{"id":"https://openalex.org/W2799433650","doi":"https://doi.org/10.1051/ro/2018026","title":"Modeling and solution of maximal covering problem considering gradual coverage with variable radius over multi-periods","display_name":"Modeling and solution of maximal covering problem considering gradual coverage with variable radius over multi-periods","publication_year":2018,"publication_date":"2018-04-30","ids":{"openalex":"https://openalex.org/W2799433650","doi":"https://doi.org/10.1051/ro/2018026","mag":"2799433650"},"language":"en","primary_location":{"id":"doi:10.1051/ro/2018026","is_oa":false,"landing_page_url":"https://doi.org/10.1051/ro/2018026","pdf_url":null,"source":{"id":"https://openalex.org/S20631277","display_name":"RAIRO - Operations Research","issn_l":"0399-0559","issn":["0399-0559","1290-3868"],"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":null,"license_id":null,"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":false,"oa_status":"closed","oa_url":null,"any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5067178270","display_name":"Alireza Eydi","orcid":"https://orcid.org/0000-0002-7432-0520"},"institutions":[{"id":"https://openalex.org/I3124704065","display_name":"University of Kurdistan","ror":"https://ror.org/04k89yk85","country_code":"IR","type":"education","lineage":["https://openalex.org/I3124704065"]}],"countries":["IR"],"is_corresponding":false,"raw_author_name":"Alireza Eydi","raw_affiliation_strings":["Faculty of Engineering, University of Kurdistan, Pasdaran Blvd., Post Box No. 416, Sanandaj, Iran"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Faculty of Engineering, University of Kurdistan, Pasdaran Blvd., Post Box No. 416, Sanandaj, Iran","institution_ids":["https://openalex.org/I3124704065"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5073039825","display_name":"Javad Mohebi","orcid":null},"institutions":[{"id":"https://openalex.org/I3124704065","display_name":"University of Kurdistan","ror":"https://ror.org/04k89yk85","country_code":"IR","type":"education","lineage":["https://openalex.org/I3124704065"]}],"countries":["IR"],"is_corresponding":false,"raw_author_name":"Javad Mohebi","raw_affiliation_strings":["MSC of Industrial Engineering, University of Kurdistan, Sanandaj, Iran"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"MSC of Industrial Engineering, University of Kurdistan, Sanandaj, Iran","institution_ids":["https://openalex.org/I3124704065"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":1.03,"has_fulltext":false,"cited_by_count":7,"citation_normalized_percentile":{"value":0.82082933,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":99},"biblio":{"volume":"52","issue":"4-5","first_page":"1245","last_page":"1260"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11502","display_name":"Facility Location and Emergency Management","score":1.0,"subfield":{"id":"https://openalex.org/subfields/1407","display_name":"Organizational Behavior and Human Resource 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"}},"topics":[{"id":"https://openalex.org/T11502","display_name":"Facility Location and Emergency Management","score":1.0,"subfield":{"id":"https://openalex.org/subfields/1407","display_name":"Organizational Behavior and Human Resource 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"}},{"id":"https://openalex.org/T10567","display_name":"Vehicle Routing Optimization Methods","score":0.9969000220298767,"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/T12306","display_name":"Urban and Freight Transport Logistics","score":0.9890000224113464,"subfield":{"id":"https://openalex.org/subfields/2215","display_name":"Building and Construction"},"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/relocation","display_name":"Relocation","score":0.8415560126304626},{"id":"https://openalex.org/keywords/simulated-annealing","display_name":"Simulated annealing","score":0.7377497553825378},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.7329436540603638},{"id":"https://openalex.org/keywords/variable","display_name":"Variable (mathematics)","score":0.6889780759811401},{"id":"https://openalex.org/keywords/1-center-problem","display_name":"1-center problem","score":0.6254971027374268},{"id":"https://openalex.org/keywords/minification","display_name":"Minification","score":0.6217172145843506},{"id":"https://openalex.org/keywords/variable-cost","display_name":"Variable cost","score":0.6115840673446655},{"id":"https://openalex.org/keywords/facility-location-problem","display_name":"Facility location problem","score":0.5921155214309692},{"id":"https://openalex.org/keywords/fixed-cost","display_name":"Fixed