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

In this paper we consider the problem of locating one new facility 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 allowable. We provide a mixed-integer nonlinear programming model for this problem. The objective is to locate this single facility such that the sum of the rectilinear distances from the facility to the demand points is minimized. To illustrate the efficiency of the proposed model, a numerical example is tested

Keywords:

Facility location problem , Arc-shaped barrier , Nonlinear Programming Model , rectilinear distance