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The multicriteria p-facility median location problem on networks

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  • Kalcsics, Jörg
  • Nickel, Stefan
  • Pozo, Miguel A.
  • Puerto, Justo
  • Rodríguez-Chía, Antonio M.

Abstract

In this paper we discuss the multicriteria p-facility median location problem on networks with positive and negative weights. We assume that the demand is located at the nodes and can be different for each criterion under consideration. The goal is to obtain the set of Pareto-optimal locations in the graph and the corresponding set of non-dominated objective values. To that end, we first characterize the linearity domains of the distance functions on the graph and compute the image of each linearity domain in the objective space. The lower envelope of a transformation of all these images then gives us the set of all non-dominated points in the objective space and its preimage corresponds to the set of all Pareto-optimal solutions on the graph. For the bicriteria 2-facility case we present a low order polynomial time algorithm. Also for the general case we propose an efficient algorithm, which is polynomial if the number of facilities and criteria is fixed.

Suggested Citation

  • Kalcsics, Jörg & Nickel, Stefan & Pozo, Miguel A. & Puerto, Justo & Rodríguez-Chía, Antonio M., 2014. "The multicriteria p-facility median location problem on networks," European Journal of Operational Research, Elsevier, vol. 235(3), pages 484-493.
    • Handle: RePEc:eee:ejores:v:235:y:2014:i:3:p:484-493
    DOI: 10.1016/j.ejor.2014.01.003
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    References listed on IDEAS

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    Cited by:

    1. Bargos, Fabiano Fernandes & Lamas, Wendell de Queiroz & Bargos, Danubia Caporusso & Neto, Morun Bernardino & Pardal, Paula Cristiane Pinto Mesquita, 2016. "Location problem method applied to sugar and ethanol mills location optimization," Renewable and Sustainable Energy Reviews, Elsevier, vol. 65(C), pages 274-282.
    2. Blanco, Víctor & Puerto, Justo & Ben-Ali, Safae El-Haj, 2016. "Continuous multifacility ordered median location problems," European Journal of Operational Research, Elsevier, vol. 250(1), pages 56-64.
    3. Nicolas Fröhlich & Stefan Ruzika, 2022. "Interdicting facilities in tree networks," TOP: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 30(1), pages 95-118, April.
    4. Nickel, Stefan & Velten, Sebastian, 2017. "Optimization problems with flexible objectives: A general modeling approach and applications," European Journal of Operational Research, Elsevier, vol. 258(1), pages 79-88.

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