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This study examined the gradual maximal covering location problem with variable radius over multiple time periods. In gradual covering location problem, it is assumed that full coverage is replaced by a coverage function, so that increasing the distance from the facility decreases the amount of demand coverage. In variable radius covering problems, however, each facility is considered to have a fixed cost along with a variable cost which has a direct impact on the coverage radius. In real-world problems, since demand may change over time, necessitating relocation of the facilities, the problem can be formulated over multiple time periods. In this study, a mixed integer programming model was presented in which not only facility capacity was considered, but also two objectives were followed: coverage maximization and relocation cost minimization. A metaheuristic algorithm was presented to solve the maximal covering location problem. A simulated annealing algorithm was proposed, with its results presented. Computational results and comparisons demonstrated good performance of the simulated annealing algorithm.<\/jats:p>","DOI":"10.1051\/ro\/2018026","type":"journal-article","created":{"date-parts":[[2018,4,30]],"date-time":"2018-04-30T18:47:55Z","timestamp":1525114075000},"page":"1245-1260","source":"Crossref","is-referenced-by-count":7,"title":["Modeling and solution of maximal covering problem considering gradual coverage with variable radius over multi-periods"],"prefix":"10.1051","volume":"52","author":[{"given":"Alireza","family":"Eydi","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Javad","family":"Mohebi","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"250","published-online":{"date-parts":[[2018,12,5]]},"reference":[{"key":"R1","doi-asserted-by":"crossref","unstructured":"Aarts E. and \nLenstra J.K., \nLocal Search in Combinatorial Optimization. \nPrinceton University Press, \nNew Jersey \n(2003).","DOI":"10.1515\/9780691187563"},{"key":"R2","doi-asserted-by":"crossref","first-page":"1356","DOI":"10.1016\/j.cor.2008.02.010","volume":"36","author":"Albareda-Sambola","year":"2009","journal-title":"Comput. 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International Series in Operations Research & Management Science, Part IV, Covering Problem, \nSpringer \n(2011).","DOI":"10.1007\/978-1-4419-7572-0"},{"key":"R13","doi-asserted-by":"crossref","first-page":"368","DOI":"10.1016\/j.cie.2011.08.020","volume":"62","author":"Farahani","year":"2011","journal-title":"Comput. Ind. Eng."},{"key":"R14","unstructured":"GAMS Development Corporation , \nGAMS \u2013 A User\u2019s Guide. Tutorial by Richard E. Rosenthal, Washington, DC, USA \n(2008)."},{"key":"R15","unstructured":"GAMS Development Corporation , \nGAMS \u2013 The Solver Manuals. Tutorial by Richard E. Rosenthal, Washington, DC, USA \n(2008)."},{"key":"R16","doi-asserted-by":"crossref","first-page":"22","DOI":"10.1057\/palgrave.jors.2601991","volume":"57","author":"Gendreau","year":"2006","journal-title":"J. Oper. Res. Soc."},{"key":"R17","doi-asserted-by":"crossref","first-page":"462","DOI":"10.1287\/opre.13.3.462","volume":"13","author":"Hakimi","year":"1965","journal-title":"Oper. 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