Error bounds for the approximative solution of restricted planar location problems

Abstract

Facility location problems in the plane play an important role in mathematical programming. When looking for new locations in modeling real-world problems, we are often confronted with forbidden regions, that are not feasible for the placement of new locations. Furthermore these forbidden regions may have complicated shapes, even if we require them to be convex. It may be more useful or even necessary to use approximations of such forbidden regions when trying to solve location problems. In this paper, we develop error bounds for the approximative solution of restricted planar location problems using the so called sandwich algorithm. The number of approximation steps required to achieve a specified error bound is analyzed. As examples of these approximation schemes, we discuss round norms and polyhedral norms. Computational tests are also included.