Assessing Continuous Demand Representation in Coverage Modeling

1. Introduction Minimizing costs and maximizing coverage are common goals in many planning contexts. Examples include locating fire stations to guarantee immediate response to calls for service, placing emergency warning sirens to alert the public of impending danger, or siting cellular towers to allow widespread access of wireless broadband. To support these planning problems, spatial optimization problem are utilized. This necessitates an abstraction of both the planning problem as well as geographic space. Unfortunately, such abstraction results in unintended errors when traditional spatial optimization coverage models are applied. In order to reduce coverage errors caused by spatial abstraction, a number of geographic representation schemes have been proposed. One intriguing approach relies on vector GIS based overlay as a way to identify the finest level of geographic resolution needed for a demand region in order to eliminate representation errors. However, this involves many GIS/geometric operations, such as polygon overlay and partitioning that are well-known to be computationally intensive (De Berg et al. 2008). Combined with issues of potential facility locations, it is possible that the resulting number demand units using overlay is excessive and beyond computational capabilities. This paper therefore investigates the operational and computational challenges of polygon overlay for representing continuous demand in coverage models, an issue that has yet to be explicitly studied. The analysis results provide insight regarding expected problem sizes and computation requirements if this is relied upon in coverage modeling.