Continuous location model of a rectangular barrier facility

This paper develops a bi-objective model for determining the location, size, and shape of a finite-size facility. The objectives are to minimize both the closest and barrier distances. The closest distance represents the accessibility of customers, whereas the barrier distance represents the interference to travelers. The distributions of the closest and barrier distances are derived for a rectangular facility in a rectangular city where the distance is measured as the rectilinear distance. The analytical expressions for the distributions demonstrate how the location, size, and shape of the facility affect the closest and barrier distances. A numerical example shows that there exists a trade-off between the closest and barrier distances.