# Stochastic analysis of ordered median problems

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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 *k*th 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### References

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