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In this paper, we address the Continuous Multifacility Monotone OrderedMedian Problem. This problem minimizes a monotone ordered weighted medianfunction of the distances between given demand points in $\mathbb{R}^d$ and itsclosest facility among the $p$ selected, also in a continuous space. We proposea new branch-and-price procedure for this problem, and two mathehuristics. Oneof them is a decomposition-based procedure and the other an aggregation-basedheuristic. We give detailed discussions of the validity of the exactformulations and also specify the implementation details of all the solutionprocedures. Besides, we assess their performance in an extensive computationalexperience that shows the superiority of the branch-and-price approach over thecompact formulation in medium-sized instances. To handle larger instances it isadvisable to resort to the matheuristics that also report rather good results.

A Branch-and-Price approach for the Continuous Multifacility Monotone Ordered Median Problem