IDEAS home Printed from
   My bibliography  Save this paper

Clustering of territorial areas: A multi-criteria districting problem


  • Rui Fragoso

    (CEFAGE-UE, and ICAAM-UE, Universidade de Évora)

  • Maria Conceição Rego

    (Department of Economics and CEFAGE-UE, Universidade de Évora)

  • Vladimir Bushenkov

    (CIMA-UE, Universidade de Évora)


Endogenous resources, economic profile and socio-economic issues are the criteria that define the level of development and identifying features of a territorial unit. The territorial units that organize the country, in political and administrative terms – parishes and counties –, have a hierarchical structure, which initially reflected the organization of productive activities as well as the traditional State organization. The success of development policies addressed to territorial agglomerates depends on the homogeneity of their territorial units. In this context, the clustering of territorial areas can be stated as a multi-criteria districting problem. Thus, this paper aims to propose a framework for obtaining homogenous territorial clusters based on a Pareto frontier that includes multiple criteria related to territories’ endogenous resources, economic profile and socio-cultural features. This framework is developed in two phases. First, the criteria correlated with development at the territorial unit level are determined through statistical and econometric methods. Then, a multi-criteria approach is developed to allocate each territorial unit to a territorial agglomerate, according to the Pareto frontier established. The framework is applied to a set of parishes and counties of the Central Alentejo region in southern Portugal. Results are presented and discussed in the scope of a regional development strategy.

Suggested Citation

  • Rui Fragoso & Maria Conceição Rego & Vladimir Bushenkov, 2014. "Clustering of territorial areas: A multi-criteria districting problem," CEFAGE-UE Working Papers 2014_02, University of Evora, CEFAGE-UE (Portugal).
  • Handle: RePEc:cfe:wpcefa:2014_02

