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On $$\lambda $$ λ -cent-dians and generalized-center for network design: definitions and properties

Author

Listed:
  • Víctor Bucarey

    (Universidad de O’Higgins
    Instituto Sistemas Complejos de Ingeniería (ISCI))

  • Natividad González-Blanco

    (Universidad Loyola Andalucía)

  • Martine Labbé

    (Université Libre de Bruxelles
    Inria Lille-Nord Europe)

  • Juan A. Mesa

    (Universidad de Sevilla
    Universidad de Sevilla)

Abstract

In this paper, we extend the notions of $$\lambda $$ λ -cent-dian and generalized-center from Facility Location Theory to the more intricate domain of Network Design. Our focus is on the task of designing a sub-network within a given underlying network while adhering to a budget constraint. This sub-network is intended to efficiently serve a collection of origin/destination pairs of demand. The $$\lambda $$ λ -cent-dian problem studies the balance between efficiency and equity. We investigate the properties of the $$\lambda $$ λ -cent-dian and generalized-center solution networks under the lens of equity, efficiency, and Pareto-optimality. We finally prove that the problems solved here are NP-hard.

Suggested Citation

  • Víctor Bucarey & Natividad González-Blanco & Martine Labbé & Juan A. Mesa, 2025. "On $$\lambda $$ λ -cent-dians and generalized-center for network design: definitions and properties," Annals of Operations Research, Springer, vol. 347(3), pages 1193-1211, April.
    • Handle: RePEc:spr:annopr:v:347:y:2025:i:3:d:10.1007_s10479-025-06536-5
    DOI: 10.1007/s10479-025-06536-5
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    References listed on IDEAS

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    1. Anthony Przybylski & Xavier Gandibleux & Matthias Ehrgott, 2010. "A Recursive Algorithm for Finding All Nondominated Extreme Points in the Outcome Set of a Multiobjective Integer Programme," INFORMS Journal on Computing, INFORMS, vol. 22(3), pages 371-386, August.
    2. Jonathan Halpern, 1978. "Finding Minimal Center-Median Convex Combination (Cent-Dian) of a Graph," Management Science, INFORMS, vol. 24(5), pages 535-544, January.
    3. Mesa, Juan A. & Brian Boffey, T., 1996. "A review of extensive facility location in networks," European Journal of Operational Research, Elsevier, vol. 95(3), pages 592-603, December.
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