Finite-size facility placement in the presence of barriers to rectilinear travel

We consider the placement (location and orientation) of a single finite-size (finite-area, arbitrary shape) facility in the plane under the assumption that all travel occurs according to the rectilinear (or Manhattan) metric in the presence of impenetrable barriers to travel. Facility users are distributed over a finite set of demand points. The facility serves the users via a service point (server) located on the boundary of the facility. We consider an interactive model in the sense that there is interaction between not only the facility and the users, but also among the users themselves. We identify the candidates for optimal placement(s) for a facility with a fixed orientation and then for a facility with a fixed server location. Finally, we present a heuristic for the solution of the general problem, when the location and orientation are both unknown.