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In this paper, we propose the Ordered Median Tree Location Problem (OMT). TheOMT is a single-allocation facility location problem where p facilities must beplaced on a network connected by a non-directed tree. The objective is tominimize the sum of the ordered weighted averaged allocation costs plus the sumof the costs of connecting the facilities in the tree. We present differentMILP formulations for the OMT based on properties of the minimum spanning treeproblem and the ordered median optimization. Given that ordered median hublocation problems are rather difficult to solve we have improved the OMTsolution performance by introducing covering variables in a valid reformulationplus developing two pre-processing phases to reduce the size of thisformulations. In addition, we propose a Benders decomposition algorithm toapproach the OMT. We establish an empirical comparison between these newformulations and we also provide enhancements that together with a properformulation allow to solve medium size instances on general random graphs.

An extended version of the Ordered Median Tree Location Problem including appendices and detailed computational results