Nonlinear Programming Model for the Facility Location Problem in the Presence of Arc-shaped Barrier

In this paper we consider the single facility location problem with respect to a given set of existing facilities in the presence of an arc-shaped barrier. A barrier is considered a region where neither facility location nor travelling is permitted. We present a mixed-integer nonlinear programming model for this single facility location problem. The objective of this problem is to locate this single facility such that the sum of the rectilinear distances from the facility to the demand points is minimized. Test problems are presented to illustrate the applicability of the proposed model.