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

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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.

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References

  • Akella MR, Delmelle E, Batta R, Rogerson P, Blatt A (2010) Adaptive cell tower location using geostatistics. Geogr Anal 42(3):227–244

    Article  Google Scholar 

  • Alexandris G, Giannikos I (2010) A new model for maximal coverage exploiting GIS capabilities. Eur J Oper Res 202(2):328–338

    Article  Google Scholar 

  • Ando A, Camm J, Polasky S, Solow A (1998) Species distributions, land values, and efficient conservation. Science 279(5359):2126–2128

    Article  Google Scholar 

  • Balas E, Carrera MC (1996) A dynamic subgradient-based branch-and-bound procedure for set covering. Oper Res 44(6):875–890

    Article  Google Scholar 

  • Beasley JE, Chu PC (1996) A genetic algorithm for the set covering problem. Eur J Oper Res 94(2):392–404

    Article  Google Scholar 

  • Berman O, Verter V, Kara BY (2007) Designing emergency response networks for hazardous materials transportation. Comput Oper Res 34(5):1374–1388

    Article  Google Scholar 

  • Berman O, Drezner Z, Krass D, Wesolowsky GO (2009) The variable radius covering problem. Eur J Oper Res 196(2):516–525

    Article  Google Scholar 

  • Capar I, Kuby M, Leon VJ, Tsai Y-J (2013) An arc cover–path-cover formulation and strategic analysis of alternative-fuel station locations. Eur J Oper Res 227(1):142–151

    Article  Google Scholar 

  • Caprara A, Fischetti M, Toth P (1999) A heuristic method for the set covering problem. Oper Res 47(5):730–743

    Article  Google Scholar 

  • CDC (2013) Mobile device use while driving more common in the US than in several European countries. Available at: http://www.cdc.gov/media/releases/2013/p0314_driving_mobile_device_use.html. Last accessed 27 Aug 2013

  • Church RL (1984) The planar maximal covering location problem. J Reg Sci 24(2):185–201

    Article  Google Scholar 

  • Church RL, Revelle CR (1974) The maximal covering location problem. Pap Reg Sci 32(1):101–118

    Article  Google Scholar 

  • Cromley RG, Lin J, Merwin DA (2012) Evaluating representation and scale error in the maximal covering location problem using GIS and intelligent areal interpolation. Int J Geogr Inf Sci 26(3):495–517

    Article  Google Scholar 

  • Current J, O’Kelly M (1992) Locating emergency warning sirens. Decis Sci 23(1):221–234

    Article  Google Scholar 

  • Drezner Z, Wesolowsky GO, Drezner T (2004) The gradual covering problem. Nav Res Logist 51(6):841–855

    Article  Google Scholar 

  • Erdemir ET, Batta R, Spielman S, Rogerson PA, Blatt A, Flanigan M (2008) Location coverage models with demand originating from nodes and paths: application to cellular network design. Eur J Oper Res 190(3):610–632

    Article  Google Scholar 

  • Erdemir ET, Batta R, Rogerson PA, Blatt A, Flanigan M (2010) Joint ground and air emergency medical services coverage models: a greedy heuristic solution approach. Eur J Oper Res 207(2):736–749

    Article  Google Scholar 

  • Fotheringham AS, Densham PJ, Curtis A (1995) The zone definition problem in location-allocation modeling. Geogr Anal 27(1):60–77

    Article  Google Scholar 

  • Geetlaa T, Batta R, Blattb A, Flaniganb M, Majkab K (2013) Optimal placement of omnidirectional sensors in a transportation network for effective emergency response and crash characterization. Draft Manuscript

  • Gleason JM (1975) A set covering approach to bus stop location. Omega 3(5):605–608

    Article  Google Scholar 

  • Goodchild MF (1979) The aggregation problem in location-allocation. Geogr Anal 11(3):240–255

    Article  Google Scholar 

  • Harlow C, Wang Y (2002) Acoustic accident detection system. ITS J Intell Transp Syst 7(1):43–56

    Google Scholar 

  • Hillsman EL, Rhoda R (1978) Errors in measuring distances from populations to service centers. Ann Reg Sci 12(3):74–88

    Article  Google Scholar 

  • Hodgson MJ (1990) A flow-capturing location-allocation model. Geogr Anal 22(3):270–279

    Article  Google Scholar 

  • Hogan K, Revelle C (1986) Concepts and applications of backup coverage. Manag Sci 32(11):1434–1444

    Article  Google Scholar 

  • Jantke K, Schneider UA (2010) Multiple-species conservation planning for European wetlands with different degrees of coordination. Biol Conserv 143(7):1812–1821

    Article  Google Scholar 

  • Kuby M, Lim S (2005) The flow-refueling location problem for alternative-fuel vehicles. Socio Econ Plan Sci 39(2):125–145

    Article  Google Scholar 

  • Matisziw TC, Murray AT (2009) Area coverage maximization in service facility siting. J Geogr Syst 11(2):175–189

    Article  Google Scholar 

  • Miller HJ (1996) GIS and geometric representation in facility location problems. Int J Geogr Inf Syst 10(7):791–816

    Google Scholar 

  • Minciardi R, Sacile R, Siccardi F (2003) Optimal planning of a weather radar network. J Atmos Ocean Technol 20(9):1251–1263

