{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,16]],"date-time":"2026-03-16T23:35:23Z","timestamp":1773704123251,"version":"3.50.1"},"reference-count":36,"publisher":"MDPI AG","issue":"11","license":[{"start":{"date-parts":[[2023,6,2]],"date-time":"2023-06-02T00:00:00Z","timestamp":1685664000000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"ERDF\u2014European Regional Development Fund through the Operational Programme for Competitiveness and Internationalisation\u2014COMPETE 2020 Programme","award":["POCI-01-0145-FEDER-031671"],"award-info":[{"award-number":["POCI-01-0145-FEDER-031671"]}]},{"name":"National Funds through the Portuguese funding agency","award":["POCI-01-0145-FEDER-031671"],"award-info":[{"award-number":["POCI-01-0145-FEDER-031671"]}]},{"name":"FCT\u2014Funda\u00e7\u00e3o para a Ci\u00eancia e a Tecnologia","award":["POCI-01-0145-FEDER-031671"],"award-info":[{"award-number":["POCI-01-0145-FEDER-031671"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Mathematics"],"abstract":"<jats:p>Sectorization is concerned with dividing a large territory into smaller areas, also known as sectors. This process usually simplifies a complex problem, leading to easier solution approaches to solving the resulting subproblems. Sectors are built with several criteria in mind, such as equilibrium, compactness, contiguity, and desirability, which vary with the applications. Sectorization appears in different contexts: sales territory design, political districting, healthcare logistics, and vehicle routing problems (agrifood distribution, winter road maintenance, parcel delivery). Environmental problems can also be tackled with a sectorization approach; for example, in municipal waste collection, water distribution networks, and even in finding more sustainable transportation routes. This work focuses on sectorization concerning the location of the area\u2019s centers and allocating basic units to each sector. Integer programming models address the location-allocation problems, and various formulations implementing different criteria are compared. Methods to deal with multiobjective optimization problems, such as the \u03f5-constraint, the lexicographic, and the weighted sum methods, are applied and compared. Computational results obtained for a set of benchmarking instances of sectorization problems are also presented.<\/jats:p>","DOI":"10.3390\/math11112553","type":"journal-article","created":{"date-parts":[[2023,6,2]],"date-time":"2023-06-02T01:33:54Z","timestamp":1685669634000},"page":"2553","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":3,"title":["Divide and Conquer: A Location-Allocation Approach to Sectorization"],"prefix":"10.3390","volume":"11","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-4833-470X","authenticated-orcid":false,"given":"Cristina","family":"Lopes","sequence":"first","affiliation":[{"name":"CEOS.PP, ISCAP, Polytechnic of Porto, 4465-004 Porto, Portugal"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-1070-3626","authenticated-orcid":false,"given":"Ana Maria","family":"Rodrigues","sequence":"additional","affiliation":[{"name":"CEOS.PP, ISCAP, Polytechnic of Porto, 4465-004 Porto, Portugal"},{"name":"INESC TEC, 4200-465 Porto, Portugal"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-5700-4016","authenticated-orcid":false,"given":"Valeria","family":"Romanciuc","sequence":"additional","affiliation":[{"name":"Millennium BCP, 1050-059 Lisbon, Portugal"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-7552-9924","authenticated-orcid":false,"given":"Jos\u00e9 Soeiro","family":"Ferreira","sequence":"additional","affiliation":[{"name":"INESC TEC, 4200-465 Porto, Portugal"},{"name":"FEUP\u2014Faculty of Engineering, University of Porto, 4200-465 Porto, Portugal"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-8407-1871","authenticated-orcid":false,"given":"Elif G\u00f6ksu","family":"\u00d6zt\u00fcrk","sequence":"additional","affiliation":[{"name":"INESC TEC, 4200-465 Porto, Portugal"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-6475-5769","authenticated-orcid":false,"given":"Cristina","family":"Oliveira","sequence":"additional","affiliation":[{"name":"CEOS.PP, ISCAP, Polytechnic of Porto, 4465-004 Porto, Portugal"}]}],"member":"1968","published-online":{"date-parts":[[2023,6,2]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1007\/BF02578982","article-title":"Towards a unified territorial design approach\u2014Applications, algorithms and GIS integration","volume":"13","author":"Kalcsics","year":"2005","journal-title":"Top"},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"369","DOI":"10.1007\/s00158-003-0368-6","article-title":"Survey of multi-objective optimization methods for engineering","volume":"26","author":"Marler","year":"2004","journal-title":"Struct. 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