A global optimal approach to facility location in the presence of forbidden regions

This paper addresses the planar 1-median problem with convex polygonal forbidden regions. A new facility is to be located to minimize the sum of weighted distances to a set of existing facilities such that the new facility is not located within any forbidden region, and no travel occurs through forbidden regions. A solution procedure using the ‘Big Square Small Square’ branch-and-bound method is developed, and used to find a global optimum.