Location of Health Care Facilities

Part of the International Series in Operations Research & Management Science book series (ISOR, volume 70)


This chapter reviews the location set covering model, maximal covering model and P-median model. These models form the heart of the models used in location planning in health care. The health care and related location literature is then classified into one of three broad areas: accessibility models, adaptability models and availability models. Each class is reviewed and selected formulations are presented. A novel application of the set covering model to the analysis of cytological samples is then discussed. The chapter concludes with directions for future work.

Key words

Facility location Covering Scenario planning 


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  1. [1]
    Handler, G.Y. and P.B. Mirchandani (1979). Location on Networks: Theory and Algorithms. MIT Press, Cambridge, MA.Google Scholar
  2. [2]
    Love, R.F., J.G. Morris, and G.O. Wesolowsky (1988). Facilities Location: Models and Methods. North Holland, New York.Google Scholar
  3. [3]
    Francis, R.L., L.F. McGinnis, and J.A. White (1992). Facility Layout and Location: An Analytical Approach. Prentice Hall, Englewood Cliffs, NJ.Google Scholar
  4. [4]
    Daskin, M.S. (1995). Network and Discrete Location: Models, Algorithms and Applications. John Wiley, New York.Google Scholar
  5. [5]
    Marianov, V. and C. ReVelle (1995). Siting emergency services, in Facility Location: A Survey of Applications and Methods, Z. Drezner, Ed., Springer, New York.Google Scholar
  6. [6]
    Current, J., M. Daskin, and D. Schilling (2002). Discrete network location models, in Facility Location: Applications and Theory, Z. Drezner and H.W. Hamacher, Eds., Springer, Berlin.Google Scholar
  7. [7]
    Marianov, V. and D. Serra (2002). Location problems in the public sector, in Facility Location: Applications and Theory, Z. Drezner and H.W. Hamacher, Eds., Springer, Berlin.Google Scholar
  8. [8]
    Berman, O. and D. Krass (2002). Facility location problems with stochastic demands and congestion, in Facility Location: Applications and Theory, Z. Drezner and H.W. Hamacher, Eds., Springer, Berlin.Google Scholar
  9. [9]
    Eaton, D., R. Church, V. Bennett, B. Hamon, and L.G. Valencia (1982). On deployment of health resources in rural Valle del Cauca, Colombia, in Planning and Development Processes in the Third World, W. Cook, Ed., Elsevier, Amsterdam.Google Scholar
  10. [10]
    Bennett, V., D. Eaton, and R. Church (1982). Selecting sites for Rural health workers. Social Science and Medicine, 16, 63–72.PubMedCrossRefGoogle Scholar
  11. [11]
    Toregas, C.S.R., C. ReVelle, and L. Bergman (1971). The location of emergency service facilities. Operations Research, 19, 1363–1373.CrossRefGoogle Scholar
  12. [12]
    Church, R. and C. ReVelle (1974). The maximal covering location problem. Papers of the Regional Science Association, 32, 101–118.CrossRefGoogle Scholar
  13. [13]
    Fisher, M.L. (1981). The Lagrangian relaxation method for solving integer programming problems. Management Science, 27, 1–18.zbMATHMathSciNetCrossRefGoogle Scholar
  14. [14]
    Fisher, M.L. (1985). An applications oriented guide to Lagrangian relaxation. Interfaces, 15, 2–21.CrossRefGoogle Scholar
  15. [15]
    Garey, M.R. and D.S. Johnson (1979). Computers and Intractability: A Guide to the Theory of NP-Completeness. W. H. Freeman, New York.Google Scholar
  16. [16]
    Megiddo, N., E. Zemel, and S.L. Hakimi (1983). The maximal coverage location problem. SIAM Journal of Algebra and Discrete Methods, 4, 253–261.MathSciNetCrossRefGoogle Scholar
  17. [17]
    Schilling, D., V. Jayaraman, and R. Barkhi (1993). A review of covering problems in facility location. Location Science, 1, 25–56.Google Scholar
  18. [18]
    Elloumi, S., M. Labbé, and Y. Pochet (2001). New formulation and resolution method for the P-center problem, Optimization Online,
