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Location Problems with Multiple Criteria

In: Location Science

Author

Listed:
  • S. Nickel

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

  • J. Puerto

    (Universidad de Sevilla, IMUS)

  • A. 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

  • S. Nickel & J. Puerto & A. M. Rodríguez-Chía, 2019. "Location Problems with Multiple Criteria," Springer Books, in: Gilbert Laporte & Stefan Nickel & Francisco Saldanha da Gama (ed.), Location Science, edition 2, chapter 0, pages 215-260, Springer.
    • Handle: RePEc:spr:sprchp:978-3-030-32177-2_9
    DOI: 10.1007/978-3-030-32177-2_9
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