In this paper, we study the k-level facility location problem with outliers (k-LFLPWO), which is an extension of the well-known k-level facility location problem (k-LFLP). In the k-LFLPWO, we are given k facility location sets, a client location set of cardinality n and a non-negative integer \(q<n\). Every facility location set has a different level which belongs to \(\{1, 2,\ldots , k\}\). For any facility location, there is an opening cost. For any two locations, there is a connecting cost. We wish to connect at least \(n-q\) clients to opened facilities from level 1 to level k, such that the total cost including opening costs and connecting costs is minimized. Our main contribution is to present a 6-approximation algorithm, which is based on the technique of primal-dual, for the k-LFLPWO.

在本文中，我们研究了具有异常值（k -LFLPWO）的k级设施选址问题，它是著名的k级设施选址问题（k -LFLP）的扩展。在k -LFLPWO中，我们得到了k个设施位置集，基数为n的客户位置集和非负整数\（q <n \）。每个设施位置集都有一个不同的级别，属于\（\ {1，2，\ ldots，k \} \）。对于任何设施地点，都有开场费。对于任何两个位置，都有连接费用。我们希望将至少\（nq \）个客户连接到1层到1层的开放设施k，从而使包括开放成本和连接成本在内的总成本最小化。我们的主要贡献是针对k -LFLPWO ，提出了一种基于原始对偶技术的6近似算法。