IDEAS home Printed from https://ideas.repec.org/a/inm/orijoc/v34y2022i4p2003-2016.html
   My bibliography  Save this article

The Capacitated and Economic Districting Problem

Author

Listed:
  • Luis Henrique Pauleti Mendes

    (Institute of Computing, University of Campinas, Campinas, São Paulo 13083-852, Brazil)

  • Fábio Luiz Usberti

    (Institute of Computing, University of Campinas, Campinas, São Paulo 13083-852, Brazil)

  • Celso Cavellucci

    (Institute of Computing, University of Campinas, Campinas, São Paulo 13083-852, Brazil)

Abstract

This paper presents the capacitated and economic districting problem (CEDP), which searches for the best edge partition defining connected, capacitated, and balanced districts in an undirected connected graph, weighing the economic value of each district. This problem provides a comprehensive description of the decision making on service networks districting, where the order by which the districts are serviced plays a role in the profit. This is observed in the arrangement of districts for meter reading, as the day in which each district is read impacts the revenue. Two integer linear programming formulations are proposed for CEDP, accompanied by a proof of N P -hardness. To tackle large instances, a greedy randomized adaptive search procedure (GRASP) metaheuristic, embedded with reactive parameter tuning, statistical filtering of solutions subjected to intensification, and a set of solution repairing procedures, is proposed. The GRASP is hybridized to each model to evaluate the outcomes of combining their individual merits. Computational experiments were performed on a new benchmark composed of 144 instances of different sizes, edge densities, network topologies, balance tolerances, and district capacities. The results show the effectiveness of the exact methodologies in solving the models and providing optimal solutions for the set of small instances. The GRASP was capable of tackling large networks, achieving feasible solutions to almost all instances. The results also show that the hybridized methodologies outperformed their standalone counterparts with respect to the attained primal and dual bounds.

Suggested Citation

  • Luis Henrique Pauleti Mendes & Fábio Luiz Usberti & Celso Cavellucci, 2022. "The Capacitated and Economic Districting Problem," INFORMS Journal on Computing, INFORMS, vol. 34(4), pages 2003-2016, July.
    • Handle: RePEc:inm:orijoc:v:34:y:2022:i:4:p:2003-2016
    DOI: 10.1287/ijoc.2022.1180
    as

    Download full text from publisher

    File URL: http://dx.doi.org/10.1287/ijoc.2022.1180
    Download Restriction: no
    File URL: https://libkey.io/10.1287/ijoc.2022.1180?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    References listed on IDEAS