  19. [19]
    Hakimi, S.L. (1964). Optimum locations of switching centers and the absolute centers and medians of a graph. Operations Research, 12, 450–459.zbMATHCrossRefGoogle Scholar
  20. [20]
    Hakimi, S.L. (1965). Optimum distribution of switching centers in a communication network and some related graph theoretic problems. Operations Research, 13, 462–475.zbMATHMathSciNetCrossRefGoogle Scholar
  21. [21]
    Maranzana, F.E. (1964). On the location of supply points to minimize transport costs. Operations Research Quarterly, 15, 261–270.CrossRefGoogle Scholar
  22. [22]
    Tietz, M.B. and P. Bart (1968). Heuristic methods for estimating generalized vertex median of a weighted graph. Operations Research, 16, 955–961.CrossRefGoogle Scholar
  23. [23]
    Bozkaya, B., J. Zhang, and E. Erkut (2002). An efficient genetic algorithm for the P-median problem, in Facility Location: Applications and Theory, Z. Drezner and H. Hamacher, Eds., Springer, Berlin.Google Scholar
  24. [24]
    Voss, S. (1996). A reverse elimination approach for the P-median problem. Studies in Locational Analysis, 8, 49–58.zbMATHGoogle Scholar
  25. [25]
    Rolland, E., J. Current, and D. Schilling (1996). An efficient tabu search procedure for the P-median problem. European Journal of Operational Research, 96, 329–342.CrossRefGoogle Scholar
  26. [26]
    Hansen, P. and N. Mladenovic (1997). Variable neighborhood Search for the P-median. Location Science, 5, 207–226.CrossRefGoogle Scholar
  27. [27]
    Correa, E.S., M.T. Steiner, A.A. Freitas, and C. Carnieri (2004). A genetic algorithm for solving a capacitated P-median problem, forthcoming in Numerical Algorithms.Google Scholar
  28. [28]
    Daskin, M. (2000). A new approach to solving the vertex P-center problem to optimality: Algorithm and computational results. Communications of the Operations Research Society of Japan, 45, 428–436.Google Scholar
  29. [29]
    Eaton, D., M. Daskin, D. Simmons, B. Bulloch, and G. Jansma (1985). Determining emergency medical service vehicle deployment in Austin, Texas. Interfaces, 15, 96–108.CrossRefGoogle Scholar
  30. [30]
    Adenso-Díaz, B. and F. Rodríguez (1997). A simple search heuristic for the MCLP: Application to the location of ambulance bases in a rural region. Omega, International Journal of Management Science, 25, 181–187.CrossRefGoogle Scholar
  31. [31]
    Sinuany-Stern, Z., A. Mehrez, A.-G. Tal, and B. Shemuel (1995). The location of a hospital in a rural region: The case of the Negev. Location Science, 3, 255–266.CrossRefGoogle Scholar
  32. [32]
    Mehrez, A., Z. Sinuany-Stern, A.-G. Tal, and B. Shemuel (1996). On the implementation of quantitative facility location models: The Case of a hospital in a rural region. Journal of the Operational Research Society, 47, 612–625.Google Scholar
  33. [33]
    Jacobs, D.A., M.N. Silan, and B.A. Clemson (1996). An Analysis of alternative locations and service areas of American Red Cross blood facilities. Interfaces, 26, 40–50.CrossRefGoogle Scholar
  34. [34]
    McAleer, W.E. and I.A. Naqvi (1994). The relocation of ambulance stations: A successful case study. European Journal of Operational Research, 75, 582–588.CrossRefGoogle Scholar
  35. [35]
    Daskin, M. (2002). SITATION Location Software, Department of Industrial Engineering and Management Sciences, Northwestern University,
  36. [36]
    Narula, S.C. (1986). Minisum hierarchical location-allocation problems on a network: A survey. Annals of Operations Research, 6, 257–272.CrossRefGoogle Scholar
  37. [37]
    Price, W.L. and M. Turcotte (1986). Locating a blood bank Interfaces, 16, 17–26.CrossRefGoogle Scholar
  38. [38]
    Drezner, Z., K. Klamroth, A. Schöbel, and G.O. Wesolowsky (2002). The Weber problem, in Facility Location: Applications and Theory, Z. Drezner and H.W. Hamacher, Eds., Springer, Berlin.Google Scholar
