Placing a finite size facility with a center objective on a rectangular plane with barriers

This paper addresses the finite size l-center placement problem on a rectangular plane in the presence of barriers. Barriers are regions in which both facility location and travel through are prohibited. The feasible region for facility placement is subdivided into cells along the lines of Larson and Sadiq. To overcome complications induced by the center (minimax) objective, we analyze the resultant cells based on the cell corners. We study the problem when the facility orientation is known a priori. We obtain domination results when the facility is fully contained inside 1, 2 and 3-cornered cells. For full containment in a 4-cornered cell, we formulate the problem as a linear program.