{"id":"https://openalex.org/W1986056047","doi":"https://doi.org/10.1002/net.3230190602","title":"The prize collecting traveling salesman problem","display_name":"The prize collecting traveling salesman problem","publication_year":1989,"publication_date":"1989-10-01","ids":{"openalex":"https://openalex.org/W1986056047","doi":"https://doi.org/10.1002/net.3230190602","mag":"1986056047"},"language":"en","primary_location":{"id":"doi:10.1002/net.3230190602","is_oa":false,"landing_page_url":"https://doi.org/10.1002/net.3230190602","pdf_url":null,"source":{"id":"https://openalex.org/S191798613","display_name":"Networks","issn_l":"0028-3045","issn":["0028-3045","1097-0037"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320595","host_organization_name":"Wiley","host_organization_lineage":["https://openalex.org/P4310320595"],"host_organization_lineage_names":["Wiley"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Networks","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/A5072070820","display_name":"Egon Balas","orcid":null},"institutions":[{"id":"https://openalex.org/I74973139","display_name":"Carnegie Mellon University","ror":"https://ror.org/05x2bcf33","country_code":"US","type":"education","lineage":["https://openalex.org/I74973139"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"Egon Balas","raw_affiliation_strings":["Carnegie Mellon University, Pittsburgh, Pennsylvania","Carnegie Mellon Univ, Pittsburgh, Pennsylvania#TAB#"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Carnegie Mellon University, Pittsburgh, Pennsylvania","institution_ids":["https://openalex.org/I74973139"]},{"raw_affiliation_string":"Carnegie Mellon Univ, Pittsburgh, Pennsylvania#TAB#","institution_ids":["https://openalex.org/I74973139"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5072070820"],"corresponding_institution_ids":["https://openalex.org/I74973139"],"apc_list":{"value":3400,"currency":"USD","value_usd":3400},"apc_paid":null,"fwci":8.8446,"has_fulltext":false,"cited_by_count":564,"citation_normalized_percentile":{"value":0.97141823,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":99,"max":100},"biblio":{"volume":"19","issue":"6","first_page":"621","last_page":"636"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10567","display_name":"Vehicle Routing Optimization Methods","score":0.9988999962806702,"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"}},"topics":[{"id":"https://openalex.org/T10567","display_name":"Vehicle Routing Optimization Methods","score":0.9988999962806702,"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/T12176","display_name":"Optimization and Packing Problems","score":0.9976999759674072,"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/T11814","display_name":"Advanced Manufacturing and Logistics Optimization","score":0.968999981880188,"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/travelling-salesman-problem","display_name":"Travelling salesman problem","score":0.9052537083625793},{"id":"https://openalex.org/keywords/convex-hull","display_name":"Convex hull","score":0.701801061630249},{"id":"https://openalex.org/keywords/polytope","display_name":"Polytope","score":0.6891454458236694},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.5159119367599487},{"id":"https://openalex.org/keywords/knapsack-problem","display_name":"Knapsack problem","score":0.5027878284454346},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.4839940071105957},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.46855005621910095},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.4677963852882385},{"id":"https://openalex.org/keywords/regular-polygon","display_name":"Regular polygon","score":0.4647217392921448},{"id":"https://openalex.org/keywords/scheduling","display_name":"Scheduling (production processes)","score":0.4474228024482727},{"id":"https://openalex.org/keywords/polyhedral-combinatorics","display_name":"Polyhedral combinatorics","score":0.4440811276435852},{"id":"https://openalex.org/keywords/convex-optimization","display_name":"Convex optimization","score":0.21436601877212524},{"id":"https://openalex.org/keywords/convex-set","display_name":"Convex set","score":0.06377077102661133}],"concepts":[{"id":"https://openalex.org/C175859090","wikidata":"https://www.wikidata.org/wiki/Q322212","display_name":"Travelling salesman problem","level":2,"score":0.9052537083625793},{"id":"https://openalex.org/C206194317","wikidata":"https://www.wikidata.org/wiki/Q1138624","display_name":"Convex hull","level":3,"score":0.701801061630249},{"id":"https://openalex.org/C145691206","wikidata":"https://www.wikidata.org/wiki/Q747980","display_name":"Polytope","level":2,"score":0.6891454458236694},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.5159119367599487},{"id":"https://openalex.org/C113138325","wikidata":"https://www.wikidata.org/wiki/Q864457","display_name":"Knapsack