Distribution of the Closest Distance to a Rectangular Facility

This paper presents an analytical expression for the closest distance to a finite size facility. The closest distance is the distance from customers to the closest point on a facility, and represents the accessibility of customers to the facility. The distributions of the rectilinear closest distance are derived for rectangular facilities of grid and random configurations. The distributions demonstrate how the density, size, and shape of facilities affect the closest distance. A numerical example shows that if the area taken up by facilities is constant, many small facilities are better than a few large facilities and that rectangular facilities are better than square facilities.