Locating and orienting facilities with anisotropic coverage

Siting facilities strategically is critical to ensure system design efficiency, enhance social equity and reduce operational costs. Coverage models look to optimize facility configuration, often to minimize the number of necessary facilities or maximize demand served within established proximity standards. Existing location models, such as maximal covering, often assume facility standards to be isotropic, resulting in a perceived circular service area. However, many facility proximity contexts, such as travel time on a transportation network, sound propagation, surveillance cameras and non-vertical lights, have irregular or noncircular service areas, potentially complicating existing coverage modeling approaches. Additionally, anisotropic coverage of facilities raises the issue of how to orient them when sited. The goal of this paper is to extend existing approaches to account for anisotropic coverage, simultaneously locating and orienting facilities. A location model is formulated to address anisotropic service coverage of facilities. A finite dominating set is derived, enabling reformulation as an integer programming problem that can be solved via branch and bound. Applications involving emergence response and surveillance camera placement in both 2-D and 3-D spaces demonstrate the effectiveness of this modeling extension. The resultant anisotropic coverage model addresses a critical aspect of system performance, highlighting that the omission of such considerations greatly overestimates what may be achieved in operation.