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Finite Dominating Sets for Network Location Problems

Author

Listed:
  • J. N. Hooker

    (Carnegie Mellon University, Pittsburgh, Pennsylvania)

  • R. S. Garfinkel

    (University of Connecticut, Storrs, Connecticut)

  • C. K. Chen

    (Petro Canada, Donmills, Ontario, Canada)

Abstract

A research theme involving location on networks, since its inception, has been the identification of a finite dominating set (FDS), or a finite set of points to which an optimal solution must belong. We attempt to unify and generalize results of this sort. We survey the literature and then prove some theorems that subsume most previous results and that are, at the same time, more general than previous results. The paper is aimed primarily at investigators who wish to know whether an FDS exists for a specific problem.

Suggested Citation

  • J. N. Hooker & R. S. Garfinkel & C. K. Chen, 1991. "Finite Dominating Sets for Network Location Problems," Operations Research, INFORMS, vol. 39(1), pages 100-118, February.
    • Handle: RePEc:inm:oropre:v:39:y:1991:i:1:p:100-118
    DOI: 10.1287/opre.39.1.100
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    Citations

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    Cited by:

    1. Tsouros, C. & Satratzemi, M., 1996. "Optimal solution of a total time distribution problem," International Journal of Production Economics, Elsevier, vol. 45(1-3), pages 473-478, August.
    2. Li, Hongmei & Luo, Taibo & Xu, Yinfeng & Xu, Jiuping, 2018. "Minimax regret vertex centdian location problem in general dynamic networks," Omega, Elsevier, vol. 75(C), pages 87-96.
    3. Conde, Eduardo, 2007. "Minmax regret location-allocation problem on a network under uncertainty," European Journal of Operational Research, Elsevier, vol. 179(3), pages 1025-1039, June.
    4. R. Francis & T. Lowe & M. Rayco & A. Tamir, 2009. "Aggregation error for location models: survey and analysis," Annals of Operations Research, Springer, vol. 167(1), pages 171-208, March.
    5. A. Rodríguez-Chía & J. Puerto & D. Pérez-Brito & J. Moreno, 2005. "Thep-facility ordered median problem on networks," TOP: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 13(1), pages 105-126, June.
    6. Bapna, Ravi & Thakur, Lakshman S. & Nair, Suresh K., 2002. "Infrastructure development for conversion to environmentally friendly fuel," European Journal of Operational Research, Elsevier, vol. 142(3), pages 480-496, November.
    7. Marilène Cherkesly & Claudio Contardo, 2021. "The conditional p-dispersion problem," Journal of Global Optimization, Springer, vol. 81(1), pages 23-83, September.
    8. R. L. Francis & T. J. Lowe & Arie Tamir, 2000. "Aggregation Error Bounds for a Class of Location Models," Operations Research, INFORMS, vol. 48(2), pages 294-307, April.
    9. Eliş, Haluk & Tansel, Barbaros & Oğuz, Osman & Güney, Mesut & Kian, Ramez, 2021. "On guarding real terrains: The terrain guarding and the blocking path problems," Omega, Elsevier, vol. 102(C).
    10. Rafael Suárez-Vega & Dolores Santos-Peñate & Pablo Dorta-González, 2014. "Location and quality selection for new facilities on a network market," The Annals of Regional Science, Springer;Western Regional Science Association, vol. 52(2), pages 537-560, March.
    11. Carrizosa, Emilio & Conde, Eduardo, 2002. "A fractional model for locating semi-desirable facilities on networks," European Journal of Operational Research, Elsevier, vol. 136(1), pages 67-80, January.
    12. E. Carrizosa & E. Conde & M. Muñoz-Márquez, 1998. "Admission Policies in Loss Queueing Models with Heterogeneous Arrivals," Management Science, INFORMS, vol. 44(3), pages 311-320, March.
    13. Berman, Oded & Drezner, Zvi, 2000. "A note on the location of an obnoxious facility on a network," European Journal of Operational Research, Elsevier, vol. 120(1), pages 215-217, January.
    14. Kress, Dominik & Pesch, Erwin, 2012. "Sequential competitive location on networks," European Journal of Operational Research, Elsevier, vol. 217(3), pages 483-499.
    15. López-de-los-Mozos, M.C. & Mesa, Juan A. & Schöbel, Anita, 2017. "A general approach for the location of transfer points on a network with a trip covering criterion and mixed distances," European Journal of Operational Research, Elsevier, vol. 260(1), pages 108-121.
    16. Michael Kuby & Seow Lim, 2007. "Location of Alternative-Fuel Stations Using the Flow-Refueling Location Model and Dispersion of Candidate Sites on Arcs," Networks and Spatial Economics, Springer, vol. 7(2), pages 129-152, June.
    17. Francis, R. L. & Lowe, T. J. & Tamir, A. & Emir-Farinas, H., 2004. "A framework for demand point and solution space aggregation analysis for location models," European Journal of Operational Research, Elsevier, vol. 159(3), pages 574-585, December.
    18. Haluk Eliş, 2017. "A finite dominating set of cardinality O(k) and a witness set of cardinality O(n) for 1.5D terrain guarding problem," Annals of Operations Research, Springer, vol. 254(1), pages 37-46, July.
    19. Oded Berman & Zvi Drezner & George O. Wesolowsky, 2002. "The collection depots location problem on networks," Naval Research Logistics (NRL), John Wiley & Sons, vol. 49(1), pages 15-24, February.
    20. Robert Cromley & Dean Hanink, 2008. "Population growth and the development of a central place system," Journal of Geographical Systems, Springer, vol. 10(4), pages 383-405, December.
    21. Lin, Zhenhong & Ogden, Joan & Fan, Yueyue & Chen, Chien-Wei, 2009. "The Fuel-Travel-Back Approach to Hydrogen Station Siting," Institute of Transportation Studies, Working Paper Series qt14p44238, Institute of Transportation Studies, UC Davis.

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    Keywords

    networks/graphs: location on networks;

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