{"id":"https://openalex.org/W2626868260","doi":"https://doi.org/10.1007/s11590-017-1159-0","title":"Location, pricing and the problem of Apollonius","display_name":"Location, pricing and the problem of Apollonius","publication_year":2017,"publication_date":"2017-06-13","ids":{"openalex":"https://openalex.org/W2626868260","doi":"https://doi.org/10.1007/s11590-017-1159-0","mag":"2626868260"},"language":"en","primary_location":{"id":"doi:10.1007/s11590-017-1159-0","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s11590-017-1159-0","pdf_url":null,"source":{"id":"https://openalex.org/S12647387","display_name":"Optimization Letters","issn_l":"1862-4472","issn":["1862-4472","1862-4480"],"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":"Optimization Letters","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"hybrid","oa_url":"https://doi.org/10.1007/s11590-017-1159-0","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5075001728","display_name":"Andr\u00e9 Berger","orcid":"https://orcid.org/0000-0002-6409-1963"},"institutions":[{"id":"https://openalex.org/I34352273","display_name":"Maastricht University","ror":"https://ror.org/02jz4aj89","country_code":"NL","type":"education","lineage":["https://openalex.org/I34352273"]}],"countries":["NL"],"is_corresponding":true,"raw_author_name":"Andr\u00e9 Berger","raw_affiliation_strings":["Department of Quantitative Economics, Maastricht University School of Business and Economics, P.O. Box 616, 6200 MD, Maastricht, The Netherlands"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Quantitative Economics, Maastricht University School of Business and Economics, P.O. Box 616, 6200 MD, Maastricht, The Netherlands","institution_ids":["https://openalex.org/I34352273"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5052039079","display_name":"Alexander Grigoriev","orcid":"https://orcid.org/0000-0002-8391-235X"},"institutions":[{"id":"https://openalex.org/I34352273","display_name":"Maastricht University","ror":"https://ror.org/02jz4aj89","country_code":"NL","type":"education","lineage":["https://openalex.org/I34352273"]}],"countries":["NL"],"is_corresponding":false,"raw_author_name":"Alexander Grigoriev","raw_affiliation_strings":["Department of Quantitative Economics, Maastricht University School of Business and Economics, P.O. Box 616, 6200 MD, Maastricht, The Netherlands"],"raw_orcid":"https://orcid.org/0000-0002-8391-235X","affiliations":[{"raw_affiliation_string":"Department of Quantitative Economics, Maastricht University School of Business and Economics, P.O. Box 616, 6200 MD, Maastricht, The Netherlands","institution_ids":["https://openalex.org/I34352273"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5004020635","display_name":"A. A. Panin","orcid":"https://orcid.org/0000-0002-1844-6276"},"institutions":[{"id":"https://openalex.org/I188973947","display_name":"Novosibirsk State University","ror":"https://ror.org/04t2ss102","country_code":"RU","type":"education","lineage":["https://openalex.org/I188973947"]},{"id":"https://openalex.org/I4210096862","display_name":"Sobolev Institute of Mathematics","ror":"https://ror.org/00shc0s02","country_code":"RU","type":"facility","lineage":["https://openalex.org/I1313323035","https://openalex.org/I1313323035","https://openalex.org/I4210096862","https://openalex.org/I4210124601","https://openalex.org/I4210127387"]}],"countries":["RU"],"is_corresponding":false,"raw_author_name":"Artem Panin","raw_affiliation_strings":["Novosibirsk State University, 2 Pirogov Str., Novosibirsk, Russia, 630090","Sobolev Institute of Mathematics, Acad. Koptyug Ave. 4, Novosibirsk, Russia, 630090"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Novosibirsk State University, 2 Pirogov Str., Novosibirsk, Russia, 630090","institution_ids":["https://openalex.org/I188973947"]},{"raw_affiliation_string":"Sobolev Institute of Mathematics, Acad. Koptyug Ave. 4, Novosibirsk, Russia, 630090","institution_ids":["https://openalex.org/I4210096862"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5044326637","display_name":"Andrej Winokurow","orcid":null},"institutions":[{"id":"https://openalex.org/I34352273","display_name":"Maastricht University","ror":"https://ror.org/02jz4aj89","country_code":"NL","type":"education","lineage":["https://openalex.org/I34352273"]}],"countries":["NL"],"is_corresponding":false,"raw_author_name":"Andrej Winokurow","raw_affiliation_strings":["Department of Quantitative Economics, Maastricht University School of Business and Economics, P.O. Box 616, 6200 MD, Maastricht, The Netherlands"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Quantitative Economics, Maastricht University School of Business and Economics, P.O. Box 616, 6200 MD, Maastricht, The Netherlands","institution_ids":["https://openalex.org/I34352273"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":4,"corresponding_author_ids":["https://openalex.org/A5075001728"],"corresponding_institution_ids":["https://openalex.org/I34352273"],"apc_list":{"value":2290,"currency":"EUR","value_usd":2890},"apc_paid":{"value":2290,"currency":"EUR","value_usd":2890},"fwci":2.6458,"has_fulltext":false,"cited_by_count":8,"citation_normalized_percentile":{"value":0.93657461,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":90,"max":97},"biblio":{"volume":"11","issue":"8","first_page":"1797","last_page":"1805"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10991","display_name":"Game Theory and Voting Systems","score":0.9571999907493591,"subfield":{"id":"https://openalex.org/subfields/2002","display_name":"Economics and Econometrics"},"field":{"id":"https://openalex.org/fields/20","display_name":"Economics, Econometrics and Finance"},"domain":{"id":"https://openalex.org/domains/2","display_name":"Social Sciences"}},"topics":[{"id":"https://openalex.org/T10991","display_name":"Game Theory and Voting