cost","score":0.5442337393760681},{"id":"https://openalex.org/keywords/maximization","display_name":"Maximization","score":0.5379655361175537},{"id":"https://openalex.org/keywords/integer-programming","display_name":"Integer programming","score":0.5141459107398987},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.4798687994480133},{"id":"https://openalex.org/keywords/metaheuristic","display_name":"Metaheuristic","score":0.4701941907405853},{"id":"https://openalex.org/keywords/function","display_name":"Function (biology)","score":0.46846458315849304},{"id":"https://openalex.org/keywords/radius","display_name":"RADIUS","score":0.4348587393760681},{"id":"https://openalex.org/keywords/location-model","display_name":"Location model","score":0.4292256236076355},{"id":"https://openalex.org/keywords/variable-neighborhood-search","display_name":"Variable neighborhood search","score":0.41258493065834045},{"id":"https://openalex.org/keywords/total-cost","display_name":"Total cost","score":0.4123205542564392},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.35610830783843994},{"id":"https://openalex.org/keywords/operations-research","display_name":"Operations research","score":0.3317336440086365}],"concepts":[{"id":"https://openalex.org/C2779019381","wikidata":"https://www.wikidata.org/wiki/Q3499564","display_name":"Relocation","level":2,"score":0.8415560126304626},{"id":"https://openalex.org/C126980161","wikidata":"https://www.wikidata.org/wiki/Q863783","display_name":"Simulated annealing","level":2,"score":0.7377497553825378},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.7329436540603638},{"id":"https://openalex.org/C182365436","wikidata":"https://www.wikidata.org/wiki/Q50701","display_name":"Variable (mathematics)","level":2,"score":0.6889780759811401},{"id":"https://openalex.org/C50524431","wikidata":"https://www.wikidata.org/wiki/Q4545814","display_name":"1-center problem","level":3,"score":0.6254971027374268},{"id":"https://openalex.org/C147764199","wikidata":"https://www.wikidata.org/wiki/Q6865248","display_name":"Minification","level":2,"score":0.6217172145843506},{"id":"https://openalex.org/C145760622","wikidata":"https://www.wikidata.org/wiki/Q174915","display_name":"Variable cost","level":2,"score":0.6115840673446655},{"id":"https://openalex.org/C108005400","wikidata":"https://www.wikidata.org/wiki/Q1305598","display_name":"Facility location problem","level":2,"score":0.5921155214309692},{"id":"https://openalex.org/C42866809","wikidata":"https://www.wikidata.org/wiki/Q466764","display_name":"Fixed cost","level":2,"score":0.5442337393760681},{"id":"https://openalex.org/C2776330181","wikidata":"https://www.wikidata.org/wiki/Q18358244","display_name":"Maximization","level":2,"score":0.5379655361175537},{"id":"https://openalex.org/C56086750","wikidata":"https://www.wikidata.org/wiki/Q6042592","display_name":"Integer programming","level":2,"score":0.5141459107398987},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.4798687994480133},{"id":"https://openalex.org/C109718341","wikidata":"https://www.wikidata.org/wiki/Q1385229","display_name":"Metaheuristic","level":2,"score":0.4701941907405853},{"id":"https://openalex.org/C14036430","wikidata":"https://www.wikidata.org/wiki/Q3736076","display_name":"Function (biology)","level":2,"score":0.46846458315849304},{"id":"https://openalex.org/C178635117","wikidata":"https://www.wikidata.org/wiki/Q747499","display_name":"RADIUS","level":2,"score":0.4348587393760681},{"id":"https://openalex.org/C2776608338","wikidata":"https://www.wikidata.org/wiki/Q6664803","display_name":"Location model","level":2,"score":0.4292256236076355},{"id":"https://openalex.org/C2776435737","wikidata":"https://www.wikidata.org/wiki/Q7915703","display_name":"Variable neighborhood search","level":3,"score":0.41258493065834045},{"id":"https://openalex.org/C182299520","wikidata":"https://www.wikidata.org/wiki/Q1289588","display_name":"Total cost","level":2,"score":0.4123205542564392},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.35610830783843994},{"id":"https://openalex.org/C42475967","wikidata":"https://www.wikidata.org/wiki/Q194292","display_name":"Operations research","level":1,"score":0.3317336440086365},{"id":"https://openalex.org/C38652104","wikidata":"https://www.wikidata.org/wiki/Q3510521","display_name":"Computer security","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/C121955636","wikidata":"https://www.wikidata.org/wiki/Q4116214","display_name":"Accounting","level":1,"score":0.0},{"id":"https://openalex.org/C86803240","wikidata":"https://www.wikidata.org/wiki/Q420","display_name":"Biology","level":0,"score":0.0},{"id":"https://openalex.org/C78458016","wikidata":"https://www.wikidata.org/wiki/Q840400","display_name":"Evolutionary