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A bounding-based solution approach for the continuous arc covering problem

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  • Ran Wei
  • Alan Murray
  • Rajan Batta

Abstract

Road segments, telecommunication wiring, water and sewer pipelines, canals and the like are important features of the urban environment. They are often conceived of and represented as network-based arcs. As a result of the usefulness and significance of arc-based features, there is a need to site facilities along arcs to serve demand. Examples of such facilities include surveillance equipment, cellular towers, refueling centers and emergency response stations, with the intent of being economically efficient as well as providing good service along the arcs. While this amounts to a continuous location problem by nature, various discretizations are generally relied upon to solve such problems. The result is potential for representation errors that negatively impact analysis and decision making. This paper develops a solution approach for the continuous arc covering problem that theoretically eliminates representation errors. The developed approach is applied to optimally place acoustic sensors and cellular base stations along a road network. The results demonstrate the effectiveness of this approach for ameliorating any error and uncertainty in the modeling process. Copyright Springer-Verlag Berlin Heidelberg 2014

Suggested Citation

  • 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.
  • Handle: RePEc:kap:jgeosy:v:16:y:2014:i:2:p:161-182
    DOI: 10.1007/s10109-013-0192-5
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    References listed on IDEAS

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    1. Erdemir, Elif Tokar & Batta, Rajan & Rogerson, Peter A. & Blatt, Alan & Flanigan, Marie, 2010. "Joint ground and air emergency medical services coverage models: A greedy heuristic solution approach," European Journal of Operational Research, Elsevier, vol. 207(2), pages 736-749, December.
    2. Dwi Groß & Horst Hamacher & Simone Horn & Anita Schöbel, 2009. "Stop location design in public transportation networks: covering and accessibility objectives," TOP: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 17(2), pages 335-346, December.
    3. 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.
    4. Egon Balas & Maria C. Carrera, 1996. "A Dynamic Subgradient-Based Branch-and-Bound Procedure for Set Covering," Operations Research, INFORMS, vol. 44(6), pages 875-890, December.
    5. Alberto Caprara & Matteo Fischetti & Paolo Toth, 1999. "A Heuristic Method for the Set Covering Problem," Operations Research, INFORMS, vol. 47(5), pages 730-743, October.
    6. Kuby, Michael & Lim, Seow, 2005. "The flow-refueling location problem for alternative-fuel vehicles," Socio-Economic Planning Sciences, Elsevier, vol. 39(2), pages 125-145, June.
    7. Gleason, John M., 1975. "A set covering approach to bus stop location," Omega, Elsevier, vol. 3(5), pages 605-608, October.
    8. Capar, Ismail & Kuby, Michael & Leon, V. Jorge & Tsai, Yu-Jiun, 2013. "An arc cover–path-cover formulation and strategic analysis of alternative-fuel station locations," European Journal of Operational Research, Elsevier, vol. 227(1), pages 142-151.
    9. Erdemir, Elif Tokar & Batta, Rajan & Spielman, Seth & Rogerson, Peter A. & Blatt, Alan & Flanigan, Marie, 2008. "Location coverage models with demand originating from nodes and paths: Application to cellular network design," European Journal of Operational Research, Elsevier, vol. 190(3), pages 610-632, November.
    10. Donald R. Plane & Thomas E. Hendrick, 1977. "Mathematical Programming and the Location of Fire Companies for the Denver Fire Department," Operations Research, INFORMS, vol. 25(4), pages 563-578, August.
    11. Kathleen Hogan & Charles ReVelle, 1986. "Concepts and Applications of Backup Coverage," Management Science, INFORMS, vol. 32(11), pages 1434-1444, November.
    12. Alan T. Murray & Daoqin Tong & Kamyoung Kim, 2010. "Enhancing Classic Coverage Location Models," International Regional Science Review, , vol. 33(2), pages 115-133, April.
    13. 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.
    14. Berman, Oded & Drezner, Zvi & Krass, Dmitry & Wesolowsky, George O., 2009. "The variable radius covering problem," European Journal of Operational Research, Elsevier, vol. 196(2), pages 516-525, July.
    15. 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.
    16. Beasley, J. E. & Chu, P. C., 1996. "A genetic algorithm for the set covering problem," European Journal of Operational Research, Elsevier, vol. 94(2), pages 392-404, October.
    17. Timothy Matisziw & Alan Murray, 2009. "Area coverage maximization in service facility siting," Journal of Geographical Systems, Springer, vol. 11(2), pages 175-189, June.
    18. 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.
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    3. Csiszár, Csaba & Csonka, Bálint & Földes, Dávid & Wirth, Ervin & Lovas, Tamás, 2020. "Location optimisation method for fast-charging stations along national roads," Journal of Transport Geography, Elsevier, vol. 88(C).
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    6. 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.

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    Keywords

    Coverage; Continuous demand; Arc; C610;
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