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A lattice covering model for evaluating existing service facilities


  • Morton O’Kelly


  • Alan Murray



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. Copyright Springer-Verlag Berlin/Heidelberg 2004

Suggested Citation

  • Morton O’Kelly & Alan Murray, 2004. "A lattice covering model for evaluating existing service facilities," Papers in Regional Science, Springer;Regional Science Association International, vol. 83(3), pages 565-580, July.
  • Handle: RePEc:spr:presci:v:83:y:2004:i:3:p:565-580 DOI: 10.1007/s10110-004-0212-4

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    References listed on IDEAS

    1. ten Raa, Thijs & Wolff, Edward N., 2000. "Engines of growth in the US economy," Structural Change and Economic Dynamics, Elsevier, vol. 11(4), pages 473-489, December.
    2. Robert Stehrer, 2001. "Industrial specialisation, trade, and labour market dynamics in a multisectoral model of technological progress," Computing in Economics and Finance 2001 230, Society for Computational Economics.
    3. Meller, Patricio & Marfan, Manuel, 1981. "Small and Large Industry: Employment Generation, Linkages, and Key Sectors," Economic Development and Cultural Change, University of Chicago Press, vol. 29(2), pages 263-274, January.
    4. Adam B. Jaffe & Manuel Trajtenberg & Rebecca Henderson, 1993. "Geographic Localization of Knowledge Spillovers as Evidenced by Patent Citations," The Quarterly Journal of Economics, Oxford University Press, vol. 108(3), pages 577-598.
    5. Keld Laursen & Valentina Meliciani, 2002. "The relative importance of international vis-ý-vis national technological spillovers for market share dynamics," Industrial and Corporate Change, Oxford University Press, vol. 11(4), pages 875-894, August.
    6. Erik Dietzenbacher & Alex R. Hoen & Bart Los, 2000. "Labor Productivity in Western Europe 1975-1985: An Intercountry, Interindustry Analysis," Journal of Regional Science, Wiley Blackwell, vol. 40(3), pages 425-452.
    7. Bart Los & Bart Verspagen, 2006. "The Evolution Of Productivity Gaps And Specialization Patterns," Metroeconomica, Wiley Blackwell, vol. 57(4), pages 464-493, November.
    8. Bart Los, 2001. "Endogenous Growth and Structural Change in a Dynamic Input-Output Model," Economic Systems Research, Taylor & Francis Journals, vol. 13(1), pages 3-34.
    9. repec:jns:jbstat:v:182:y:1968:i:1:p:211-215:n:14 is not listed on IDEAS
    10. Bart Los & Bart Verspagen, 2000. "R&D spillovers and productivity: Evidence from U.S. manufacturing microdata," Empirical Economics, Springer, vol. 25(1), pages 127-148.
    11. Jan Fagerberg, 1999. "The Economic Challenge for Europe: Adapting to Innovation-Based Growth," Working Papers 2, Centre for Technology, Innovation and Culture, University of Oslo.
    12. Soete, Luc & Verspagen, Bart & ter Weel, Bas, 2010. "Systems of Innovation," Handbook of the Economics of Innovation, Elsevier.
    13. Zvi Griliches, 1998. "The Search for R&D Spillovers," NBER Chapters,in: R&D and Productivity: The Econometric Evidence, pages 251-268 National Bureau of Economic Research, Inc.
    14. Dietzenbacher, Erik, 1992. "The measurement of interindustry linkages : Key sectors in the Netherlands," Economic Modelling, Elsevier, vol. 9(4), pages 419-437, October.
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    Cited by:

    1. Matisziw, Timothy C. & Murray, Alan T., 2009. "Siting a facility in continuous space to maximize coverage of a region," Socio-Economic Planning Sciences, Elsevier, vol. 43(2), pages 131-139, June.


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