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Demand Point Aggregation for Planar Covering Location Models

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  • H. Emir-Farinas
  • R. Francis

Abstract

The covering location problem seeks the minimum number of facilities such that each demand point is within some given radius of its nearest facility. Such a model finds application mostly in locating emergency types of facilities. Since the problem is NP-hard in the plane, a common practice is to aggregate the demand points in order to reduce the computational burden. Aggregation makes the size of the problem more manageable but also introduces error. Identifying and controlling the magnitude of the error is the subject of this study. We suggest several aggregation methods with a priori error bounds, and conduct experiments to compare their performance. We find that the manner by which infeasibility is measured greatly affects the best choice of an aggregation method. Copyright Springer Science + Business Media, Inc. 2005

Suggested Citation

  • H. Emir-Farinas & R. Francis, 2005. "Demand Point Aggregation for Planar Covering Location Models," Annals of Operations Research, Springer, vol. 136(1), pages 175-192, April.
    • Handle: RePEc:spr:annopr:v:136:y:2005:i:1:p:175-192:10.1007/s10479-005-2044-2
    DOI: 10.1007/s10479-005-2044-2
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    References listed on IDEAS

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    1. Zhao, Peiwu & Batta, Rajan, 1999. "Analysis of centroid aggregation for the Euclidean distance p-median problem," European Journal of Operational Research, Elsevier, vol. 113(1), pages 147-168, February.
    2. S. L. Hakimi, 1965. "Optimum Distribution of Switching Centers in a Communication Network and Some Related Graph Theoretic Problems," Operations Research, INFORMS, vol. 13(3), pages 462-475, June.
    3. R. L. Francis & T. J. Lowe & M. B. Rayco, 1996. "Row-Column Aggregation for Rectilinear Distance p -Median Problems," Transportation Science, INFORMS, vol. 30(2), pages 160-174, May.
    4. 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.
    5. ReVelle, Charles, 1989. "Review, extension and prediction in emergency service siting models," European Journal of Operational Research, Elsevier, vol. 40(1), pages 58-69, May.
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    Cited by:

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    2. Tapia-Ubeda, Francisco J. & Miranda, Pablo A. & Macchi, Marco, 2018. "A Generalized Benders Decomposition based algorithm for an inventory location problem with stochastic inventory capacity constraints," European Journal of Operational Research, Elsevier, vol. 267(3), pages 806-817.
    3. Liting Chen & Sebastian Wandelt & Weibin Dai & Xiaoqian Sun, 2022. "Scalable Vertiport Hub Location Selection for Air Taxi Operations in a Metropolitan Region," INFORMS Journal on Computing, INFORMS, vol. 34(2), pages 834-856, March.
    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. Vidovic, Milorad & Dimitrijevic, Branka & Ratkovic, Branislava & Simic, Vladimir, 2011. "A novel covering approach to positioning ELV collection points," Resources, Conservation & Recycling, Elsevier, vol. 57(C), pages 1-9.
    6. Carlos García-Alonso & Leonor Pérez-Naranjo & Juan Fernández-Caballero, 2014. "Multiobjective evolutionary algorithms to identify highly autocorrelated areas: the case of spatial distribution in financially compromised farms," Annals of Operations Research, Springer, vol. 219(1), pages 187-202, August.

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