Systems","score":0.9571999907493591,"subfield":{"id":"https://openalex.org/subfields/2002","display_name":"Economics and Econometrics"},"field":{"id":"https://openalex.org/fields/20","display_name":"Economics, Econometrics and Finance"},"domain":{"id":"https://openalex.org/domains/2","display_name":"Social Sciences"}},{"id":"https://openalex.org/T11161","display_name":"Consumer Market Behavior and Pricing","score":0.9291999936103821,"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/T11182","display_name":"Auction Theory and Applications","score":0.9157999753952026,"subfield":{"id":"https://openalex.org/subfields/1803","display_name":"Management Science and Operations Research"},"field":{"id":"https://openalex.org/fields/18","display_name":"Decision Sciences"},"domain":{"id":"https://openalex.org/domains/2","display_name":"Social Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/computational-intelligence","display_name":"Computational intelligence","score":0.6691976189613342},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.3829647898674011},{"id":"https://openalex.org/keywords/mathematical-economics","display_name":"Mathematical economics","score":0.34870797395706177},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.30831778049468994},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.19644653797149658}],"concepts":[{"id":"https://openalex.org/C139502532","wikidata":"https://www.wikidata.org/wiki/Q1122090","display_name":"Computational intelligence","level":2,"score":0.6691976189613342},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.3829647898674011},{"id":"https://openalex.org/C144237770","wikidata":"https://www.wikidata.org/wiki/Q747534","display_name":"Mathematical economics","level":1,"score":0.34870797395706177},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.30831778049468994},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.19644653797149658}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1007/s11590-017-1159-0","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s11590-017-1159-0","pdf_url":null,"source":{"id":"https://openalex.org/S12647387","display_name":"Optimization Letters","issn_l":"1862-4472","issn":["1862-4472","1862-4480"],"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":"Optimization Letters","raw_type":"journal-article"},{"id":"pmh:oai:cris.maastrichtuniversity.nl:openaire/71a7f915-4dfa-43b1-bd8d-6c51d43133f0","is_oa":true,"landing_page_url":"https://cris.maastrichtuniversity.nl/en/publications/71a7f915-4dfa-43b1-bd8d-6c51d43133f0","pdf_url":null,"source":{"id":"https://openalex.org/S4306402616","display_name":"Research Publications (Maastricht University)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I34352273","host_organization_name":"Maastricht University","host_organization_lineage":["https://openalex.org/I34352273"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Berger, A, Grigoriev, A, Panin, A & Winokurow, A 2017, 'Location, pricing and the problem of Apollonius', Optimization Letters, vol. 11, no. 8, pp. 1797\u20131805. https://doi.org/10.1007/s11590-017-1159-0","raw_type":"info:eu-repo/semantics/publishedVersion"}],"best_oa_location":{"id":"doi:10.1007/s11590-017-1159-0","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s11590-017-1159-0","pdf_url":null,"source":{"id":"https://openalex.org/S12647387","display_name":"Optimization Letters","issn_l":"1862-4472","issn":["1862-4472","1862-4480"],"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":"Optimization Letters","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[],"funders":[{"id":"https://openalex.org/F4320321016","display_name":"Universiteit Maastricht","ror":"https://ror.org/02jz4aj89"}],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":14,"referenced_works":["https://openalex.org/W1482186473","https://openalex.org/W1520010392","https://openalex.org/W1520111182","https://openalex.org/W1977541023","https://openalex.org/W2018541722","https://openalex.org/W2028742519","https://openalex.org/W2031502124","https://openalex.org/W2046559210","https://openalex.org/W2069134712","https://openalex.org/W2132970009","https://openalex.org/W2597141206","https://openalex.org/W4230138514","https://openalex.org/W6628849155","https://openalex.org/W6712832319"],"related_works":["https://openalex.org/W2748952813","https://openalex.org/W1979597421","https://openalex.org/W2007980826","https://openalex.org/W4245490552","https://openalex.org/W2061531152","https://openalex.org/W3002753104","https://openalex.org/W2077600819","https://openalex.org/W2042127053","https://openalex.org/W2142036596","https://openalex.org/W2072657027"],"abstract_inverted_index":{"In":[0],"Euclidean":[1],"plane":[2,13,87],"geometry,":[3],"Apollonius\u2019":[4],"problem":[5,29],"is":[6,15,41,62,78,103],"to":[7,17,26,30,79],"construct":[8],"a":[9,12,24,42,52,55,58],"circle":[10],"in":[11,47,85],"that":[14,95],"tangent":[16],"three":[18],"given":[19],"circles.":[20],"We":[21],"will":[22],"use":[23],"solution":[25],"this":[27],"ancient":[28],"solve":[31],"several":[32],"versions":[33],"of":[34,44,82],"the":[35,48,74,86,92,96,100],"following":[36],"geometric":[37],"optimization":[38],"problem.":[39],"Given":[40],"set":[43],"customers":[45,102],"located":[46],"plane,":[49],"each":[50],"having":[51],"demand":[53],"for":[54,91],"product":[56,93],"and":[57,68,88],"budget.":[59,75],"A":[60],"customer":[61],"satisfied":[63,101],"if":[64],"her":[65],"total,":[66],"travel":[67],"purchase,":[69],"costs":[70],"do":[71],"not":[72],"exceed":[73],"The":[76],"task":[77],"determine":[80],"location":[81],"production":[83],"facilities":[84],"one":[89],"price":[90],"such":[94],"revenue":[97],"generated":[98],"from":[99],"maximized.":[104]},"counts_by_year":[{"year":2024,"cited_by_count":3},{"year":2022,"cited_by_count":3},{"year":2019,"cited_by_count":1},{"year":2018,"cited_by_count":1}],"updated_date":"2026-03-27T05:58:40.876381","created_date":"2025-10-10T00:00:00"}