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The p-Median Problem

In: Location Science

Author

Listed:
  • Mark S. Daskin

    (University of Michigan)

  • Kayse Lee Maass

    (University of Michigan)

Abstract

The p-median problem is central to much of discrete location modeling and theory. While the p-median problem is $$ \mathcal{N}\mathcal{P} $$ -hard on a general graph, it can be solved in polynomial time on a tree. A linear time algorithm for the 1-median problem on a tree is described. We also present a classical formulation of the problem. Basic construction and improvement algorithms are outlined. Results from the literature using various metaheuristics including tabu search, heuristic concentration, genetic algorithms, and simulated annealing are summarized. A Lagrangian relaxation approach is presented and used for computational results on 40 classical test instances as well as a 500-node instance derived from the most populous counties in the contiguous United States. We conclude with a discussion of multi-objective extensions of the p-median problem.

Suggested Citation

  • Mark S. Daskin & Kayse Lee Maass, 2015. "The p-Median Problem," Springer Books, in: Gilbert Laporte & Stefan Nickel & Francisco Saldanha da Gama (ed.), Location Science, edition 127, chapter 0, pages 21-45, Springer.
    • Handle: RePEc:spr:sprchp:978-3-319-13111-5_2
    DOI: 10.1007/978-3-319-13111-5_2
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    Citations

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    Cited by:

    1. Huizing, Dylan & Schäfer, Guido & van der Mei, Rob D. & Bhulai, Sandjai, 2020. "The median routing problem for simultaneous planning of emergency response and non-emergency jobs," European Journal of Operational Research, Elsevier, vol. 285(2), pages 712-727.
    2. Sánchez-Oro, J. & López-Sánchez, A.D. & Hernández-Díaz, A.G. & Duarte, A., 2022. "GRASP with strategic oscillation for the α-neighbor p-center problem," European Journal of Operational Research, Elsevier, vol. 303(1), pages 143-158.
    3. Marilène Cherkesly & Claudio Contardo, 2021. "The conditional p-dispersion problem," Journal of Global Optimization, Springer, vol. 81(1), pages 23-83, September.
    4. Mercedes Landete & Gilbert Laporte, 2019. "Facility location problems with user cooperation," TOP: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 27(1), pages 125-145, April.
    5. Pawel Kalczynski & Jack Brimberg & Zvi Drezner, 2022. "Less is more: discrete starting solutions in the planar p-median problem," TOP: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 30(1), pages 34-59, April.
    6. Ashley, Thomas & Carrizosa, Emilio & Fernández-Cara, Enrique, 2019. "Heliostat field cleaning scheduling for Solar Power Tower plants: A heuristic approach," Applied Energy, Elsevier, vol. 235(C), pages 653-660.
    7. Buffat, René & Raubal, Martin, 2019. "Spatio-temporal potential of a biogenic micro CHP swarm in Switzerland," Renewable and Sustainable Energy Reviews, Elsevier, vol. 103(C), pages 443-454.
    8. Kalczynski, Pawel & Drezner, Zvi, 2022. "The Obnoxious Facilities Planar p-Median Problem with Variable Sizes," Omega, Elsevier, vol. 111(C).
    9. Musolino, Giuseppe & Rindone, Corrado & Polimeni, Antonio & Vitetta, Antonino, 2019. "Planning urban distribution center location with variable restocking demand scenarios: General methodology and testing in a medium-size town," Transport Policy, Elsevier, vol. 80(C), pages 157-166.
    10. 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.
    11. F. Antonio Medrano, 2020. "The complete vertex p-center problem," EURO Journal on Computational Optimization, Springer;EURO - The Association of European Operational Research Societies, vol. 8(3), pages 327-343, October.
    12. Rafael Bernardo Carmona-Benítez, 2020. "Dimensionality-reduction Procedure for the Capacitated p-Median Transportation Inventory Problem," Mathematics, MDPI, vol. 8(4), pages 1-16, March.
    13. Richard L. Church & Zvi Drezner & Pawel Kalczynski, 2023. "Extensions to the planar p-median problem," Annals of Operations Research, Springer, vol. 326(1), pages 115-135, July.
    14. Ranon Jientrakul & Chumpol Yuangyai & Klongkwan Boonkul & Pakinai Chaicharoenwut & Suriyaphong Nilsang & Sittiporn Pimsakul, 2022. "Integrating Spatial Risk Factors with Social Media Data Analysis for an Ambulance Allocation Strategy: A Case Study in Bangkok," Sustainability, MDPI, vol. 14(16), pages 1-15, August.
    15. Pawel Kalczynski & Zvi Drezner, 2021. "The obnoxious facilities planar p-median problem," OR Spectrum: Quantitative Approaches in Management, Springer;Gesellschaft für Operations Research e.V., vol. 43(2), pages 577-593, June.

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