IDEAS home Printed from https://ideas.repec.org/a/eee/ejores/v241y2015i3p622-630.html
   My bibliography  Save this article

On the unified dispersion problem: Efficient formulations and exact algorithms

Author

Listed:
  • Lei, Ting L.
  • Church, Richard L.

Abstract

Facility dispersion problems involve placing a number of facilities as far apart from each other as possible. Four different criteria of facility dispersal have been proposed in the literature (Erkut & Neuman, 1991). Despite their formal differences, these four classic dispersion objectives can be expressed in a unified model called the partial-sum dispersion model (Lei & Church, 2013). In this paper, we focus on the unweighted partial sum dispersion problem and introduce an efficient formulation for this generalized dispersion problem based on a construct by Ogryczak and Tamir (2003). We also present a fast branch-and-bound based exact algorithm.

Suggested Citation

  • Lei, Ting L. & Church, Richard L., 2015. "On the unified dispersion problem: Efficient formulations and exact algorithms," European Journal of Operational Research, Elsevier, vol. 241(3), pages 622-630.
    • Handle: RePEc:eee:ejores:v:241:y:2015:i:3:p:622-630
    DOI: 10.1016/j.ejor.2014.10.020
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0377221714008418
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.ejor.2014.10.020?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
    ---><---

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

    References listed on IDEAS

    as
    1. Kevin Curtin & Richard Church, 2007. "Optimal dispersion and central places," Journal of Geographical Systems, Springer, vol. 9(2), pages 167-187, June.
    2. Thomas A. Feo & Mauricio G. C. Resende & Stuart H. Smith, 1994. "A Greedy Randomized Adaptive Search Procedure for Maximum Independent Set," Operations Research, INFORMS, vol. 42(5), pages 860-878, October.
    3. Prokopyev, Oleg A. & Kong, Nan & Martinez-Torres, Dayna L., 2009. "The equitable dispersion problem," European Journal of Operational Research, Elsevier, vol. 197(1), pages 59-67, August.
    4. Drezner, Tammy & Drezner, Zvi, 2007. "The gravity p-median model," European Journal of Operational Research, Elsevier, vol. 179(3), pages 1239-1251, June.
    5. Jerry R. Weaver & Richard L. Church, 1985. "A Median Location Model with Nonclosest Facility Service," Transportation Science, INFORMS, vol. 19(1), pages 58-74, February.
    6. D. R. Shier, 1977. "A Min-Max Theorem for p -Center Problems on a Tree," Transportation Science, INFORMS, vol. 11(3), pages 243-252, August.
    7. Hyun Kim, 2012. "P-hub protection models for survivable hub network design," Journal of Geographical Systems, Springer, vol. 14(4), pages 437-461, October.
    8. Rosing, K. E. & ReVelle, C. S., 1997. "Heuristic concentration: Two stage solution construction," European Journal of Operational Research, Elsevier, vol. 97(1), pages 75-86, February.
    9. Michael B. Teitz & Polly Bart, 1968. "Heuristic Methods for Estimating the Generalized Vertex Median of a Weighted Graph," Operations Research, INFORMS, vol. 16(5), pages 955-961, October.
    10. Erkut, Erhan, 1990. "The discrete p-dispersion problem," European Journal of Operational Research, Elsevier, vol. 46(1), pages 48-60, May.
    11. Fernández, Elena & Kalcsics, Jörg & Nickel, Stefan, 2013. "The maximum dispersion problem," Omega, Elsevier, vol. 41(4), pages 721-730.
    12. I. Douglas Moon & Sohail S. Chaudhry, 1984. "An Analysis of Network Location Problems with Distance Constraints," Management Science, INFORMS, vol. 30(3), pages 290-307, March.
    13. Ting L. Lei & Richard L. Church, 2011. "Constructs for Multilevel Closest Assignment in Location Modeling," International Regional Science Review, , vol. 34(3), pages 339-367, July.
    14. R A Whitaker, 1982. "Some Interchange Algorithms for Median Location Problems," Environment and Planning B, , vol. 9(2), pages 119-129, June.
    15. S. S. Ravi & D. J. Rosenkrantz & G. K. Tayi, 1994. "Heuristic and Special Case Algorithms for Dispersion Problems," Operations Research, INFORMS, vol. 42(2), pages 299-310, April.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Niblett, Matthew R. & Church, Richard L., 2015. "The disruptive anti-covering location problem," European Journal of Operational Research, Elsevier, vol. 247(3), pages 764-773.
    2. Sergey Kovalev & Isabelle Chalamon & Fabio J. Petani, 2023. "Maximizing single attribute diversity in group selection," Annals of Operations Research, Springer, vol. 320(1), pages 535-540, January.
    3. San Segundo, Pablo & Coniglio, Stefano & Furini, Fabio & Ljubić, Ivana, 2019. "A new branch-and-bound algorithm for the maximum edge-weighted clique problem," European Journal of Operational Research, Elsevier, vol. 278(1), pages 76-90.

