Advertisement

Classic Beginnings

  • Richard L. Church
  • Alan Murray
Chapter
Part of the Advances in Spatial Science book series (ADVSPATIAL)

Abstract

The central theme of this book is the ability to identify the best location of one or more facilities or objects in order to provide some type or level of coverage. For example, let us suppose that we wish to place guards in an art gallery in such a manner that all areas of the gallery are within sight of one or more guards. In essence, we want the set of guard positions to “cover” or view the entire public area of the gallery. There can, of course, be many different configurations in which guards can view the entire gallery; however, it is of practical necessity to seek a pattern that deploys the fewest number of guards. As a second example, consider the case where we desire to provide fire protection to all neighborhoods of a city. In order to respond to a fire in a timely manner, we may set a standard that each neighborhood of the city should be no more than a mile and a half away from their nearest fire station (where fire trucks and crews can be housed to quickly respond when called). The fire service deployment problem can then be defined as finding the fewest fire stations (and their locations) so that each neighborhood is served or covered within a mile and a half of a station. Both the gallery guard positioning problem and the fire station location problem are examples of the Location Set Covering Problem, one of many covering problems that will be addressed in this book.

References

  1. Agnetis A, Grande E, Mirchandani PB, Pacifici A (2009) Covering a line segment with variable radius discs. Comput Oper Res 36(5):1423–1436CrossRefGoogle Scholar
  2. Armour GC, Buffa ES (1963) A heuristic algorithm and simulation approach to relative location of facilities. Manag Sci 9(2):294–309CrossRefGoogle Scholar
  3. Balcik B, Beamon BM (2008) Facility location in humanitarian relief. Int J Logist 11(2):101–121CrossRefGoogle Scholar
  4. Balinski ML (1965) Integer programming: methods, uses, computations. Manag Sci 12(3):253–313CrossRefGoogle Scholar
  5. Bennett VL, Eaton DJ, Church RL (1982) Selecting sites for rural health workers. Soc Sci Med 16(1):63–72CrossRefGoogle Scholar
  6. Berge C (1957) Two theorems in graph theory. Proc Natl Acad Sci 43(9):842–844CrossRefGoogle Scholar
  7. Berlin GN, Liebman JC (1974) Mathematical analysis of emergency ambulance location. Socio Econ Plan Sci 8(6):323–328CrossRefGoogle Scholar
  8. Christaller W (1933) Die zentralen Orte in Süddeutschland: Eine ökonomisch-geographische Untersuchung über die Gesetzmässigkeit der Verbreitung und Entwicklung der Siedlungen mit städtischen Funktionen. Gustav Fischer, JenaGoogle Scholar
  9. Chung C-H (1986) Recent applications of the maximal covering location planning (M.C.L.P.) model. J Oper Res Soc 37:735–746CrossRefGoogle Scholar
  10. Church R, ReVelle C (1974) The maximal covering location model. Pap Reg Sci Assoc 32:101–118CrossRefGoogle Scholar
  11. Church RL (1974) Synthesis of a class of public facility location models, PhD dissertation, The Johns Hopkins University, Baltimore, MDGoogle Scholar
  12. Church RL, Davis RR (1992) The fixed charge maximal covering location problem. Pap Reg Sci 71(3):199–215CrossRefGoogle Scholar
  13. Church RL, Stoms DM, Davis FW (1996) Reserve selection as a maximal covering location problem. Biol Conserv 76(2):105–112CrossRefGoogle Scholar
  14. Chvatal V (1975) A combinatorial theory in plane geometry. J Comb Theory B 18:39–41CrossRefGoogle Scholar
  15. Cocking C, Cevirgen E, Helling S, Oswald M, Corcodel N, Rammelsberg P, Reinelt G, Hassel AJ (2009) Colour compatibility between teeth and dental shade guides in Quinquagenarians and Septuagenarians. J Oral Rehabil 36:848–855CrossRefGoogle Scholar
