Combinatorial algorithms for some 1-facility median problems in the plane

Facility location problems in the plane are widely used tools of Operations Research in modeling real-world problems. In many of these problems restrictions have to be considered which correspond to regions in which a placement of new locations is forbidden. This paper investigates restrictions in 1-facility median problems in the plane. We introduce efficient algorithms for problems where the unrestricted problem can be solved in polynomial time. The algorithms are of a combinatorial nature and reduce the search for an optimal solution of the restricted problem to a finite number of candidates. The assumptions on the model are very weak. We only require that the forbidden area is a union of pairwise disjoint convex sets.