Mathematical Methods of Operations Research

, Volume 71, Issue 2, pp 283–306

Extensions to the continuous ordered median problem

Article

DOI: 10.1007/s00186-009-0296-3

Cite this article as:
Krebs, J. & Nickel, S. Math Meth Oper Res (2010) 71: 283. doi:10.1007/s00186-009-0296-3

Abstract

Classical location models fix an objective function and then attempt to find optimal points to this objective. In the last years a flexible approach, the ordered median problem, has been introduced. It handles a wide class of objectives, such as the median, the center and the centdian function. In this paper we present new properties of the ordered median problem such as solvability for the situation of attractive and repulsive locations. We also develop a new solution method that even yields local optimal points for non-convex objective functions. Furthermore, we discuss separability of ordered median problems without repulsion and derive a sufficient criterion. Finally, we introduce a useful model extension, the facility class model, which allows to deal with a wider range of real world problems in the ordered median setting.

Keywords

Ordered median problem Attraction and repulsion Solvability Non-convex optimization Separability Class model 

Copyright information

© Springer-Verlag 2009

Authors and Affiliations

  1. 1.Institut für Angewandte MathematikUniversität des SaarlandesSaarbrückenGermany
  2. 2.Institut für Operations ResearchUniversität Karlsruhe (TH)KarlsruheGermany