IDEAS home Printed from
   My bibliography  Save this article

A multi-objective districting problem applied to agricultural machinery maintenance service network


  • Han, Jialin
  • Hu, Yaoguang
  • Mao, Mingsong
  • Wan, Shuping


The prompt and reliable response to malfunctioning agricultural machinery of a maintenance service network is extremely critical for the safety and stability of agricultural production during the harvest. This research aims to cluster a set of given agricultural production areas into a specified number of service regions while assigning a service facility to maintenance demands in each region. The service region districting problem is formulated as a multi-objective mixed integer program (MIP) that seeks to minimize the total service mileage between facilities and demand points while minimizing the service demand overload in each service region. Additionally, we use modified contiguity constraints to enforce a single service region as geographically connected, which means that one can travel between any two locations in the region without leaving it. To solve our multi-objective MIP problem, the ɛ-constraint method is used to develop a set of non-inferior solutions that allow us to examine the trade-off between minimizing service mileage and minimizing demand overload and offer us a set of Pareto optimal decisions to consider for implementation. Lastly, our model and methodology are illustrated in handling a real-world problem in China. Computational results are presented that analyze the trade-off between objectives, examine the impact of selected parameters and demonstrate the advantage of implementing the modified contiguity constraints.

Suggested Citation

  • 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.
  • Handle: RePEc:eee:ejores:v:287:y:2020:i:3:p:1120-1130
    DOI: 10.1016/j.ejor.2020.05.008

