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To derive equity distribution between municipalities, this paper developed lower bounds and eleven heuristics to be utilized in the branch-and-bound algorithms. The performance of the developed heuristics, lower bounds and the exact solutions are presented in the experimental study.<\/jats:p>","DOI":"10.1051\/ro\/2021043","type":"journal-article","created":{"date-parts":[[2021,3,19]],"date-time":"2021-03-19T19:56:21Z","timestamp":1616183781000},"page":"873-897","source":"Crossref","is-referenced-by-count":18,"title":["An optimal solution for the budgets assignment problem"],"prefix":"10.1051","volume":"55","author":[{"ORCID":"https:\/\/orcid.org\/0000-0003-3462-8739","authenticated-orcid":false,"given":"Mahdi","family":"Jemmali","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"250","published-online":{"date-parts":[[2021,5,6]]},"reference":[{"key":"R1","doi-asserted-by":"crossref","first-page":"3607547","DOI":"10.1155\/2020\/3607547","volume":"2020","author":"Alharbi","year":"2020","journal-title":"Comput. Intell. 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