Comparative error bound theory for three location models: continuous demand versus discrete demand

We develop a unified error bound theory to compare a given p-median, p-center or covering location model with continuously distributed demand points in R <Superscript> n </Superscript> to a corresponding given original model of the same type having a finite collection of demand points in R <Superscript> n </Superscript>. We give ways to construct either a continuous or finite demand point model from the other model and also control the error bound. Our work uses Voronoi tilings extensively, and is related to earlier error bound theory for aggregating finitely many demand points. Copyright Sociedad de Estadística e Investigación Operativa 2014