Advertisement

Extended Forms of Coverage

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

Abstract

Industrial and public sector planning is often complex. Example contexts include making a city safer or designing a manufacturing supply chain. Models can assist in the design of such systems by tracking the major components and generating top performing solutions. Some of the best planning models are simple, easy to understand, and easily applied and solved. At a minimum, a model must capture the main essence of the problem. Two examples of such planning models are the LSCP (location set covering problem) and MCLP (maximal covering location problem) described in Chap.  2. Because they are so simple and powerful as planning models, they have been used in many different ways, from biological reserve design (Underhill 1994) to advertising (Dwyer and Evans 1981) to prosthetic teeth coloring (Cocking et al. 2009) to health clinic location (Bennett et al. 1982). There are, however, a number of elements and conditions that are not captured exactly using these two basic constructs of complete coverage or maximal coverage. Because of this, researchers have proposed a wide variety of extended model forms to better reflect specific elements of a given problem. In this chapter we present some of the work, including multi-service, hierarchical, and multi-factor issues, in coverage modeling.

References

  1. Akbari A, Pelot R, Eiselt HA (2017) A modular capacitated multi-objective model for locating maritime search and rescue vessels. Ann Oper Res 267:1–26.  https://doi.org/10.1007/s10479-017-2593-1 CrossRefGoogle Scholar
  2. Arthur JL, Hachey M, Sahr K, Huso M, Kiester AR (1997) Finding all optimal solutions to the reserve site selection problem: formulation and computational analysis. Environ Ecol Stat 4(2):153–165CrossRefGoogle Scholar
  3. Bennett VL, Eaton DJ, Church RL (1982) Selecting sites for rural health workers. Soc Sci Med 16:63–72CrossRefGoogle Scholar
  4. Branas CC, MacKenzie EJ, ReVelle CS (2000) A trauma resource allocation model for ambulances and hospitals. Health Serv Res 35(2):489Google Scholar
  5. Branas CC, Revelle CS (2001) An iterative switching heuristic to locate hospitals and helicopters. Socio Econ Plan Sci 35(1):11–30CrossRefGoogle Scholar
  6. Brill ED Jr (1979) The use of optimization models in public-sector planning. Manag Sci 25(5):413–422CrossRefGoogle Scholar
  7. Brotcorne L, Laporte G, Semet F (2003) Ambulance location and relocation models. Eur J Oper Res 147(3):451–463CrossRefGoogle Scholar
  8. Camm JD, Polasky S, Solow A, Csuti B (1996) A note on optimal algorithms for reserve site selection. Biol Conserv 78:353–355CrossRefGoogle Scholar
  9. Chaudhry SS, Moon ID, McCormick ST (1987) Conditional covering: greedy heuristics and computational results. Comput Oper Res 14(1):11–18CrossRefGoogle Scholar
  10. Cocking C, Cevirgen E, Helling S, Oswald M, Corcodel N, Rammelsberg P, Hassel AJ (2009) Colour compatibility between teeth and dental shade guides in Quinquagenarians and Septuagenarians. J Oral Rehabil 36(11):848–855CrossRefGoogle Scholar
  11. Cohon JL (1978) Multiobjective programming and planning. Academic Press, New YorkGoogle Scholar
  12. Church RL (1974) Synthesis of a class of public facility location models. PhD Dissertation, The Johns Hopkins University, Baltimore, MDGoogle Scholar
  13. Church RL, Eaton DJ (1987) Hierarchical location analysis utilizing covering objectives. In: Ghosh A, Rushton G (eds) Spatial analysis and location-allocation models. Van Nostrand Reinhold, New YorkGoogle Scholar
  14. Church RL, Gerrard RA (2003) The multi-level location set covering problem. Geogr Anal 35:278–289CrossRefGoogle Scholar
  15. Church R, Gerrard R, Hollander A, Stoms D (2000) Understanding the tradeoffs between site quality and species presence in reserve site selection. For Sci 46:157–167Google Scholar
  16. Church RL, Stoms D, Davis F (1996) Reserve design as a maximal covering location problem. Biol Conserv 76:105–112CrossRefGoogle Scholar
  17. Current JR, Schilling DA (1994) The median tour and maximal covering tour problems: formulations and heuristics. Eur J Oper Res 73(1):114–126CrossRefGoogle Scholar
  18. Daskin MS, Stern EH (1981) A hierarchical objective set covering model for emergency medical service vehicle deployment. Transp Sci 15:137–152CrossRefGoogle Scholar
  19. Dökmeci VF (1973) An optimization model for a hierarchical spatial system. J Reg Sci 13(3):439–451CrossRefGoogle 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. Engel AD (1968) Perspectives in health planning. Athlone Press, LondonGoogle Scholar
