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Equity-Efficiency Bicriteria Location with Squared Euclidean Distances

Author

Listed:
  • Yoshiaki Ohsawa

    (Institute of Policy and Planning Sciences, University of Tsukuba, Tsukuba 305-8573, Japan)

  • Naoya Ozaki

    (Railway Technical Research Institute, Kokubunji 185-8540, Japan)

  • Frank Plastria

    (MOSI, Vrije Universiteit Brussel, Pleinlaan 2, B-1050 Brussels, Belgium)

Abstract

A facility must be located within a given region taking two criteria of equity and efficiency into account. Equity is sought by minimizing the inequality in the facility-inhabitant distances, as measured by the sum of the absolute differences between all pairs of squared Euclidean distances from inhabitants to the facility. This measure meets the Pigou-Dalton condition of transfers and can easily be minimized. Efficiency is measured through optimizing the sum of squared inhabitant-facility distances, either to be minimized or maximized for an attracting or repellent facility, respectively. Geometric localization results are obtained for the whole set of Pareto-optimal solutions for each of the two resulting bicriteria problems within a convex polygonal region. A polynomial procedure is developed to obtain the full bicriteria plot, both trade-off curves, and the corresponding efficient sets.

Suggested Citation

  • Yoshiaki Ohsawa & Naoya Ozaki & Frank Plastria, 2008. "Equity-Efficiency Bicriteria Location with Squared Euclidean Distances," Operations Research, INFORMS, vol. 56(1), pages 79-87, February.
    • Handle: RePEc:inm:oropre:v:56:y:2008:i:1:p:79-87
    DOI: 10.1287/opre.1070.0502
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    References listed on IDEAS

    as
    1. Yoshiaki Ohsawa & Kazuki Tamura, 2003. "Efficient Location for a Semi-Obnoxious Facility," Annals of Operations Research, Springer, vol. 123(1), pages 173-188, October.
    2. Marvin B. Mandell, 1991. "Modelling Effectiveness-Equity Trade-Offs in Public Service Delivery Systems," Management Science, INFORMS, vol. 37(4), pages 467-482, April.
    3. Drezner, Z. & Thisse, J.-F. & Wesolowsky, G.O., 1986. "The minimax-min location problem," LIDAM Reprints CORE 677, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    4. Egon Balas & Eitan Zemel, 1980. "An Algorithm for Large Zero-One Knapsack Problems," Operations Research, INFORMS, vol. 28(5), pages 1130-1154, October.
    5. Marsh, Michael T. & Schilling, David A., 1994. "Equity measurement in facility location analysis: A review and framework," European Journal of Operational Research, Elsevier, vol. 74(1), pages 1-17, April.
    6. Ogryczak, Wlodzimierz, 2000. "Inequality measures and equitable approaches to location problems," European Journal of Operational Research, Elsevier, vol. 122(2), pages 374-391, April.
    7. Ohsawa, Yoshiaki, 1999. "A geometrical solution for quadratic bicriteria location models," European Journal of Operational Research, Elsevier, vol. 114(2), pages 380-388, April.
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    Cited by:

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    2. Karsu, Özlem & Morton, Alec, 2015. "Inequity averse optimization in operational research," European Journal of Operational Research, Elsevier, vol. 245(2), pages 343-359.
    3. Maria Barbati & Giuseppe Bruno & Alfredo Marín, 2016. "Balancing the arrival times of users in a two-stage location problem," Annals of Operations Research, Springer, vol. 246(1), pages 273-288, November.
    4. Akoluk, Damla & Karsu, Özlem, 2022. "Ensuring multidimensional equality in public service," Socio-Economic Planning Sciences, Elsevier, vol. 80(C).
    5. Chung, Byung Do & Park, Sungjae & Kwon, Changhyun, 2018. "Equitable distribution of recharging stations for electric vehicles," Socio-Economic Planning Sciences, Elsevier, vol. 63(C), pages 1-11.
    6. Argyris, Nikolaos & Karsu, Özlem & Yavuz, Mirel, 2022. "Fair resource allocation: Using welfare-based dominance constraints," European Journal of Operational Research, Elsevier, vol. 297(2), pages 560-578.

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