Journal of the Operational Research Society

, Volume 63, Issue 11, pp 1578–1588

Stochastic analysis of ordered median problems

  • Z Drezner
  • S Nickel
  • H-P Ziegler
General Paper

DOI: 10.1057/jors.2012.2

Cite this article as:
Drezner, Z., Nickel, S. & Ziegler, HP. J Oper Res Soc (2012) 63: 1578. doi:10.1057/jors.2012.2
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Abstract

Many location problems can be expressed as ordered median objective. In this paper, we investigate the ordered median objective when the demand points are generated in a circle. We find the mean and variance of the kth distance from the centre of the circle and the correlation matrix between all pairs of ordered distances. By applying these values, we calculate the mean and variance of any ordered median objective and the correlation coefficient between two ordered median objectives. The usefulness of the results is demonstrated by calculating various probabilities such as: What is the probability that the mean distance is greater than the truncated mean distance? What is the probability that the maximum distance is greater than 0.9? What is the probability that the range of distances is greater than 0.8? An analysis of an illustrative example also demonstrates the usefulness of the analysis.

Keywords

location stochastic models ordered median order statistics 

Copyright information

© Operational Research Society 2012

Authors and Affiliations

  • Z Drezner
    • 1
  • S Nickel
    • 2
  • H-P Ziegler
    • 2
  1. 1.California State University-FullertonFullerton
  2. 2.Karlsruhe Institute of Technology (KIT)KarlsruheGermany