051/ro/2021185","raw_type":"Text"},{"id":"pmh:oai:numdam.org:RO_2022__56_1_293_0","is_oa":false,"landing_page_url":"https://www.numdam.org/articles/10.1051/ro/2021185/","pdf_url":null,"source":{"id":"https://openalex.org/S4306402264","display_name":"French digital mathematics library (Numdam)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I70900168","host_organization_name":"Universit\u00e9 Savoie Mont Blanc","host_organization_lineage":["https://openalex.org/I70900168"],"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":{"id":"doi:10.1051/ro/2021185","is_oa":true,"landing_page_url":"https://doi.org/10.1051/ro/2021185","pdf_url":"https://www.rairo-ro.org/articles/ro/pdf/2022/01/ro210042.pdf","source":{"id":"https://openalex.org/S20631277","display_name":"RAIRO - Operations Research","issn_l":"0399-0559","issn":["0399-0559","1290-3868","2804-7303"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319748","host_organization_name":"EDP Sciences","host_organization_lineage":["https://openalex.org/P4310319748"],"host_organization_lineage_names":["EDP Sciences"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"RAIRO - Operations Research","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[],"funders":[{"id":"https://openalex.org/F4320306111","display_name":"U.S. Department of Commerce","ror":"https://ror.org/04chq2495"}],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W4200103884.pdf","grobid_xml":"https://content.openalex.org/works/W4200103884.grobid-xml"},"referenced_works_count":86,"referenced_works":["https://openalex.org/W106943091","https://openalex.org/W181661487","https://openalex.org/W1491972678","https://openalex.org/W1511493290","https://openalex.org/W1515389728","https://openalex.org/W1520396195","https://openalex.org/W1963929545","https://openalex.org/W1964332562","https://openalex.org/W1964374481","https://openalex.org/W1967348600","https://openalex.org/W1967880331","https://openalex.org/W1971489618","https://openalex.org/W1972843349","https://openalex.org/W1974403532","https://openalex.org/W1982199694","https://openalex.org/W1992590811","https://openalex.org/W1992983421","https://openalex.org/W1993267546","https://openalex.org/W1995944656","https://openalex.org/W2000152357","https://openalex.org/W2003846176","https://openalex.org/W2007103412","https://openalex.org/W2012076552","https://openalex.org/W2016491906","https://openalex.org/W2017845106","https://openalex.org/W2022514154","https://openalex.org/W2023776874","https://openalex.org/W2025842679","https://openalex.org/W2027945080","https://openalex.org/W2028961802","https://openalex.org/W2030722820","https://openalex.org/W2032195237","https://openalex.org/W2033910905","https://openalex.org/W2034700435","https://openalex.org/W2035893651","https://openalex.org/W2041724917","https://openalex.org/W2046204418","https://openalex.org/W2047675070","https://openalex.org/W2049562131","https://openalex.org/W2049949638","https://openalex.org/W2051848379","https://openalex.org/W2055388930","https://openalex.org/W2062626207","https://openalex.org/W2065976012","https://openalex.org/W2066807662","https://openalex.org/W2071082401","https://openalex.org/W2073536208","https://openalex.org/W2075799239","https://openalex.org/W2075846432","https://openalex.org/W2081489435","https://openalex.org/W2084575232","https://openalex.org/W2085896490","https://openalex.org/W2089509243","https://openalex.org/W2091157695","https://openalex.org/W2091785779","https://openalex.org/W2092928556","https://openalex.org/W2097156392","https://openalex.org/W2101285332","https://openalex.org/W2105308124","https://openalex.org/W2107108437","https://openalex.org/W2111240209","https://openalex.org/W2116348957","https://openalex.org/W2124374377","https://openalex.org/W2124659975","https://openalex.org/W2131683518","https://openalex.org/W2139248159","https://openalex.org/W2161768084","https://openalex.org/W2163194391","https://openalex.org/W2168004073","https://openalex.org/W2259507927","https://openalex.org/W2481910659","https://openalex.org/W2501549495","https://openalex.org/W2586617429","https://openalex.org/W2608451515","https://openalex.org/W2614367549","https://openalex.org/W2617497116","https://openalex.org/W2794754233","https://openalex.org/W2892754290","https://openalex.org/W2896107780","https://openalex.org/W2898562400","https://openalex.org/W2938372244","https://openalex.org/W2986487249","https://openalex.org/W2990826067","https://openalex.org/W2996704268","https://openalex.org/W3004812768","https://openalex.org/W4237365337"],"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":{"In":[0],"this":[1,34],"paper,":[2],"a":[3,8,58,79,90,167],"decision-support":[4],"is":[5,55,89,105,125,149,160],"developed":[6,157],"for":[7,15,129],"strategic":[9],"problem":[10,50,62],"of":[11,28,39,51,102,133,136,166],"identifying":[12,52],"target":[13,47],"prices":[14,38,54],"the":[16,71,87,98,120,134,147,153,164],"single":[17,144],"buyer":[18,88],"to":[19,24,43,82,96,112,151],"negotiate":[20],"with":[21,93,140],"multiple":[22,72,141,176],"suppliers":[23,40,73],"achieve":[25],"common":[26],"goal":[27],"maintaining":[29],"sustained":[30],"business":[31],"environment.":[32],"For":[33],"purpose,":[35],"oligopolistic-competitive":[36],"equilibrium":[37],"are":[41,74],"suggested":[42],"be":[44],"considered":[45,75],"as":[46,57],"prices.":[48],"The":[49,156],"these":[53],"modeled":[56,154],"multi-leader-single-follower":[59],"bilevel":[60,137],"programming":[61,138],"involving":[63],"linear":[64],"constraints":[65],"and":[66,86,143,146],"bilinear":[67],"objective":[68],"functions.":[69],"Herein,":[70],"leaders":[76,142],"competing":[77],"in":[78,127],"Nash":[80],"game":[81],"maximize":[83],"individual":[84],"profits,":[85],"follower":[91],"responding":[92],"demand-order":[94],"allocations":[95],"minimize":[97],"total":[99],"procurement-cost.":[100],"Profit":[101],"each":[103],"supplier":[104],"formulated":[106],"on":[107,163],"assessing":[108],"respective":[109],"operational":[110],"cost":[111],"fulfill":[113],"demand-orders":[114],"by":[115],"integrating":[116],"aggregate-production-distribution-planning":[117],"mechanism":[118],"into":[119],"problem.":[121,155],"A":[122],"genetic-algorithm-based":[123],"technique":[124],"designed":[126],"general":[128],"solving":[130],"large-scale":[131],"instances":[132],"variant":[135],"problems":[139],"follower,":[145],"same":[148],"applied":[150],"solve":[152],"decision":[158],"support":[159],"appropriately":[161],"demonstrated":[162],"data":[165],"leading":[168],"FMCG":[169],"manufacturing":[170],"firm,":[171],"which":[172],"manufactures":[173],"goods":[174],"through":[175],"sourcing.":[177]},"counts_by_year":[{"year":2025,"cited_by_count":2},{"year":2024,"cited_by_count":3},{"year":2023,"cited_by_count":4},{"year":2022,"cited_by_count":1}],"updated_date":"2026-07-07T06:14:10.401900","created_date":"2025-10-10T00:00:00"}