Divide and Conquer: A Location-Allocation Approach to Sectorization
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, c...
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| Format: | Article |
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MDPI AG
2023-06-01
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| Series: | Mathematics |
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| Online Access: | https://www.mdpi.com/2227-7390/11/11/2553 |
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| author | Cristina Lopes Ana Maria Rodrigues Valeria Romanciuc José Soeiro Ferreira Elif Göksu Öztürk Cristina Oliveira |
| author_facet | Cristina Lopes Ana Maria Rodrigues Valeria Romanciuc José Soeiro Ferreira Elif Göksu Öztürk Cristina Oliveira |
| author_sort | Cristina Lopes |
| collection | DOAJ |
| description | 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’s 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 <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi>ϵ</mi></semantics></math></inline-formula>-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. |
| first_indexed | 2024-03-11T03:01:29Z |
| format | Article |
| id | doaj.art-409db46f5adb4a29b7ccef1571a8325e |
| institution | Directory Open Access Journal |
| issn | 2227-7390 |
| language | English |
| last_indexed | 2024-03-11T03:01:29Z |
| publishDate | 2023-06-01 |
| publisher | MDPI AG |
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| series | Mathematics |
| spelling | doaj.art-409db46f5adb4a29b7ccef1571a8325e2023-11-18T08:13:36ZengMDPI AGMathematics2227-73902023-06-011111255310.3390/math11112553Divide and Conquer: A Location-Allocation Approach to SectorizationCristina Lopes0Ana Maria Rodrigues1Valeria Romanciuc2José Soeiro Ferreira3Elif Göksu Öztürk4Cristina Oliveira5CEOS.PP, ISCAP, Polytechnic of Porto, 4465-004 Porto, PortugalCEOS.PP, ISCAP, Polytechnic of Porto, 4465-004 Porto, PortugalMillennium BCP, 1050-059 Lisbon, PortugalINESC TEC, 4200-465 Porto, PortugalINESC TEC, 4200-465 Porto, PortugalCEOS.PP, ISCAP, Polytechnic of Porto, 4465-004 Porto, PortugalSectorization 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’s 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 <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi>ϵ</mi></semantics></math></inline-formula>-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.https://www.mdpi.com/2227-7390/11/11/2553sectorizationmultiobjective optimizationinteger programmingdistricting problemslexicographic methodϵ-constraint method |
| spellingShingle | Cristina Lopes Ana Maria Rodrigues Valeria Romanciuc José Soeiro Ferreira Elif Göksu Öztürk Cristina Oliveira Divide and Conquer: A Location-Allocation Approach to Sectorization Mathematics sectorization multiobjective optimization integer programming districting problems lexicographic method ϵ-constraint method |
| title | Divide and Conquer: A Location-Allocation Approach to Sectorization |
| title_full | Divide and Conquer: A Location-Allocation Approach to Sectorization |
| title_fullStr | Divide and Conquer: A Location-Allocation Approach to Sectorization |
| title_full_unstemmed | Divide and Conquer: A Location-Allocation Approach to Sectorization |
| title_short | Divide and Conquer: A Location-Allocation Approach to Sectorization |
| title_sort | divide and conquer a location allocation approach to sectorization |
| topic | sectorization multiobjective optimization integer programming districting problems lexicographic method ϵ-constraint method |
| url | https://www.mdpi.com/2227-7390/11/11/2553 |
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