In this paper, we address the Continuous Multifacility Monotone Ordered Median Problem. The goal of this problem is to locate $p$ facilities in ${\mathbb{R}}^d$ minimizing a monotone ordered weighted median function of the distances between given demand points and its closest facility. We propose a new branch-and-price procedure for this problem, and three families of matheuristics based on: solving heuristically the pricer problem, aggregating the demand points, and discretizing the decision space. We give detailed discussions of the validity of the exact formulations and also specify the implementation details of all the solution procedures. Besides, we assess their performances in an extensive computational experience that shows the superiority of the branch-and-price approach over the compact formulation in medium-sized instances. To handle larger instances it is advisable to resort to the matheuristics that also report rather good results.

在本文中，我们解决了连续多设施单调有序中值问题。这个问题的目标是定位$p$设施在${\mathbb{R}}^d$最小化给定需求点与其最近设施之间距离的单调有序加权中值函数。我们为这个问题提出了一个新的分支和价格程序，以及三个基于启发式的数学家族：启发式解决定价问题、聚合需求点和离散化决策空间。我们详细讨论了确切公式的有效性，并指定了所有解决方案的实施细节。此外，我们在广泛的计算经验中评估了它们的性能，这些经验表明分支价格方法优于中型实例中的紧凑公式。为了处理更大的实例，建议求助于也报告了相当好的结果的数学。