    Download full text from publisher

    File URL:
    Download Restriction: Full text for ScienceDirect subscribers only

    File URL:
    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

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    1. Wheatley, David & Gzara, Fatma & Jewkes, Elizabeth, 2015. "Logic-based Benders decomposition for an inventory-location problem with service constraints," Omega, Elsevier, vol. 55(C), pages 10-23.
    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. Eskandarpour, Majid & Dejax, Pierre & Miemczyk, Joe & Péton, Olivier, 2015. "Sustainable supply chain network design: An optimization-oriented review," Omega, Elsevier, vol. 54(C), pages 11-32.
    4. Y. Kergosien & V. Bélanger & P. Soriano & M. Gendreau & A. Ruiz, 2015. "A generic and flexible simulation-based analysis tool for EMS management," International Journal of Production Research, Taylor & Francis Journals, vol. 53(24), pages 7299-7316, December.
    5. Peter C. Belford & H. Donald Ratliff, 1972. "A Network-Flow Model for Racially Balancing Schools," Operations Research, INFORMS, vol. 20(3), pages 619-628, June.
    6. Contreras, Ivan & Fernández, Elena & Reinelt, Gerhard, 2012. "Minimizing the maximum travel time in a combined model of facility location and network design," Omega, Elsevier, vol. 40(6), pages 847-860.
    7. Samanlioglu, Funda, 2013. "A multi-objective mathematical model for the industrial hazardous waste location-routing problem," European Journal of Operational Research, Elsevier, vol. 226(2), pages 332-340.
    8. Juan Carlos Duque & Raúl Ramos & Jordi Suriñach, 2007. "Supervised Regionalization Methods: A Survey," International Regional Science Review, , vol. 30(3), pages 195-220, July.
    9. Whittaker, Gerald & Färe, Rolf & Grosskopf, Shawna & Barnhart, Bradley & Bostian, Moriah & Mueller-Warrant, George & Griffith, Stephen, 2017. "Spatial targeting of agri-environmental policy using bilevel evolutionary optimization," Omega, Elsevier, vol. 66(PA), pages 15-27.
    10. Douglas M. King & Sheldon H. Jacobson & Edward C. Sewell & Wendy K. Tam Cho, 2012. "Geo-Graphs: An Efficient Model for Enforcing Contiguity and Hole Constraints in Planar Graph Partitioning," Operations Research, INFORMS, vol. 60(5), pages 1213-1228, October.
    11. 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.
    12. 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.
    13. S. W. Hess & J. B. Weaver & H. J. Siegfeldt & J. N. Whelan & P. A. Zitlau, 1965. "Nonpartisan Political Redistricting by Computer," Operations Research, INFORMS, vol. 13(6), pages 998-1006, December.
    14. Beraldi, P. & Bruni, M.E., 2009. "A probabilistic model applied to emergency service vehicle location," European Journal of Operational Research, Elsevier, vol. 196(1), pages 323-331, July.
    15. Rodolfo Carvajal & Miguel Constantino & Marcos Goycoolea & Juan Pablo Vielma & Andrés Weintraub, 2013. "Imposing Connectivity Constraints in Forest Planning Models," Operations Research, INFORMS, vol. 61(4), pages 824-836, August.
    16. 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.
    17. 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.
    18. GARFINKEL, Robert S. & NEMHAUSER, Geroge L., 1970. "Optimal political districting by implicit enumeration techniques," LIDAM Reprints CORE 54, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    19. Önal, Hayri & Wang, Yicheng & Dissanayake, Sahan T.M. & Westervelt, James D., 2016. "Optimal design of compact and functionally contiguous conservation management areas," European Journal of Operational Research, Elsevier, vol. 251(3), pages 957-968.
    20. Farahani, Reza Zanjirani & Rezapour, Shabnam & Drezner, Tammy & Fallah, Samira, 2014. "Competitive supply chain network design: An overview of classifications, models, solution techniques and applications," Omega, Elsevier, vol. 45(C), pages 92-118.
    21. Syam, Siddhartha S. & Côté, Murray J., 2010. "A location-allocation model for service providers with application to not-for-profit health care organizations," Omega, Elsevier, vol. 38(3-4), pages 157-166, June.
    22. Andris A. Zoltners & Prabhakant Sinha, 1983. "Sales Territory Alignment: A Review and Model," Management Science, INFORMS, vol. 29(11), pages 1237-1256, November.
    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. 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.
    2. R. Church & J. C. Duque & D. E. Restrepo, 2020. "The p-Innovation ecosystems model," Papers 2008.05885,
    3. 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.
    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. F Caro & T Shirabe & M Guignard & A Weintraub, 2004. "School redistricting: embedding GIS tools with integer programming," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 55(8), pages 836-849, August.
    6. 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.
    7. Sommer Gentry & Eric Chow & Allan Massie & Dorry Segev, 2015. "Gerrymandering for Justice: Redistricting U.S. Liver Allocation," Interfaces, INFORMS, vol. 45(5), pages 462-480, October.
    8. 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.
    9. 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.
    10. 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).
    11. 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.
    12. Tammy Drezner & Zvi Drezner, 2011. "A note on equity across groups in facility location," Naval Research Logistics (NRL), John Wiley & Sons, vol. 58(7), pages 705-711, October.
    13. 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.
    14. Anderson Kenji Hirose & Cassius Tadeu Scarpin & José Eduardo Pécora Junior, 2020. "Goal programming approach for political districting in Santa Catarina State: Brazil," Annals of Operations Research, Springer, vol. 287(1), pages 209-232, April.
    15. 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.
    16. Oded Berman & Zvi Drezner & Arie Tamir & George Wesolowsky, 2009. "Optimal location with equitable loads," Annals of Operations Research, Springer, vol. 167(1), pages 307-325, March.
    17. 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.
    18. Alexander Butsch & Jörg Kalcsics & Gilbert Laporte, 2014. "Districting for Arc Routing," INFORMS Journal on Computing, INFORMS, vol. 26(4), pages 809-824, November.
    19. 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.
    20. Van Engeland, Jens & Beliën, Jeroen & De Boeck, Liesje & De Jaeger, Simon, 2020. "Literature review: Strategic network optimization models in waste reverse supply chains," Omega, Elsevier, vol. 91(C).


    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:eee:ejores:v:287:y:2020:i:3:p:1120-1130. 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: Catherine Liu (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.