  22. Gerrard RA, Church RL (1994) A generalized approach to modeling the hierarchical maximal covering location problem with referral. Pap Reg Sci 73:425–453CrossRefGoogle Scholar
  23. Grubesic TH, Matisziw TC, Murray AT (2012) Assessing geographic coverage of the essential air service program. Socio Econ Plan Sci 46(2):124–135CrossRefGoogle Scholar
  24. Grubesic TH, Murray AT (2002) Constructing the divide: spatial disparities in broadband access. Pap Reg Sci 81(2):197–221CrossRefGoogle Scholar
  25. Hall NG, Hochbaum DS (1992) The multicovering problem. Eur J Oper Res 62(3):323–339CrossRefGoogle Scholar
  26. Hogan K, ReVelle C (1986a) Concepts and applications of backup coverage. Manag Sci 32:1434–1444CrossRefGoogle Scholar
  27. Hogan K, ReVelle C (1986b) Backup coverage concepts in the location of emergency services. Proc Pittsburgh Conf Model Simul 17:1423–1429Google Scholar
  28. Kolesar P, Walker WE (1974) An algorithm for the dynamic relocation of fire companies. Oper Res 22(2):249–274CrossRefGoogle Scholar
  29. Margules CR (1986) Conservation evaluation in practice. In: Usher MB (ed) Wildlife conservation evaluation. Chapman and Hall, London, pp 297–314CrossRefGoogle Scholar
  30. Margules CR, Nicholls AO, Pressey RL (1988) Selecting networks of reserves to maximise biological diversity. Biol Conserv 43(1):63–76CrossRefGoogle Scholar
  31. Matisziw TC, Murray AT, Kim C (2006) Strategic route extension in transit networks. Eur J Oper Res 171(2):661–673CrossRefGoogle Scholar
  32. Moon ID, Chaudhry SS (1984) An analysis of network location problems with distance constraints. Manag Sci 30:290–307CrossRefGoogle Scholar
  33. Moore GC, ReVelle C (1982) The hierarchical service location problem. Manag Sci 28:775–780CrossRefGoogle Scholar
  34. Murray AT (2013) Optimising the spatial location of urban fire stations. Fire Saf J 62:64–71CrossRefGoogle Scholar
  35. Osleeb JP, Mclaferty S (1992) A weighted covering model to aid in Dracunculiasis eradication. Pap Reg Sci 71:243–257CrossRefGoogle Scholar
  36. Penalba JR (1980) Incorporating planning preferences into location models. Master’s project report, University of Tennessee, Knoxville, TNGoogle Scholar
  37. Plane DR, Hendrick TE (1977) Mathematical programming and the location of fire companies for the Denver Fire Department. Operat Res 25:563–578CrossRefGoogle Scholar
  38. Pressey RL, Humphries CJ, Margules CR, Vane-Wright RI, Williams PH (1993) Beyond opportunism: key principles for systematic reserve selection. Trends Ecol Evol 8(4):124–128CrossRefGoogle Scholar
  39. Ratick SJ, Osleeb JP, Hozumi D (2009) Application and extension of the Moore and ReVelle hierarchical maximal covering model. Socio Econ Plan Sci 43:92–101CrossRefGoogle Scholar
  40. ReVelle C, Toregas C, Falkson L (1996) Applications of the location set covering problem. Geogr Anal 8:65–76CrossRefGoogle Scholar
  41. ReVelle C, Schweitzer J, Snyder S (1996) The maximal conditional covering problem. INFOR 34:77–91Google Scholar
  42. Schilling D, Elzinga DJ, Cohon J, Church R, ReVelle C (1979) The Team/Fleet models for simultaneous facility and equipment placement. Transp Sci 13:163–175CrossRefGoogle Scholar
  43. Schilling DA, ReVelle C, Cohon J, Elzinga DJ (1980) Some models for fire protection location decisions. Eur J Oper Res 5:1–7CrossRefGoogle Scholar
  44. Solanki R (1991) Generating the noninferior set in mixed integer biobjective linear programs: an application to a location problem. Comput Oper Res 18(1):1–15CrossRefGoogle Scholar
  45. Steuer RE (1986) Multiple criteria optimization. Theory, computation and applications. Wiley, New YorkGoogle Scholar
  46. Steuer RE, Choo EU (1983) An interactive weighted Tchebycheff procedure for multiple objective programming. Math Program 26(3):326–344CrossRefGoogle Scholar
  47. Storbeck JE (1982) Slack, natural slack, and location covering. Socio Econ Plan Sci 16:99–105CrossRefGoogle Scholar
  48. Storbeck JE (1988) The spatial structuring of central places. Geogr Anal 20(2):93–110CrossRefGoogle Scholar
  49. Storbeck JE (1990) Classical central places as protected thresholds. Geogr Anal 22(1):4–21CrossRefGoogle Scholar
  50. Toregas C (1970) A covering formulation for the location of public facilities. M.S. Thesis, Cornell University, Ithaca, NYGoogle Scholar
  51. Underhill LG (1994) Optimal and suboptimal reserve selection algorithms. Biol Conserv 70:85–87CrossRefGoogle Scholar
  52. Wu C, Murray AT (2005) Optimizing public transit quality and system access: the multiple-route, maximal covering/shortest-path problem. Environ Plan B Plan Des 32(2):163–178CrossRefGoogle 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