    as
    1. Pierre de la Poix de Fréminville & Guy Desaulniers & Louis-Martin Rousseau & Sylvain Perron, 2015. "A column generation heuristic for districting the price of a financial product," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 66(6), pages 965-978, June.
    2. John Silberholz & Bruce Golden, 2010. "Comparison of Metaheuristics," International Series in Operations Research & Management Science, in: Michel Gendreau & Jean-Yves Potvin (ed.), Handbook of Metaheuristics, chapter 0, pages 625-640, Springer.
    3. H. W. Kuhn, 1955. "The Hungarian method for the assignment problem," Naval Research Logistics Quarterly, John Wiley & Sons, vol. 2(1‐2), pages 83-97, March.
    4. Jörg Kalcsics, 2015. "Districting Problems," Springer Books, in: Gilbert Laporte & Stefan Nickel & Francisco Saldanha da Gama (ed.), Location Science, edition 127, chapter 0, pages 595-622, Springer.
    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. Justin C. Williams, 1995. "Political Redistricting: A Review," Papers in Regional Science, Wiley Blackwell, vol. 74(1), pages 13-40, January.
    7. Alexander Butsch & Jörg Kalcsics & Gilbert Laporte, 2014. "Districting for Arc Routing," INFORMS Journal on Computing, INFORMS, vol. 26(4), pages 809-824, November.
    8. 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.
    9. Federico Liberatore & Miguel Camacho-Collados & Begoña Vitoriano, 2020. "Police Districting Problem: Literature Review and Annotated Bibliography," International Series in Operations Research & Management Science, in: Roger Z. Ríos-Mercado (ed.), Optimal Districting and Territory Design, chapter 0, pages 9-29, Springer.
    10. 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.
    11. Wang, Dian & Zhao, Jun & D’Ariano, Andrea & Peng, Qiyuan, 2021. "Simultaneous node and link districting in transportation networks: Model, algorithms and railway application," European Journal of Operational Research, Elsevier, vol. 292(1), pages 73-94.
    12. Julie Wunderlich & Martin Collette & Laurence Levy & Lawrence Bodin, 1992. "Scheduling Meter Readers for Southern California Gas Company," Interfaces, INFORMS, vol. 22(3), pages 22-30, June.
    13. Federica Ricca & Andrea Scozzari, 2020. "Mathematical Programming Formulations for Practical Political Districting," International Series in Operations Research & Management Science, in: Roger Z. Ríos-Mercado (ed.), Optimal Districting and Territory Design, chapter 0, pages 105-128, Springer.
    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. Sandoval, M. Gabriela & Álvarez-Miranda, Eduardo & Pereira, Jordi & Ríos-Mercado, Roger Z. & Díaz, Juan A., 2022. "A novel districting design approach for on-time last-mile delivery: An application on an express postal company," Omega, Elsevier, vol. 113(C).
    2. Alexander Butsch & Jörg Kalcsics & Gilbert Laporte, 2014. "Districting for Arc Routing," INFORMS Journal on Computing, INFORMS, vol. 26(4), pages 809-824, November.
    3. Verónica Arredondo & Miguel Martínez-Panero & Teresa Peña & Federica Ricca, 2021. "Mathematical political districting taking care of minority groups," Annals of Operations Research, Springer, vol. 305(1), pages 375-402, October.
    4. 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.
    5. Swamy, Rahul & King, Douglas M. & Ludden, Ian G. & Dobbs, Kiera W. & Jacobson, Sheldon H., 2024. "A practical optimization framework for political redistricting: A case study in Arizona," Socio-Economic Planning Sciences, Elsevier, vol. 92(C).
    6. Elena Fernández & Jessica Rodríguez-Pereira, 2017. "Multi-depot rural postman problems," TOP: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 25(2), pages 340-372, July.
    7. 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.
    8. 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.
    9. Christian Haas & Lee Hachadoorian & Steven O Kimbrough & Peter Miller & Frederic Murphy, 2020. "Seed-Fill-Shift-Repair: A redistricting heuristic for civic deliberation," PLOS ONE, Public Library of Science, vol. 15(9), pages 1-34, September.
    10. Hyun Kim & Yongwan Chun & Kamyoung Kim, 2015. "Delimitation of Functional Regions Using a p-Regions Problem Approach," International Regional Science Review, , vol. 38(3), pages 235-263, July.
    11. Elena Fernández & Gilbert Laporte & Jessica Rodríguez-Pereira, 2018. "A Branch-and-Cut Algorithm for the Multidepot Rural Postman Problem," Transportation Science, INFORMS, vol. 52(2), pages 353-369, March.
    12. 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.
    13. 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.
    14. L Muyldermans & D Cattrysse & D Van Oudheusden, 2003. "District design for arc-routing applications," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 54(11), pages 1209-1221, November.
    15. Bruno, Giuseppe & Genovese, Andrea & Piccolo, Carmela, 2017. "Territorial amalgamation decisions in local government: Models and a case study from Italy," Socio-Economic Planning Sciences, Elsevier, vol. 57(C), pages 61-72.
    16. 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.
    17. Lu Chen & Boxiao Chen & Quoc Trung Bui & Minh Hoàng Hà, 2017. "Designing service sectors for daily maintenance operations in a road network," International Journal of Production Research, Taylor & Francis Journals, vol. 55(8), pages 2251-2265, April.
    18. 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.
    19. 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.
    20. Eduardo Álvarez-Miranda & Camilo Campos-Valdés & Maurcio Morales Quiroga & Matías Moreno-Faguett & Jordi Pereira, 2020. "A Multi-Criteria Pen for Drawing Fair Districts: When Democratic and Demographic Fairness Matter," Mathematics, MDPI, vol. 8(9), pages 1-26, August.

    Corrections

    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:inm:orijoc:v:34:y:2022:i:4:p:2003-2016. See general information about how to correct material in RePEc.

    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: Chris Asher (email available below). General contact details of provider: https://edirc.repec.org/data/inforea.html .

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

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.