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Area coverage maximization in service facility siting

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Abstract

Traditionally, models for siting facilities in order to optimize coverage of area demand have made use of discrete space representations to efficiently handle both candidate facility locations and demand. These discretizations of space are often necessary given the linear functional forms of many siting models and the complexities associated with evaluating continuous space. Recently, several spatial optimization approaches have been proposed to address the more general problem of identifying facility sites that maximize regional coverage for the case where candidate sites and demand are continuously distributed across space. One assumption of existing approaches is that only demand falling within a prescribed radius of the facility can be effectively served. In many practical applications, however, service areas are not necessarily circular, as terrain, transportation, and service characteristics of the facility often result in irregular shapes. This paper develops a generalized service coverage approach, allowing a sited facility to have any continuous service area shape, not simply a circle. Given that demand and facility sites are assumed to be continuous throughout a region, geometrical properties of the demand region and the service facility coverage area are exploited to identify a facility site to optimize the correspondence between the two areas. In particular, we consider the case where demand is uniformly distributed and the service area is translated to maximize coverage. A heuristic approach is proposed for efficient model solution. Application results are presented for siting a facility given differently shaped service areas.

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Notes

  1. The medial axis of a simple polygon can be found in \( O (n\log n) \) time, where n is the number of edges in the polygon (see Lee 1982).

  2. Iteration = w, search distance = η, objective change = ϑ, arc density = γ, stop tolerance = λ.

  3. Implemented on a workstation with 3.0 GHz Xeon processor with 2 M cache and 800 MHz FSB, 2 GB of 4 MHz RAM, and a 7.2 K, 8 M hard disk drive.

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Acknowledgments

This material is based upon work supported by the National Science Foundation under Grant No. 0518967. Any opinions, findings, and conclusions or recommendations expressed in this material are those of the author(s) and do not necessarily reflect the views of the National Science Foundation.

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Correspondence to Timothy C. Matisziw.

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Matisziw, T.C., Murray, A.T. Area coverage maximization in service facility siting. J Geogr Syst 11, 175–189 (2009). https://doi.org/10.1007/s10109-009-0081-0

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  • DOI: https://doi.org/10.1007/s10109-009-0081-0

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