    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. Martí, Rafael & Martínez-Gavara, Anna & Pérez-Peló, Sergio & Sánchez-Oro, Jesús, 2022. "A review on discrete diversity and dispersion maximization from an OR perspective," European Journal of Operational Research, Elsevier, vol. 299(3), pages 795-813.
    2. Sayyady, Fatemeh & Fathi, Yahya, 2016. "An integer programming approach for solving the p-dispersion problem," European Journal of Operational Research, Elsevier, vol. 253(1), pages 216-225.
    3. Erkut, E. & ReVelle, C. & Ulkusal, Y., 1996. "Integer-friendly formulations for the r-separation problem," European Journal of Operational Research, Elsevier, vol. 92(2), pages 342-351, July.
    4. Niblett, Matthew R. & Church, Richard L., 2015. "The disruptive anti-covering location problem," European Journal of Operational Research, Elsevier, vol. 247(3), pages 764-773.
    5. ReVelle, C. S. & Eiselt, H. A., 2005. "Location analysis: A synthesis and survey," European Journal of Operational Research, Elsevier, vol. 165(1), pages 1-19, August.
    6. Prokopyev, Oleg A. & Kong, Nan & Martinez-Torres, Dayna L., 2009. "The equitable dispersion problem," European Journal of Operational Research, Elsevier, vol. 197(1), pages 59-67, August.
    7. Anna Martínez-Gavara & Vicente Campos & Manuel Laguna & Rafael Martí, 2017. "Heuristic solution approaches for the maximum minsum dispersion problem," Journal of Global Optimization, Springer, vol. 67(3), pages 671-686, March.
    8. Gliesch, Alex & Ritt, Marcus, 2021. "A hybrid heuristic for the maximum dispersion problem," European Journal of Operational Research, Elsevier, vol. 288(3), pages 721-735.
    9. Batta, Rajan & Lejeune, Miguel & Prasad, Srinivas, 2014. "Public facility location using dispersion, population, and equity criteria," European Journal of Operational Research, Elsevier, vol. 234(3), pages 819-829.
    10. Tao Zhuolin & Zheng Qingjing & Kong Hui, 2018. "A Modified Gravity p-Median Model for Optimizing Facility Locations," Journal of Systems Science and Information, De Gruyter, vol. 6(5), pages 421-434, October.
    11. Parreño, Francisco & Álvarez-Valdés, Ramón & Martí, Rafael, 2021. "Measuring diversity. A review and an empirical analysis," European Journal of Operational Research, Elsevier, vol. 289(2), pages 515-532.
    12. Rolland, Erik & Schilling, David A. & Current, John R., 1997. "An efficient tabu search procedure for the p-Median Problem," European Journal of Operational Research, Elsevier, vol. 96(2), pages 329-342, January.
    13. Rennen, G., 2008. "Subset Selection from Large Datasets for Kriging Modeling," Discussion Paper 2008-26, Tilburg University, Center for Economic Research.
    14. Jackson, Laura E. & Rouskas, George N. & Stallmann, Matthias F.M., 2007. "The directional p-median problem: Definition, complexity, and algorithms," European Journal of Operational Research, Elsevier, vol. 179(3), pages 1097-1108, June.
    15. Nicolas Dupin & Frank Nielsen & El-Ghazali Talbi, 2021. "Unified Polynomial Dynamic Programming Algorithms for P-Center Variants in a 2D Pareto Front," Mathematics, MDPI, vol. 9(4), pages 1-30, February.
    16. Wang, Yang & Wu, Qinghua & Glover, Fred, 2017. "Effective metaheuristic algorithms for the minimum differential dispersion problem," European Journal of Operational Research, Elsevier, vol. 258(3), pages 829-843.
    17. Vladimir Marianov & Daniel Serra, 2009. "Median problems in networks," Economics Working Papers 1151, Department of Economics and Business, Universitat Pompeu Fabra.
    18. Loree, Nick & Aros-Vera, Felipe, 2018. "Points of distribution location and inventory management model for Post-Disaster Humanitarian Logistics," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 116(C), pages 1-24.
    19. Mark S. Daskin, 2008. "What you should know about location modeling," Naval Research Logistics (NRL), John Wiley & Sons, vol. 55(4), pages 283-294, June.
    20. Michael Brusco & Hans-Friedrich Köhn, 2009. "Exemplar-Based Clustering via Simulated Annealing," Psychometrika, Springer;The Psychometric Society, vol. 74(3), pages 457-475, September.

    More about this item

    Keywords

    Location; Facility dispersion;

    Statistics

    Access and download statistics

    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:eee:ejores:v:241:y:2015:i:3:p:622-630. 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: Catherine Liu (email available below). General contact details of provider: http://www.elsevier.com/locate/eor .

    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.