    Download full text from publisher

    File URL:
    Download Restriction: no

    References listed on IDEAS

    1. Pierre Hansen & Brigitte Jaumard & Christophe Meyer & Bruno Simeone & Valeria Doring, 2003. "Maximum Split Clustering Under Connectivity Constraints," Journal of Classification, Springer;The Classification Society, vol. 20(2), pages 143-180, September.
    2. R. S. Garfinkel & G. L. Nemhauser, 1970. "Optimal Political Districting by Implicit Enumeration Techniques," Management Science, INFORMS, vol. 16(8), pages 495-508, April.
    3. Boris A. Portnov & Moshe Schwartz, 2009. "Urban Clusters As Growth Foci," Journal of Regional Science, Wiley Blackwell, vol. 49(2), pages 287-310, May.
    4. Gordon, A. D., 1996. "A survey of constrained classification," Computational Statistics & Data Analysis, Elsevier, vol. 21(1), pages 17-29, January.
    5. Muyldermans, L. & Cattrysse, D. & Van Oudheusden, D. & Lotan, T., 2002. "Districting for salt spreading operations," European Journal of Operational Research, Elsevier, vol. 139(3), pages 521-532, June.
    6. Roy J. Shanker & Ronald E. Turner & Andris A. Zoltners, 1975. "Sales Territory Design: An Integrated Approach," Management Science, INFORMS, vol. 22(3), pages 309-320, November.
    7. Anuj Mehrotra & Ellis L. Johnson & George L. Nemhauser, 1998. "An Optimization Based Heuristic for Political Districting," Management Science, INFORMS, vol. 44(8), pages 1100-1114, August.
    8. Bozkaya, Burcin & Erkut, Erhan & Laporte, Gilbert, 2003. "A tabu search heuristic and adaptive memory procedure for political districting," European Journal of Operational Research, Elsevier, vol. 144(1), pages 12-26, January.
    9. Anuška Ferligoj & Vladimir Batagelj, 1982. "Clustering with relational constraint," Psychometrika, Springer;The Psychometric Society, vol. 47(4), pages 413-426, December.
    10. Juan C. Duque & Luc Anselin & Sergio J. Rey, 2012. "The Max-P-Regions Problem," Journal of Regional Science, Wiley Blackwell, vol. 52(3), pages 397-419, August.
    11. Fischer, Manfred M., 1980. "Regional taxonomy : A comparison of some hierarchic and non-hierarchic strategies," Regional Science and Urban Economics, Elsevier, vol. 10(4), pages 503-537, November.
    12. Sidney W. Hess & Stuart A. Samuels, 1971. "Experiences with a Sales Districting Model: Criteria and Implementation," Management Science, INFORMS, vol. 18(4-Part-II), pages 41-54, December.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Rui Fragoso & Conceição Rego & Vladimir Bushenkov, 2016. "Clustering of Territorial Areas: A Multi-Criteria Districting Problem," Journal of Quantitative Economics, Springer;The Indian Econometric Society (TIES), vol. 14(2), pages 179-198, December.
    2. Maria da Conceição Rego & Rui Fragoso & Vladimir Bushenkov, 2014. "Clustering of Territorial Areas: A Multi-Criteria Districting Problem," ERSA conference papers ersa14p218, European Regional Science Association.
    3. Tavares Pereira, Fernando & Figueira, José Rui & Mousseau, Vincent & Roy, Bernard, 2009. "Comparing two territory partitions in districting problems: Indices and practical issues," Socio-Economic Planning Sciences, Elsevier, vol. 43(1), pages 72-88, March.
    4. Fernando Tavares-Pereira & José Figueira & Vincent Mousseau & Bernard Roy, 2007. "Multiple criteria districting problems," Annals of Operations Research, Springer, vol. 154(1), pages 69-92, October.
    5. Sebastián Moreno & Jordi Pereira & Wilfredo Yushimito, 2020. "A hybrid K-means and integer programming method for commercial territory design: a case study in meat distribution," Annals of Operations Research, Springer, vol. 286(1), pages 87-117, March.
    6. Alexander Butsch & Jörg Kalcsics & Gilbert Laporte, 2014. "Districting for Arc Routing," INFORMS Journal on Computing, INFORMS, vol. 26(4), pages 809-824, November.
    7. Han, Jialin & Hu, Yaoguang & Mao, Mingsong & Wan, Shuping, 2020. "A multi-objective districting problem applied to agricultural machinery maintenance service network," European Journal of Operational Research, Elsevier, vol. 287(3), pages 1120-1130.
    8. M Blais & S D Lapierre & G Laporte, 2003. "Solving a home-care districting problem in an urban setting," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 54(11), pages 1141-1147, November.
    9. R. Church & J. C. Duque & D. E. Restrepo, 2020. "The p-Innovation ecosystems model," Papers 2008.05885,
    10. Ricca, Federica & Simeone, Bruno, 2008. "Local search algorithms for political districting," European Journal of Operational Research, Elsevier, vol. 189(3), pages 1409-1426, September.
    11. Brian Lunday & Hanif Sherali & Kevin Lunday, 2012. "The coastal seaspace patrol sector design and allocation problem," Computational Management Science, Springer, vol. 9(4), pages 483-514, November.
    12. Ram Gopalan & Steven O. Kimbrough & Frederic H. Murphy & Nicholas Quintus, 2013. "The Philadelphia Districting Contest: Designing Territories for City Council Based Upon the 2010 Census," Interfaces, INFORMS, vol. 43(5), pages 477-489, October.
    13. Xin Tang & Ameur Soukhal & Vincent T’kindt, 2014. "Preprocessing for a map sectorization problem by means of mathematical programming," Annals of Operations Research, Springer, vol. 222(1), pages 551-569, November.
    14. Balázs Fleiner & Balázs Nagy & Attila Tasnádi, 2017. "Optimal partisan districting on planar geographies," Central European Journal of Operations Research, Springer;Slovak Society for Operations Research;Hungarian Operational Research Society;Czech Society for Operations Research;Österr. Gesellschaft für Operations Research (ÖGOR);Slovenian Society Informatika - Section for Operational Research;Croatian Operational Research Society, vol. 25(4), pages 879-888, December.
    15. María Salazar-Aguilar & Roger Ríos-Mercado & Mauricio Cabrera-Ríos, 2011. "New Models for Commercial Territory Design," Networks and Spatial Economics, Springer, vol. 11(3), pages 487-507, September.
    16. Federica Ricca & Andrea Scozzari & Bruno Simeone, 2013. "Political Districting: from classical models to recent approaches," Annals of Operations Research, Springer, vol. 204(1), pages 271-299, April.
    17. Djordje Dugošija & Aleksandar Savić & Zoran Maksimović, 2020. "A new integer linear programming formulation for the problem of political districting," Annals of Operations Research, Springer, vol. 288(1), pages 247-263, May.
    18. Yanık, Seda & Sürer, Özge & Öztayşi, Başar, 2016. "Designing sustainable energy regions using genetic algorithms and location-allocation approach," Energy, Elsevier, vol. 97(C), pages 161-172.
    19. Mendez, Carlos & Gonzales, Erick, 2020. "Human Capital Constraints, Spatial Dependence, and Regionalization in Bolivia: A Spatial Clustering Approach," MPRA Paper 104303, University Library of Munich, Germany.
    20. Camacho-Collados, M. & Liberatore, F. & Angulo, J.M., 2015. "A multi-criteria Police Districting Problem for the efficient and effective design of patrol sector," European Journal of Operational Research, Elsevier, vol. 246(2), pages 674-684.

    More about this item


    Alentejo; Cluster; Districting; Multi-criteria.;
    All these keywords.

    JEL classification:

    • C31 - Mathematical and Quantitative Methods - - Multiple or Simultaneous Equation Models; Multiple Variables - - - Cross-Sectional Models; Spatial Models; Treatment Effect Models; Quantile Regressions; Social Interaction Models
    • R12 - Urban, Rural, Regional, Real Estate, and Transportation Economics - - General Regional Economics - - - Size and Spatial Distributions of Regional Economic Activity; Interregional Trade (economic geography)

    NEP fields

    This paper has been announced in the following NEP Reports:


    Access and download statistics


    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:cfe:wpcefa:2014_02. See general information about how to correct material in RePEc.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: . General contact details of provider: .

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Angela Pacheco (email available below). General contact details of provider: .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service hosted by the Research Division of the Federal Reserve Bank of St. Louis . RePEc uses bibliographic data supplied by the respective publishers.