IDEAS home Printed from https://ideas.repec.org/a/eee/ejores/v220y2012i2p320-327.html
   My bibliography  Save this article

Some heuristic methods for solving p-median problems with a coverage constraint

Author

Listed:
  • Sáez-Aguado, Jesús
  • Trandafir, Paula Camelia

Abstract

The aim of this paper is to solve p-median problems with an additional coverage constraint. These problems arise in location applications, when the trade-off between distance and coverage is being calculated. Three kinds of heuristic algorithms are developed. First, local search procedures are designed both for constructing and improving feasible solutions. Second, a multistart GRASP heuristic is developed, based on the previous local search methods. Third, by employing Lagrangean relaxation methods, a very efficient Lagrangean heuristic algorithm is designed, which extends the well known algorithm of Handler and Zang, for constrained shortest path problems, to constrained p-median problems. Finally, a comparison of the computational efficiency of the developed methods is made between a variety of problems of different sizes.

Suggested Citation

  • Sáez-Aguado, Jesús & Trandafir, Paula Camelia, 2012. "Some heuristic methods for solving p-median problems with a coverage constraint," European Journal of Operational Research, Elsevier, vol. 220(2), pages 320-327.
    • Handle: RePEc:eee:ejores:v:220:y:2012:i:2:p:320-327
    DOI: 10.1016/j.ejor.2012.02.011
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0377221712001282
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.ejor.2012.02.011?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. Olivier Briant & Denis Naddef, 2004. "The Optimal Diversity Management Problem," Operations Research, INFORMS, vol. 52(4), pages 515-526, August.
    2. Monique Guignard, 2003. "Lagrangean relaxation," TOP: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 11(2), pages 151-200, December.
    3. Resende, Mauricio G.C. & Werneck, Renato F., 2006. "A hybrid multistart heuristic for the uncapacitated facility location problem," European Journal of Operational Research, Elsevier, vol. 174(1), pages 54-68, October.
    4. Labbé, M. & Peeters, D. & Thisse, J.-F., 1995. "Location on Network. Network Routing," LIDAM Reprints CORE 1182, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    5. 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.
    6. Mladenovic, Nenad & Brimberg, Jack & Hansen, Pierre & Moreno-Perez, Jose A., 2007. "The p-median problem: A survey of metaheuristic approaches," European Journal of Operational Research, Elsevier, vol. 179(3), pages 927-939, June.
    7. labbe, M. & Peeters, D. & Thisse, J.F., 1992. "Location on Networks," Papers 9216, Universite Libre de Bruxelles - C.E.M.E..
    8. John M. Mulvey & Harlan P. Crowder, 1979. "Cluster Analysis: An Application of Lagrangian Relaxation," Management Science, INFORMS, vol. 25(4), pages 329-340, April.
    9. Mauricio Resende & Renato Werneck, 2007. "A fast swap-based local search procedure for location problems," Annals of Operations Research, Springer, vol. 150(1), pages 205-230, March.
    10. B. L. Fox & D. M. Landi, 1970. "Searching for the Multiplier in One-Constraint Optimization Problems," Operations Research, INFORMS, vol. 18(2), pages 253-262, April.
    11. Alberto Caprara & Matteo Fischetti & Paolo Toth, 1999. "A Heuristic Method for the Set Covering Problem," Operations Research, INFORMS, vol. 47(5), pages 730-743, October.
    12. Nozick, L. K., 2001. "The fixed charge facility location problem with coverage restrictions," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 37(4), pages 281-296, August.
    13. Juan Villegas & Fernando Palacios & Andrés Medaglia, 2006. "Solution methods for the bi-objective (cost-coverage) unconstrained facility location problem with an illustrative example," Annals of Operations Research, Springer, vol. 147(1), pages 109-141, October.
    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. Jianing Zhi & Burcu B. Keskin, 2018. "A Multi-Product Production/Distribution System Design Problem with Direct Shipments and Lateral Transshipments," Networks and Spatial Economics, Springer, vol. 18(4), pages 937-972, December.
    2. Jesús Sáez-Aguado & Paula Camelia Trandafir, 2018. "Variants of the $$ \varepsilon $$ ε -constraint method for biobjective integer programming problems: application to p-median-cover problems," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 87(2), pages 251-283, April.
    3. Santi, Éverton & Aloise, Daniel & Blanchard, Simon J., 2016. "A model for clustering data from heterogeneous dissimilarities," European Journal of Operational Research, Elsevier, vol. 253(3), pages 659-672.

