Skip to main content
SpringerLink
Log in

Polynomial algorithms for parametric minquantile and maxcovering planar location problems with locational constraints

  • Published:
Top Aims and scope Submit manuscript

Abstract

A location is sought within some convex region of the plane for the central site of some public service to a finite number of demand points. The parametric maxcovering problem consists in finding for eachR>0 the point from which the total weight of the demand points within distanceR is maximal. The parametric minimal quantile problem asks for each percentage α the point minimising the distance necessary for covering demand points of total weight at least α. We investigate the properties of these two closely related problems and derive polynomial algorithms to solve them both in case of either (possibly inflated) Euclidean or polyhedral distances.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  • Carrizosa, E. and F. Plastria (1995). On minquantile and maxcovering optimisation.Mathematical Programming,71, 101–112.

    Google Scholar 

  • Chazelle, B. and D.T. Lee (1986). On a circle placement problem.Computing,36, 1–16.

    Article  Google Scholar 

  • Church, R. and C. ReVelle (1974). Maximal covering location problem.Papers of Regional Science Association,32, 101–118.

    Article  Google Scholar 

  • Drezner, Z. (1981). On a modified one-center model.Management Science,27, 848–851.

    Article  Google Scholar 

  • Durier, R. and C. Michelot (1985). Geometrical properties of the Fermat-Weber problem.European Journal of Operational Research,20, 332–343.

    Article  Google Scholar 

  • Hearn, D.W. and J. Vijay (1982). Efficient algorithms for the (weighted) minimum circle problem.Operations Research,30, 777–795.

    Google Scholar 

  • Mehrez, A. and A. Stulman (1982). The maximal covering location problem with facility placement on the entire plane.Journal of Regional Science,22, 361–365.

    Article  Google Scholar 

  • Pelegrín, B., Michelot C. and F. Plastria (1985). On the uniqueness of optimal solutions in continuous location theory.European Journal of Operational Research,20, 327–331.

    Article  Google Scholar 

  • Tamir, A. (1993). Private communication.

Download references

Author information

Authors and Affiliations

  1. Departamento de Estadística e. I.O., Universidad de Sevilla, Tarfia s/n, 41012, Sevilla, Spain

    Emilio Carrizosa

  2. Center for Industrial Location, Vrije Universiteit Brussel, Pleinlaan, 2, 1050, Brussels, Belgium

    Frank Plastria

Authors
  1. Emilio Carrizosa
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Frank Plastria
    View author publications

    You can also search for this author in PubMed Google Scholar

Additional information

The research of the first author is partially supported by Grant PB96-1416-C02-02 of Ministerio de Educación y Cultura, Spain.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Carrizosa, E., Plastria, F. Polynomial algorithms for parametric minquantile and maxcovering planar location problems with locational constraints. Top 6, 179–194 (1998). https://doi.org/10.1007/BF02564786

Download citation

  • Received:

  • Accepted:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF02564786

Key Words

AMS subject classification

Search

Navigation