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Location Problems with Multiple Criteria

In: Location Science

Author

Listed:
  • Stefan Nickel

    (Karlsruhe Institute of Technology (KIT)
    Fraunhofer Institute for Industrial Mathematics (ITWM))

  • Justo Puerto

    (Universidad de Sevilla)

  • Antonio M. Rodríguez-Chía

    (Universidad de Cádiz)

Abstract

This chapter analyzes multicriteria continuous, network, and discrete location problems. In the continuous framework, we provide a complete description of the set of weak Pareto, Pareto, and strict Pareto locations for a general Q-criteria location problem based on the characterization of three criteria problems. In the network case, the set of Pareto locations is characterized for general networks as well as for tree networks using the concavity and convexity properties of the distance function on the edges. In the discrete setting, the entire set of Pareto locations is characterized using rational generating functions of integer points in polytopes. Moreover, we describe algorithms to obtain the solutions sets (the different Pareto locations) using the above characterizations. We also include a detailed complexity analysis. A number of references has been cited throughout the chapter to avoid the inclusion of unnecessary technical details and also to be useful for a deeper analysis.

Suggested Citation

  • Stefan Nickel & Justo Puerto & Antonio M. Rodríguez-Chía, 2015. "Location Problems with Multiple Criteria," Springer Books, in: Gilbert Laporte & Stefan Nickel & Francisco Saldanha da Gama (ed.), Location Science, edition 127, chapter 0, pages 205-247, Springer.
    • Handle: RePEc:spr:sprchp:978-3-319-13111-5_9
    DOI: 10.1007/978-3-319-13111-5_9
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    Citations

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    Cited by:

    1. Alzorba, Shaghaf & Günther, Christian & Popovici, Nicolae & Tammer, Christiane, 2017. "A new algorithm for solving planar multiobjective location problems involving the Manhattan norm," European Journal of Operational Research, Elsevier, vol. 258(1), pages 35-46.
    2. Kınay, Ömer Burak & Saldanha-da-Gama, Francisco & Kara, Bahar Y., 2019. "On multi-criteria chance-constrained capacitated single-source discrete facility location problems," Omega, Elsevier, vol. 83(C), pages 107-122.
    3. Christian Günther & Christiane Tammer, 2016. "Relationships between constrained and unconstrained multi-objective optimization and application in location theory," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 84(2), pages 359-387, October.

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