  16. Current J, O’Kelly M (1992) Locating emergency warning sirens. Decis Sci 23(1):221–234CrossRefGoogle Scholar
  17. Curtin KM, Hayslett-McCall K, Qiu F (2010) Determining optimal police patrol areas with maximal covering and backup covering location models. Netw Spat Econ 10(1):125–145CrossRefGoogle Scholar
  18. Densham PJ, Rushton G (1992) A more efficient heuristic for solving large p-median problems. Pap Reg Sci 71(3):307–329CrossRefGoogle Scholar
  19. Downs BT, Camm JD (1996) An exact algorithm for the maximal covering problem. Nav Res Logist 43(3):435–461CrossRefGoogle Scholar
  20. Dwyer FR, Evans JR (1981) A branch and bound algorithm for the list selection problem in direct mail advertising. Manag Sci 27(6):658–667CrossRefGoogle Scholar
  21. Edmonds J (1962) Covers and packings in a family of sets. Bull Am Math Soc 68(5):494–499CrossRefGoogle Scholar
  22. Erlenkotter D (1978) A dual-based procedure for uncapacitated facility location. Oper Res 26:992–1009CrossRefGoogle Scholar
  23. Fulkerson DR, Ryser HJ (1961) Widths and heights of (0, 1)-matrices. Rand Corporation, Santa Monica, CACrossRefGoogle Scholar
  24. Galvão RD, ReVelle C (1996) A Lagrangean heuristic for the maximal covering location problem. Eur J Oper Res 88(1):114–123CrossRefGoogle Scholar
  25. Garey MR, Johnson DS (1979) Computers and Intractability: a guide to theory of NP-completeness. W.H. Freeman, New YorkGoogle Scholar
  26. Gerrard RA, Stoms DA, Church RL, Davis FW (1996) Using GIS models for reserve site selection. Trans GIS 1(2):45–60Google Scholar
  27. Gleason JM (1975) A set covering approach to bus stop location. Omega 3(5):605–608CrossRefGoogle Scholar
  28. Grinde RB, Daniels K (1999) Solving an apparel trim placement problem using a maximum cover problem approach. IIE Trans 31(8):763–769Google Scholar
  29. Hakimi SL (1964) Optimum locations of switching centers and the absolute centers and medians of a graph. Oper Res 12(3):450–459CrossRefGoogle Scholar
  30. Hakimi SL (1965) Optimum distribution of switching centers in a communication network and some related graph theoretic problems. Oper Res 13(3):462–475CrossRefGoogle Scholar
  31. Hall P (1935) On representatives of subsets. J Lond Math Soc 1(1):26–30CrossRefGoogle Scholar
  32. Hillsman EL (1984) The p-median structure as a unified linear model for location-allocation analysis. Environ Plan A 16:305–318CrossRefGoogle Scholar
  33. Hotelling H (1929) Stability in competition. Econ J 39(153):41–57CrossRefGoogle Scholar
  34. Isard W (1956) Location and space-economy. MIT Press, Cambridge, MAGoogle Scholar
  35. Karp RM (1972) Reducibility among combinatorial problems. In: Miller RE, Thatcher JW (eds) Complexity of computer computations. Springer, Boston, MA, pp 85–103CrossRefGoogle Scholar
  36. Klimberg R, ReVelle C, Cohon J (1991) A multiobjective approach to evaluating and planning the allocation of inspection resources. Eur J Oper Res 52(1):55–64CrossRefGoogle Scholar
  37. Kolesar P, Walker WE (1974) An algorithm for the dynamic relocation of fire companies. Oper Res 22(2):249–274CrossRefGoogle Scholar
  38. Kwan MP, Murray AT, O’Kelly ME, Tiefelsdorf M (2003) Recent advances in accessibility research: representation, methodology and applications. J Geogr Syst 5(1):129–138CrossRefGoogle Scholar
  39. Launhardt W (1872) Kommercielle Tracirung der Verkehrswege. Arch IngenieurvereinGoogle Scholar
  40. Manne AS (1964) Plant location under economies-of-scale—decentralization and computation. Manag Sci 11(2):213–235CrossRefGoogle Scholar
  41. Mladenović N, Hansen P (1997) Variable neighborhood search. Comput Oper Res 24(11):1097–1100CrossRefGoogle Scholar
  42. Murray AT (2001) Strategic analysis of public transport coverage. Socio Econ Plan Sci 35:175–188CrossRefGoogle Scholar
  43. Murray AT (2013) Optimising the spatial location of urban fire stations. Fire Saf J 62:64–71CrossRefGoogle Scholar
