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Location of Dimensional Facilities in a Continuous Space

In: Location Science

Author

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  • Anita Schöbel

    (University of Göttingen)

Abstract

In many cases, the facilities to be located cannot be represented by isolated points, but may be modeled as dimensional structures. Examples for one-dimensional facilities are straight lines, line segments, or circles while boxes, strips, or balls are two-dimensional facilities. The goal of this chapter is to review the location of lines and circles in the plane and the location of hyperplanes and hyperspheres in higher dimensional spaces. We also discuss the location of some other dimensional facilities. We formulate the resulting location problems, point out some of their important properties and review the basic solution techniques and algorithmic approaches. Our focus lies on presenting a unified understanding of the common characteristics these problems have, and on reviewing the new findings obtained in this field within the last 10 years.

Suggested Citation

  • Anita Schöbel, 2015. "Location of Dimensional Facilities in a Continuous Space," Springer Books, in: Gilbert Laporte & Stefan Nickel & Francisco Saldanha da Gama (ed.), Location Science, edition 127, chapter 0, pages 135-175, Springer.
    • Handle: RePEc:spr:sprchp:978-3-319-13111-5_7
    DOI: 10.1007/978-3-319-13111-5_7
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