Abstract.
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.
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Received: 12 August 2002, Accepted: 21 May 2003,
JEL Classification:
R53
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.
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O’Kelly, M.E., Murray, A.T. A lattice covering model for evaluating existing service facilities. Papers Reg. Sci. 83, 565–580 (2004). https://doi.org/10.1007/s10110-004-0212-4
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DOI: https://doi.org/10.1007/s10110-004-0212-4