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The Planar Two-Center and Two-Median Problems

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  • Zvi Drezner

    (The University of Michigan-Dearborn, Dearborn, Michigan)

Abstract

We present algorithms for the solution of planar location-allocation problems with two new facilities. Euclidean distances are assumed. We address both the minimax (or “two-center”), and minisum (or “two-median”) problems. Computational results are presented.

Suggested Citation

  • Zvi Drezner, 1984. "The Planar Two-Center and Two-Median Problems," Transportation Science, INFORMS, vol. 18(4), pages 351-361, November.
    • Handle: RePEc:inm:ortrsc:v:18:y:1984:i:4:p:351-361
    DOI: 10.1287/trsc.18.4.351
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    Citations

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    Cited by:

    1. Zvi Drezner & Jack Brimberg & Nenad Mladenović & Said Salhi, 2015. "Solving the planar p-median problem by variable neighborhood and concentric searches," Journal of Global Optimization, Springer, vol. 63(3), pages 501-514, November.
    2. Elshaikh, Abdalla & Salhi, Said & Nagy, Gábor, 2015. "The continuous p-centre problem: An investigation into variable neighbourhood search with memory," European Journal of Operational Research, Elsevier, vol. 241(3), pages 606-621.
    3. Prahalad Venkateshan & Kamlesh Mathur, 2015. "A Heuristic for the Multisource Weber Problem with Service Level Constraints," Transportation Science, INFORMS, vol. 49(3), pages 472-483, August.
    4. Klose, Andreas & Drexl, Andreas, 2005. "Facility location models for distribution system design," European Journal of Operational Research, Elsevier, vol. 162(1), pages 4-29, April.
    5. Díaz-Báñez, J.M. & Heredia, M. & Pelegrín, B. & Pérez-Lantero, P. & Ventura, I., 2011. "Finding all pure strategy Nash equilibria in a planar location game," European Journal of Operational Research, Elsevier, vol. 214(1), pages 91-98, October.
    6. Pey-Chun Chen & Pierre Hansen & Brigitte Jaumard & Hoang Tuy, 1998. "Solution of the Multisource Weber and Conditional Weber Problems by D.-C. Programming," Operations Research, INFORMS, vol. 46(4), pages 548-562, August.
    7. R. Chen & G. Y. Handler, 1987. "Relaxation method for the solution of the minimax location‐allocation problem in euclidean space," Naval Research Logistics (NRL), John Wiley & Sons, vol. 34(6), pages 775-788, December.
    8. Jack Brimberg & Pierre Hansen & Nenad Mladenović & Eric D. Taillard, 2000. "Improvements and Comparison of Heuristics for Solving the Uncapacitated Multisource Weber Problem," Operations Research, INFORMS, vol. 48(3), pages 444-460, June.
    9. Schöbel, Anita & Scholz, Daniel, 2014. "A solution algorithm for non-convex mixed integer optimization problems with only few continuous variables," European Journal of Operational Research, Elsevier, vol. 232(2), pages 266-275.
    10. Cem Iyigun, 2013. "The planar hub location problem: a probabilistic clustering approach," Annals of Operations Research, Springer, vol. 211(1), pages 193-207, December.
    11. Zvi Drezner & Said Salhi, 2017. "Incorporating neighborhood reduction for the solution of the planar p-median problem," Annals of Operations Research, Springer, vol. 258(2), pages 639-654, November.
    12. Zvi Drezner & Jack Brimberg & Nenad Mladenović & Said Salhi, 2016. "New local searches for solving the multi-source Weber problem," Annals of Operations Research, Springer, vol. 246(1), pages 181-203, November.
    13. Drexl, Andreas & Klose, Andreas, 2001. "Facility location models for distribution system design," Manuskripte aus den Instituten für Betriebswirtschaftslehre der Universität Kiel 546, Christian-Albrechts-Universität zu Kiel, Institut für Betriebswirtschaftslehre.
    14. 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.
    15. R. Chen & Y. Handler, 1993. "The conditional p‐center problem in the plane," Naval Research Logistics (NRL), John Wiley & Sons, vol. 40(1), pages 117-127, February.
    16. Lozano, S. & Guerrero, F. & Onieva, L. & Larraneta, J., 1998. "Kohonen maps for solving a class of location-allocation problems," European Journal of Operational Research, Elsevier, vol. 108(1), pages 106-117, July.
    17. Tammy Drezner & Zvi Drezner, 2016. "Sequential location of two facilities: comparing random to optimal location of the first facility," Annals of Operations Research, Springer, vol. 246(1), pages 5-18, November.
    18. Venkateshan, Prahalad & Ballou, Ronald H. & Mathur, Kamlesh & Maruthasalam, Arulanantha P.P., 2017. "A Two-echelon joint continuous-discrete location model," European Journal of Operational Research, Elsevier, vol. 262(3), pages 1028-1039.

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