A lattice covering model for evaluating existing service facilities**A preliminary version of this article was presented at the RSAI Meetings in Charleston, SC, November 2001. We are grateful to John Hodgson and Harvey Miller for their comments

This article presents the following location problem: align a regularly spaced grid of new facilities as well as possible with a set of existing centres. The problem has some similarity to a problem in classical central place theory, namely the spatial arrangement of services with a particular range of coverage. The article poses the problem, gives a non linear formulation, and details solution approaches. A robust heuristic, based on geometric insights, is also devised: if the basis for the new grid is centred on at least one fixed centre, an enumeration of various rotation angles will be effective for finding local minima (and maxima). As a practical application of this problem, a region may wish to supplement an existing system of fixed siren locations with additional facilities in such a way as to fill in, or complete, the partial coverage pattern. An evaluation of the siren system in Dublin, OH, USA, is utilised to demonstrate the effectiveness of the technique.