biology","level":1,"score":0.0},{"id":"https://openalex.org/C175444787","wikidata":"https://www.wikidata.org/wiki/Q39072","display_name":"Microeconomics","level":1,"score":0.0},{"id":"https://openalex.org/C144133560","wikidata":"https://www.wikidata.org/wiki/Q4830453","display_name":"Business","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/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","level":0,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1051/ro/2018026","is_oa":false,"landing_page_url":"https://doi.org/10.1051/ro/2018026","pdf_url":null,"source":{"id":"https://openalex.org/S20631277","display_name":"RAIRO - Operations Research","issn_l":"0399-0559","issn":["0399-0559","1290-3868"],"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":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"RAIRO - Operations Research","raw_type":"journal-article"},{"id":"pmh:oai:numdam.org:RO_2018__52_4-5_1245_0","is_oa":false,"landing_page_url":"https://www.numdam.org/articles/10.1051/ro/2018026/","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":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":23,"referenced_works":["https://openalex.org/W126787311","https://openalex.org/W381492219","https://openalex.org/W1595498733","https://openalex.org/W2000318055","https://openalex.org/W2007468983","https://openalex.org/W2023174570","https://openalex.org/W2024060531","https://openalex.org/W2029076288","https://openalex.org/W2035535234","https://openalex.org/W2064453600","https://openalex.org/W2064938506","https://openalex.org/W2070048370","https://openalex.org/W2073697327","https://openalex.org/W2075936903","https://openalex.org/W2094868816","https://openalex.org/W2106371135","https://openalex.org/W2113854449","https://openalex.org/W2127859636","https://openalex.org/W2136272408","https://openalex.org/W2313758466","https://openalex.org/W2570178494","https://openalex.org/W2810799211","https://openalex.org/W4243898524"],"related_works":["https://openalex.org/W2210166395","https://openalex.org/W4245915041","https://openalex.org/W4255485615","https://openalex.org/W81787812","https://openalex.org/W2783359165","https://openalex.org/W2972248930","https://openalex.org/W4238210700","https://openalex.org/W3157715565","https://openalex.org/W4231153919","https://openalex.org/W2357407088"],"abstract_inverted_index":{"Facility":[0],"location":[1,49,61,181],"is":[2,64,69,97],"a":[3,25,35,72,101,106,111,144],"critical":[4],"component":[5],"of":[6,18,38,86,129,200],"strategic":[7],"planning":[8],"for":[9,23],"public":[10],"and":[11,167,195],"private":[12],"firms.":[13],"Due":[14],"to":[15,99,176],"high":[16],"cost":[17,103,108,169],"facility":[19,82,96,155],"location,":[20],"making":[21],"decisions":[22],"such":[24],"problem":[26,50,133],"has":[27,110],"become":[28],"an":[29],"important":[30],"issue":[31],"which":[32,109,152],"have":[33,100],"gained":[34],"large":[36],"deal":[37],"attention":[39],"from":[40,80],"researchers.":[41],"This":[42],"study":[43],"examined":[44],"the":[45,78,81,84,115,130,132,178,201],"gradual":[46,59],"maximal":[47,179],"covering":[48,60,92,180],"with":[51,105,189],"variable":[52,90,107],"radius":[53,91],"over":[54,125,137],"multiple":[55,138],"time":[56,139],"periods.":[57,140],"In":[58,89,118,141],"problem,":[62],"it":[63],"assumed":[65],"that":[66,76],"full":[67],"coverage":[68,73,116,165],"replaced":[70],"by":[71],"function,":[74],"so":[75],"increasing":[77],"distance":[79],"decreases":[83],"amount":[85],"demand":[87,122],"coverage.":[88],"problems,":[93,120],"however,":[94],"each":[95],"considered":[98],"fixed":[102],"along":[104],"direct":[112],"impact":[113],"on":[114],"radius.":[117],"real-world":[119],"since":[121],"may":[123],"change":[124],"time,":[126],"necessitating":[127],"relocation":[128,168],"facilities,":[131],"can":[134],"be":[135],"formulated":[136],"this":[142],"study,":[143],"mixed":[145],"integer":[146],"programming":[147],"model":[148],"was":[149,157,174,187],"presented":[150,175],"in":[151],"not":[153],"only":[154],"capacity":[156],"considered,":[158],"but":[159],"also":[160],"two":[161],"objectives":[162],"were":[163],"followed:":[164],"maximization":[166],"minimization.":[170],"A":[171,183],"metaheuristic":[172],"algorithm":[173,186],"solve":[177],"problem.":[182],"simulated":[184,202],"annealing":[185,203],"proposed,":[188],"its":[190],"results":[191,194],"presented.":[192],"Computational":[193],"comparisons":[196],"demonstrated":[197],"good":[198],"performance":[199],"algorithm.":[204]},"counts_by_year":[{"year":2026,"cited_by_count":2},{"year":2024,"cited_by_count":1},{"year":2022,"cited_by_count":1},{"year":2021,"cited_by_count":1},{"year":2020,"cited_by_count":1},{"year":2018,"cited_by_count":1}],"updated_date":"2026-06-11T09:08:48.828518","created_date":"2025-10-10T00:00:00"}