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A computational approach for eliminating error in the solution of the location set covering problem

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  • Murray, Alan T.
  • Wei, Ran

Abstract

The location set covering problem continues to be an important and challenging spatial optimization problem. The range of practical planning applications underscores its importance, spanning fire station siting, warning siren positioning, security monitoring and nature reserve design, to name but a few. It is challenging on a number of fronts. First, it can be difficult to solve for medium to large size problem instances, which are often encountered in combination with geographic information systems (GIS) based analysis. Second, the need to cover a region efficiently often brings about complications associated with the abstraction of geographic space. Representation as points can lead to significant gaps in actual coverage, whereas representation as polygons can result in a substantial overestimate of facilities needed. Computational complexity along with spatial abstraction sensitivity combine to make advances in solving this problem much needed. To this end, a solution framework for ensuring complete coverage of a region with a minimum number of facilities is proposed that eliminates potential error. Applications to emergency warning siren and fire station siting are presented to demonstrate the effectiveness of the developed approach. The approach can be applied to convex, non-convex and non-contiguous regions and is unaffected by arbitrary initial spatial representations of space.

Suggested Citation

  • Murray, Alan T. & Wei, Ran, 2013. "A computational approach for eliminating error in the solution of the location set covering problem," European Journal of Operational Research, Elsevier, vol. 224(1), pages 52-64.
    • Handle: RePEc:eee:ejores:v:224:y:2013:i:1:p:52-64
    DOI: 10.1016/j.ejor.2012.07.027
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    References listed on IDEAS

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    1. ReVelle, C. S. & Eiselt, H. A., 2005. "Location analysis: A synthesis and survey," European Journal of Operational Research, Elsevier, vol. 165(1), pages 1-19, August.
    2. Constantine Toregas & Ralph Swain & Charles ReVelle & Lawrence Bergman, 1971. "The Location of Emergency Service Facilities," Operations Research, INFORMS, vol. 19(6), pages 1363-1373, October.
    3. Owen, Susan Hesse & Daskin, Mark S., 1998. "Strategic facility location: A review," European Journal of Operational Research, Elsevier, vol. 111(3), pages 423-447, December.
    4. Alan T. Murray & Daoqin Tong & Kamyoung Kim, 2010. "Enhancing Classic Coverage Location Models," International Regional Science Review, , vol. 33(2), pages 115-133, April.
    5. Daoqin Tong & Alan T. Murray, 2009. "Maximising coverage of spatial demand for service," Papers in Regional Science, Wiley Blackwell, vol. 88(1), pages 85-97, March.
    6. S. L. Hakimi, 1964. "Optimum Locations of Switching Centers and the Absolute Centers and Medians of a Graph," Operations Research, INFORMS, vol. 12(3), pages 450-459, June.
    7. Kamyoung Kim & Alan T. Murray, 2008. "Enhancing Spatial Representation In Primary And Secondary Coverage Location Modeling," Journal of Regional Science, Wiley Blackwell, vol. 48(4), pages 745-768, October.
    8. Alexandris, George & Giannikos, Ioannis, 2010. "A new model for maximal coverage exploiting GIS capabilities," European Journal of Operational Research, Elsevier, vol. 202(2), pages 328-338, April.
    9. CONSTANTINE TOREGAS & CHARLES ReVELLE, 1972. "Optimal Location Under Time Or Distance Constraints," Papers in Regional Science, Wiley Blackwell, vol. 28(1), pages 133-144, January.
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    Cited by:

    1. Alan T. Murray, 2017. "Regional analytics," The Annals of Regional Science, Springer;Western Regional Science Association, vol. 59(1), pages 1-13, July.
    2. Ran Wei, 2016. "Coverage Location Models," International Regional Science Review, , vol. 39(1), pages 48-76, January.
    3. Muren, & Li, Hao & Mukhopadhyay, Samar K. & Wu, Jian-jun & Zhou, Li & Du, Zhiping, 2020. "Balanced maximal covering location problem and its application in bike-sharing," International Journal of Production Economics, Elsevier, vol. 223(C).
    4. Ran Wei & Alan Murray & Rajan Batta, 2014. "A bounding-based solution approach for the continuous arc covering problem," Journal of Geographical Systems, Springer, vol. 16(2), pages 161-182, April.
    5. Sadeghi, Mohammad & Yaghoubi, Saeed, 2024. "Optimization models for cloud seeding network design and operations," European Journal of Operational Research, Elsevier, vol. 312(3), pages 1146-1167.
    6. Elshaikh, Abdalla & Salhi, Said & Nagy, Gábor, 2015. "The continuous p-centre problem: An investigation into variable neighbourhood search with memory," European Journal of Operational Research, Elsevier, vol. 241(3), pages 606-621.
    7. Briskorn, Dirk & Dienstknecht, Michael, 2020. "Covering polygons with discs: The problem of crane selection and location on construction sites," Omega, Elsevier, vol. 97(C).
    8. Murray, Alan T. & Feng, Xin, 2016. "Public street lighting service standard assessment and achievement," Socio-Economic Planning Sciences, Elsevier, vol. 53(C), pages 14-22.
    9. Huanfa Chen & Alan T. Murray & Rui Jiang, 2021. "Open-source approaches for location cover models: capabilities and efficiency," Journal of Geographical Systems, Springer, vol. 23(3), pages 361-380, July.

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