    Article  Google Scholar 

  • Minieka E (1970) The m-center problem. Siam Rev 12(1):138–139

    Article  Google Scholar 

  • Murray AT (2005) Geography in coverage modeling: exploiting spatial structure to address complementary partial service of areas. Ann Assoc Am Geogr 95(4):761–772

    Article  Google Scholar 

  • Murray AT, O'Kelly ME (2002) Assessing representation error in point-based coverage modeling. J Geogr Syst 4(2):171–191

    Article  Google Scholar 

  • Murray AT, Tong D (2007) Coverage optimization in continuous space facility siting. Int J Geogr Inf Sci 21(7):757–776

    Article  Google Scholar 

  • Murray AT, Wei R (2013) A computational approach for eliminating error in the solution of the location set covering problem. Eur J Oper Res 224(1):52–64

    Article  Google Scholar 

  • Murray AT, O’Kelly ME, Church RL (2008) Regional service coverage modeling. Comput Oper Res 35(2):339–355

    Article  Google Scholar 

  • Murray AT, Tong D, Kim K (2010) Enhancing classic coverage location models. Int Reg Sci Rev 33(2):115–133

    Article  Google Scholar 

  • Plane DR, Hendrick TE (1977) Mathematical programming and the location of fire companies for the Denver fire department. Oper Res 25(4):563–578

    Article  Google Scholar 

  • Poetranto DR, Hamacher HW, Horn S, Schöbel A (2009) Stop location design in public transportation networks: covering and accessibility objectives. TOP 17(2):335–346

    Article  Google Scholar 

  • Ren ZG, Feng ZR, Ke LJ, Zhang ZJ (2010) New ideas for applying ant colony optimization to the set covering problem. Comput Ind Eng 58(4):774–784

    Article  Google Scholar 

  • ReVelle C, Toregas C, Falkson L (1976) Applications of the location set covering problem. Geogr Anal 8(1):65–76

    Article  Google Scholar 

  • ReVelle CS, Williams JC, Boland JJ (2002) Counterpart models in facility location science and reserve selection science. Environ Model Assess 7(2):71–80

    Article  Google Scholar 

  • Rogerson PA, Delmelle E, Batta R, Akella M, Blatt A, Wilson G (2004) Optimal sampling design for variables with varying spatial importance. Geogr Anal 36(2):177–194

    Article  Google Scholar 

  • Rushton G (1989) Applications of location models. Ann Oper Res 18(1):25–42

    Article  Google Scholar 

  • Schöbel A, Hamacher HW, Liebers A, Wagner D (2009) The continuous stop location problem in public transportation networks. Asia-Pac J Oper Res 26(01):13–30

    Article  Google Scholar 

  • Straitiff SL, Cromley RG (2010) Using GIS and K = 3 central place lattices for efficient solutions to the location set covering problem in a bounded plane. Trans GIS 14(3):331–349

    Article  Google Scholar 

  • Suzuki A, Drezner Z (1996) The p-center location problem in an area. Locat Sci 4(1):69–82

    Article  Google Scholar 

  • Suzuki A, Okabe A (1995) Using voronoi diagrams. In: Drezner Z (ed) Facility location: a survey of applications and methods, Springer Verlag, New York, pp 103-118

  • Tong D (2012) Regional coverage maximization: a new model to account implicitly for complementary coverage. Geogr Anal 44(1):1–14

    Article  Google Scholar 

  • Tong D, Church RL (2012) Aggregation in continuous space coverage modeling. Int J Geogr Inf Sci 26(5):795–816

    Article  Google Scholar 

  • Tong D, Murray AT (2009) Maximising coverage of spatial demand for service. Pap Reg Sci 88(1):85–97

    Article  Google Scholar 

  • Toregas C, Revelle C (1973) Binary logic solutions to a class of location problem. Geogr Anal 5(2):145–155

    Article  Google Scholar 

  • Toregas C, Swain R, ReVelle C, Bergman L (1971) The location of emergency service facilities. Oper Res 19(6):1363–1373

    Article  Google Scholar 

  • Wei H, Murray AT, Xiao N (2006) Solving the continuous space p-centre problem: planning application issues. IMA J Manag Math 17(4):413–425

    Article  Google Scholar 

  • Whitney DA, Pisano JJ (1995) AutoAlert: automated acoustic detection of incidents. IDEA Program, Transportation Research Board, National Research Council

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Acknowledgments

The first author acknowledges support from the 2012–2013 Benjamin H. Stevens Graduate Fellowship in Regional Science.

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Authors and Affiliations

  1. Geospatial Intelligence and Planning, College of Earth, Ocean, and Atmospheric Sciences, Oregon State University, Corvallis, OR, 97331, USA

    Ran Wei

  2. GeoDa Center for Geospatial Analysis and Computation, School of Geographical Sciences and Urban Planning, Arizona State University, Tempe, AZ, 85287-5302, USA

    Alan T. Murray

  3. Department of Industrial and Systems Engineering, University at Buffalo, State University of New York, Buffalo, NY, 14260, USA

    Rajan Batta

Authors
  1. Ran Wei
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  2. Alan T. Murray
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  3. Rajan Batta
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Correspondence to Ran Wei.

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Wei, R., Murray, A.T. & Batta, R. A bounding-based solution approach for the continuous arc covering problem. J Geogr Syst 16, 161–182 (2014). https://doi.org/10.1007/s10109-013-0192-5

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  • DOI: https://doi.org/10.1007/s10109-013-0192-5

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