Coverage optimization in continuous space facility siting

Abstract

Facility placement and associated service coverage are major concerns in urban and regional planning. In this paper an approach is detailed for the problem of covering spatial demand for service, where potential facilities are located in the continuous plane. It is shown that weighted demand, represented as points, lines or polygons, can be optimally served by a finite number of potential facility locations, called the polygon intersection point set (PIPS). The developed approach is an extension of a point‐based abstraction of demand to more general representations (e.g. points, lines or polygons). An empirical analysis of warning siren siting in Ohio is carried out, highlighting the applicability of this approach.

Keywords:

• Location modeling
• Spatial representation
• Geometry

Acknowledgments

The study was partially funded by the Center for Urban and Regional Analysis at Ohio State University and by the National Science Foundation (Geography and Regional Science and Decision, Risk and Management Science) under grant BCS‐0518967.

Notes

*. Richard Church originally presented this research at the ORSA/TIMS meeting in Philadelphia, PA, April 1976 (‘The planar maximal covering location problem’), with a manuscript produced as well. The paper was ultimately published with the same title (Church 1984).

*. Finding the smallest enclosing circle for an object, or set of points, is itself an optimization problem. It is also referred to as a minimum circle, minimum spanning circle, smallest enclosing circle, smallest enclosing disc or a minimal covering circle in the literature. A discussion and review of this problem is given in Wei et al. (2006).

*. If an intersection point does not exist for an object i, the object vertices (Step 2) are necessary critical points.