  44. Murray AT, Church RL (1996) Applying simulated annealing to location-planning models. J Heuristics 2(1):31–53CrossRefGoogle Scholar
  45. Murray AT, Church RL, Gerrard RA, Tsui WS (1998) Impact models for siting undesirable facilities. Pap Reg Sci 77:19–36CrossRefGoogle Scholar
  46. Murray AT, Kim K, Davis JW, Machiraju R, Parent R (2007) Coverage optimization to support security monitoring. Comput Environ Urban Syst 31(2):133–147CrossRefGoogle Scholar
  47. Plane DR, Hendrick TE (1977) Mathematical programming and the location of fire companies for the Denver fire department. Oper Res 25(4):563–578CrossRefGoogle Scholar
  48. Psaraftis HN, Ziogas BO (1985) A tactical decision algorithm for the optimal dispatching of oil spill cleanup equipment. Manag Sci 31(12):1475–1491CrossRefGoogle Scholar
  49. Quine WV (1955) A way to simplify truth functions. Am Math Mon 62(9):627–631CrossRefGoogle Scholar
  50. ReVelle C, Scholssberg M, Williams J (2008) Solving the maximal covering location problem with heuristic concentration. Comput Oper Res 35(2):427–435CrossRefGoogle Scholar
  51. ReVelle CS, Swain RW (1970) Central facilities location. Geogr Anal 2(1):30–42CrossRefGoogle Scholar
  52. Rolland E, Schilling DA, Current JR (1997) An efficient tabu search procedure for the p-median problem. Eur J Oper Res 96(2):329–342CrossRefGoogle Scholar
  53. Rosing KE, ReVelle CS (1997) Heuristic concentration: two stage solution construction. Eur J Oper Res 97(1):75–86CrossRefGoogle Scholar
  54. Roth R (1969) Computer solutions to minimum-cover problems. Oper Res 17:455–465CrossRefGoogle Scholar
  55. Saydam C, McKnew M (1985) Applications and implementation a separable programming approach to expected coverage: an application to ambulance location. Decis Sci 16(4):381–398CrossRefGoogle Scholar
  56. Swersey AJ, Thakur LS (1995) An integer programming model for locating vehicle emissions testing stations. Manag Sci 41(3):496–512CrossRefGoogle Scholar
  57. Teitz MB, Bart P (1968) Heuristic methods for estimating the generalized vertex median of a weighted graph. Oper Res 16(5):955–961CrossRefGoogle Scholar
  58. Tong D, Murray A, Xiao N (2009) Heuristics in spatial analysis: a genetic algorithm for coverage maximization. Ann Assoc Am Geogr 99(4):698–711CrossRefGoogle Scholar
  59. Toregas C (1970) A covering formulation for the location of public facilities. Master’s Thesis, Cornell University, Ithaca, NYGoogle Scholar
  60. Toregas C (1971) Location under maximal travel time constraints. Ph.D. dissertation, Cornell University, Ithaca, NYGoogle Scholar
  61. Toregas C, Revelle C (1973) Binary logic solutions to a class of location problem. Geogr Anal 5(2):145–155CrossRefGoogle Scholar
  62. Toregas C, Swain R, ReVelle C, Bergman L (1971) The location of emergency services. Oper Res 19:1363–1373CrossRefGoogle Scholar
  63. Underhill LG (1994) Optimal and suboptimal reserve selection algorithms. Biol Conserv 70(1):85–87CrossRefGoogle Scholar
  64. Von Thünen JH (1826) Uer lsolierte Staat in Beziehung auf’ Landwirtschaft un!d NutionaZokonomi,e, Part I, Perthes, HamburgGoogle Scholar
  65. Walker W (1974) Using the set-covering problem to assign fire companies to fire houses. Oper Res 22(2):275–277CrossRefGoogle Scholar
  66. Weber A (1909) Uber den Standort der Industrien, Tubingen, Translated as Alfred Weber’s Theory of the Location of Industries (1929) by C. J. Friedrich, ChicagoGoogle Scholar
  67. White JA, Case KE (1974) On covering problems and the central facilities location problem. Geogr Anal 6:281–293CrossRefGoogle Scholar

Copyright information

© Springer International Publishing AG, part of Springer Nature 2018

Authors and Affiliations

  • Richard L. Church
    • 1
  • Alan Murray
    • 1
  1. 1.Department of GeographyUniversity of CaliforniaSanta BarbaraUSA

Personalised recommendations