    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. J Brimberg & P Hansen & G Laporte & N Mladenović & D Urošević, 2008. "The maximum return-on-investment plant location problem with market share," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 59(3), pages 399-406, March.
    2. Michael Brusco & Hans-Friedrich Köhn, 2009. "Exemplar-Based Clustering via Simulated Annealing," Psychometrika, Springer;The Psychometric Society, vol. 74(3), pages 457-475, September.
    3. Amaldi, Edoardo & Coniglio, Stefano, 2013. "A distance-based point-reassignment heuristic for the k-hyperplane clustering problem," European Journal of Operational Research, Elsevier, vol. 227(1), pages 22-29.
    4. B. Jayalakshmi & Alok Singh, 2017. "A hybrid artificial bee colony algorithm for the p-median problem with positive/negative weights," OPSEARCH, Springer;Operational Research Society of India, vol. 54(1), pages 67-93, March.
    5. Wangshu Mu & Daoqin Tong, 2020. "On solving large p-median problems," Environment and Planning B, , vol. 47(6), pages 981-996, July.
    6. Francisco Casas & Claudio E. Torres & Ignacio Araya, 2022. "A heuristic search based on diversity for solving combinatorial problems," Journal of Heuristics, Springer, vol. 28(3), pages 287-328, June.
    7. Sayarshad, Hamid R. & Chow, Joseph Y.J., 2017. "Non-myopic relocation of idle mobility-on-demand vehicles as a dynamic location-allocation-queueing problem," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 106(C), pages 60-77.
    8. Antiopi Panteli & Basilis Boutsinas & Ioannis Giannikos, 2021. "On solving the multiple p-median problem based on biclustering," Operational Research, Springer, vol. 21(1), pages 775-799, March.
    9. de Palma, André & Lindsey, Robin, 2001. "Optimal timetables for public transportation," Transportation Research Part B: Methodological, Elsevier, vol. 35(8), pages 789-813, September.
    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. Michael Brusco & Douglas Steinley, 2015. "Affinity Propagation and Uncapacitated Facility Location Problems," Journal of Classification, Springer;The Classification Society, vol. 32(3), pages 443-480, October.
    12. Joshua Q. Hale & Enlu Zhou & Jiming Peng, 2017. "A Lagrangian search method for the P-median problem," Journal of Global Optimization, Springer, vol. 69(1), pages 137-156, September.
    13. C. Beltran-Royo & J.-P. Vial & A. Alonso-Ayuso, 2012. "Semi-Lagrangian relaxation applied to the uncapacitated facility location problem," Computational Optimization and Applications, Springer, vol. 51(1), pages 387-409, January.
    14. Jacques-Francois Thisse, 2014. "The New Science of Cities by Michael Batty: The Opinion of an Economist," Journal of Economic Literature, American Economic Association, vol. 52(3), pages 805-819, September.
    15. Vladimir Marianov & Daniel Serra, 2009. "Median problems in networks," Economics Working Papers 1151, Department of Economics and Business, Universitat Pompeu Fabra.
    16. Brimberg, Jack & Drezner, Zvi & Mladenović, Nenad & Salhi, Said, 2014. "A new local search for continuous location problems," European Journal of Operational Research, Elsevier, vol. 232(2), pages 256-265.
    17. Irawan, Chandra Ade & Salhi, Said & Scaparra, Maria Paola, 2014. "An adaptive multiphase approach for large unconditional and conditional p-median problems," European Journal of Operational Research, Elsevier, vol. 237(2), pages 590-605.
    18. C. Arbib & F. Marinelli, 2009. "Exact and Asymptotically Exact Solutions for a Class of Assortment Problems," INFORMS Journal on Computing, INFORMS, vol. 21(1), pages 13-25, February.
    19. Duran-Mateluna, Cristian & Ales, Zacharie & Elloumi, Sourour, 2023. "An efficient benders decomposition for the p-median problem," European Journal of Operational Research, Elsevier, vol. 308(1), pages 84-96.
    20. Carreras, Miquel & Serra, Daniel, 1999. "On optimal location with threshold requirements," Socio-Economic Planning Sciences, Elsevier, vol. 33(2), pages 91-103, June.

    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:220:y:2012:i:2:p:320-327. 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.