Exact and approximate heuristics for the rectilinear Weber location problem with a line barrier

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.