problem","level":2,"score":0.5027878284454346},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.4839940071105957},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.46855005621910095},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.4677963852882385},{"id":"https://openalex.org/C112680207","wikidata":"https://www.wikidata.org/wiki/Q714886","display_name":"Regular polygon","level":2,"score":0.4647217392921448},{"id":"https://openalex.org/C206729178","wikidata":"https://www.wikidata.org/wiki/Q2271896","display_name":"Scheduling (production processes)","level":2,"score":0.4474228024482727},{"id":"https://openalex.org/C174248988","wikidata":"https://www.wikidata.org/wiki/Q8348314","display_name":"Polyhedral combinatorics","level":5,"score":0.4440811276435852},{"id":"https://openalex.org/C157972887","wikidata":"https://www.wikidata.org/wiki/Q463359","display_name":"Convex optimization","level":3,"score":0.21436601877212524},{"id":"https://openalex.org/C49870271","wikidata":"https://www.wikidata.org/wiki/Q193657","display_name":"Convex set","level":4,"score":0.06377077102661133},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1002/net.3230190602","is_oa":false,"landing_page_url":"https://doi.org/10.1002/net.3230190602","pdf_url":null,"source":{"id":"https://openalex.org/S191798613","display_name":"Networks","issn_l":"0028-3045","issn":["0028-3045","1097-0037"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320595","host_organization_name":"Wiley","host_organization_lineage":["https://openalex.org/P4310320595"],"host_organization_lineage_names":["Wiley"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Networks","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":10,"referenced_works":["https://openalex.org/W5720473","https://openalex.org/W307896644","https://openalex.org/W1967535666","https://openalex.org/W2006934540","https://openalex.org/W2008200956","https://openalex.org/W2041989601","https://openalex.org/W2064366623","https://openalex.org/W2075339720","https://openalex.org/W2124452917","https://openalex.org/W2324108981"],"related_works":["https://openalex.org/W1967232806","https://openalex.org/W2164572645","https://openalex.org/W2064263748","https://openalex.org/W2016944804","https://openalex.org/W2557288725","https://openalex.org/W2768257653","https://openalex.org/W2950719732","https://openalex.org/W1989517190","https://openalex.org/W2949890362","https://openalex.org/W2922236301"],"abstract_inverted_index":{"Abstract":[0],"The":[1],"following":[2],"is":[3],"a":[4,25,33,43,68,152],"valid":[5],"model":[6],"for":[7,112,141],"an":[8],"important":[9],"class":[10],"of":[11,22,71,90,97,108,116,123,131,151],"scheduling":[12],"and":[13,41,59],"routing":[14],"problems.":[15],"A":[16],"salesman":[17],"who":[18],"travels":[19],"between":[20],"pairs":[21],"cities":[23,65],"at":[24],"cost":[26],"depending":[27],"only":[28],"on":[29],"the":[30,78,91,94,100,124,132,142],"pair,":[31],"gets":[32],"prize":[34,72],"in":[35,139],"every":[36,46],"city":[37,47],"that":[38,48],"he":[39,49],"vitis":[40],"pays":[42],"penalty":[44],"to":[45,51,54,66,99,121,129],"fails":[50],"visit,":[52],"wishes":[53],"minimize":[55],"his":[56],"travel":[57],"costs":[58],"net":[60],"penalties,":[61],"while":[62],"visiting":[63],"enough":[64],"collect":[67],"prescribed":[69],"amount":[70],"money.":[73],"We":[74],"call":[75],"this":[76,113],"problem":[77],"Prize":[79],"Collecting":[80],"Traveling":[81],"Salesman":[82],"Problem":[83],"(PCTSP).":[84],"This":[85],"paper":[86],"discusses":[87],"structural":[88],"properties":[89],"PCTS":[92],"polytope,":[93,127],"convex":[95],"hull":[96],"solutions":[98],"PCTSP.":[101],"In":[102],"particular,":[103],"it":[104],"identifies":[105],"several":[106],"families":[107],"facet":[109],"defining":[110],"inequalities":[111,118],"polytope.":[114,134],"Some":[115],"these":[117],"are":[119],"related":[120],"facets":[122,130],"ordinary":[125],"TS":[126],"others":[128],"knapsack":[133],"They":[135],"can":[136],"be":[137],"used":[138],"algorithms":[140],"PCTSP":[143],"either":[144],"as":[145,149],"cutting":[146],"planes":[147],"or":[148],"ingredients":[150],"Lagrangean":[153],"optimand.":[154]},"counts_by_year":[{"year":2026,"cited_by_count":4},{"year":2025,"cited_by_count":26},{"year":2024,"cited_by_count":26},{"year":2023,"cited_by_count":27},{"year":2022,"cited_by_count":18},{"year":2021,"cited_by_count":19},{"year":2020,"cited_by_count":25},{"year":2019,"cited_by_count":23},{"year":2018,"cited_by_count":25},{"year":2017,"cited_by_count":15},{"year":2016,"cited_by_count":17},{"year":2015,"cited_by_count":26},{"year":2014,"cited_by_count":22},{"year":2013,"cited_by_count":30},{"year":2012,"cited_by_count":20}],"updated_date":"2026-06-06T09:05:17.133730","created_date":"2025-10-10T00:00:00"}