A p-center grid-positioning aggregation procedure

Abstract

We present an algorithm for aggregating p-center demand points such that the resulting aggregate set imposes a grid structure on the plane consisting of identical “diamonds” of user-specified dimensions. The grid is positioned so that a well-defined upper bound on the objective function error is smallest. Scope and purpose A model often proposed for locating emergency service facilities is the p-center model. Its solution recommends locations for such facilities to minimize the maximum time (or distance) to respond to an emergency at some demand point. In an urban context, there could be millions of possible emergency demand points. Thus, it is common to aggregate demand points. The aggregation creates error. For a certain type of p-center problem, we present an aggregation procedure which can also be used to predict the maximum error, thus allowing the error to be kept within acceptable limits.