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Mass transportation and the consistency of the empirical optimal conditional locations

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  • Florent Bonneu
  • Abdelaati Daouia

Abstract

We consider the problem of finding the optimal locations of new facilities given the locations of existing facilities and clients. We analyze the general situation where the locations of existing facilities are deterministic while the locations of clients are stochastic with the same unknown marginal distribution. We show how this conditional location-allocation problem can be modeled as a variation of the standard Monge-Kantorovich mass transference problem. We provide a probabilistic formulation of the optimal locations of the new facilities and derive consistent estimators of these theoretical locations from a sample of identically distributed random clients. The integrity of our method is illustrated through some simulation experiments and a real case study. Copyright Springer Science+Business Media, LLC 2010

Suggested Citation

  • Florent Bonneu & Abdelaati Daouia, 2010. "Mass transportation and the consistency of the empirical optimal conditional locations," Annals of Operations Research, Springer, vol. 181(1), pages 159-170, December.
    • Handle: RePEc:spr:annopr:v:181:y:2010:i:1:p:159-170:10.1007/s10479-010-0711-4
    DOI: 10.1007/s10479-010-0711-4
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    1. Cuesta-Albertos, J. A. & Matrán, C. & Tuero-Diaz, A., 1997. "Optimal Transportation Plans and Convergence in Distribution," Journal of Multivariate Analysis, Elsevier, vol. 60(1), pages 72-83, January.
    2. Bonneu, Florent & Thomas-Agnan, Christine, 2009. "Spatial point process models for location-allocation problems," Computational Statistics & Data Analysis, Elsevier, vol. 53(8), pages 3070-3081, June.
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    Cited by:

    1. Daouia, Abdelaati & Van Keilegom, Ingrid, 2015. "A random locational M-estimation problem based on the L2-Wasserstein distance," LIDAM Discussion Papers ISBA 2015017, Université catholique de Louvain, Institute of Statistics, Biostatistics and Actuarial Sciences (ISBA).

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