In this article, we propose an extension of the multi-Weber facility location problem with rectilinear-distance in the presence of passages over a non-horizontal line barrier. For the single-facility case, we develop an exact heuristic based on a divide-and-conquer approach that outperforms alternative heuristics available in literature. The multiple facilities case is solved by means of the application of an alternate-location-allocation heuristic, characterized by embedded exact and approximate procedures. For large instances, we propose a heuristic (with polynomial time complexity) which provides near-optimal solutions in a short computational time and a negligible gap. Finally, for testing purposes, we use a benchmark based on the transformation of the main problem into an equivalent p-median problem. Experimental results evidence the efficiency and validity of the proposed heuristics, which are capable of obtaining high quality solutions within acceptable computation times.

在本文中，我们提出了在非水平线障碍物上存在通道的情况下使用直线距离扩展多Weber设施位置问题的方法。对于单设施案例，我们基于分而治之方法开发了一种精确的启发式方法，该方法优于文献中提供的其他启发式方法。通过应用以嵌入式精确和近似过程为特征的交替位置-分配启发法，解决了多设施案例。对于大型实例，我们提出了一种启发式算法（具有多项式时间复杂度），该算法可在较短的计算时间内提供几乎最优的解决方案，并且可以忽略不计。最后，出于测试目的，我们使用基于主要问题到等效p中位数问题转换的基准。