  39. [39]
    Kouvelis, P. and G. Yu (1996). Robust Discrete Optimization and its Applications. Kluwer Academic Publishers, Dordrecht.Google Scholar
  40. [40]
    Ringland, G. (1998). Scenario Planning: Managing for the Future. John Wiley, New York.Google Scholar
  41. [41]
    Sheppard, E.S. (1974). A conceptual framework for dynamic location-allocation analysis. Environment and Planning A, 6, 547–564.CrossRefGoogle Scholar
  42. [42]
    Daskin, M., S.M. Hesse, and C.S. ReVelle (1997). α-Reliable P-minimax regret: A new model for strategic facility location modeling. Location Science, 5, 227–246.CrossRefGoogle Scholar
  43. [43]
    Carson, Y.M. and R. Batta (1990). Locating an ambulance on the Amherst campus of the State University of New York at Buffalo. Interfaces, 20, 43–49.CrossRefGoogle Scholar
  44. [44]
    ReVelle, C., J. Schweitzer, and S. Snyder (1994). The maximal conditional covering problem. INFOR, 34, 77–91.Google Scholar
  45. [45]
    Current, J., S. Ratick, and C.S. ReVelle (1998). Dynamic facility location when the total number of facilities is uncertain: A decision analysis approach. European Journal of Operational Research, 110, 597–609.CrossRefGoogle Scholar
  46. [46]
    Daskin, M. and E. Stern (1981). A hierarchical objective set covering model for EMS vehicle deployment. Transportation Science, 15, 137–152.MathSciNetCrossRefGoogle Scholar
  47. [47]
    Benedict, J.M. (1983). Three Hierarchical Objective Models Which Incorporate the Concept of Excess Coverage to Locate EMS Vehicles or Hospitals. Department of Civil Engineering, Northwestern University, Evanston, IL.Google Scholar
  48. [48]
    Eaton, D.J., H.M. Sanchez, R.R. Lantigua, and J. Morgan (1986). Determining ambulance deployment in Santo Domingo, Dominican Republic. Journal of the Operational Research Society, 37, 113–126.Google Scholar
  49. [49]
    Hogan, K. and C. ReVelle (1986). Concepts and applications of backup coverage. Management Science, 32, 1434–1444.CrossRefGoogle Scholar
  50. [50]
    Daskin, M., K. Hogan, and C. ReVelle (1988). Integration of multiple, excess, backup and expected covering models. Environment and Planning B: Planning and Design, 15, 15–35.CrossRefGoogle Scholar
  51. [51]
    Gendreau, M., G. Laporte, and F. Semet (1997). Solving an ambulance location model by tabu search. Location Science, 5, 75–88.CrossRefGoogle Scholar
  52. [52]
    Pirkul, H. and D.A. Schilling (1988). The siting of emergency service facilities with workload capacities and backup service. Management Science, 34, 896–908.CrossRefGoogle Scholar
  53. [53]
    Narasimhan, S., H. Pirkul, and D.A. Schilling (1992). Capacitated emergency facility siting with multiple levels of backup. Annals of Operations Research, 40, 323–337.CrossRefGoogle Scholar
  54. [54]
    Fitzsimmons, J.A. (1973). A methodology for emergency ambulance deployment. Management Science, 19, 627–636.CrossRefGoogle Scholar
  55. [55]
    Eaton, D.J. (1979). Location Techniques for Emergency Medical Service Vehicles: Volume I-An Analytical Framework for Austin, Texas, University of Texas, Austin, TX.Google Scholar
  56. [56]
    Larson, R.C. (1974). A hypercube queueing model to facility location and redistricting in urban emergency services. Computers and Operations Research, 1, 67–95.CrossRefMathSciNetGoogle Scholar
  57. [57]
    Larson, R.C. (1975). Approximating the performance of urban emergency service systems. Operations Research, 23, 845–868.zbMATHCrossRefGoogle Scholar
  58. [58]
    Jarvis, J.P. (1975). Optimization in Stochastic Service Systems with Distinguishable Servers, Doctoral Dissertation, Massachusetts Institute of Technology, Cambridge, MA.Google Scholar
  59. [59]
    Brandeau, M.L. and R.C. Larson (1986). Extending and applying the hypercube queueing model to deploy ambulances in Boston, in Management Science and the Delivery of Urban Service, E. Ignall and A.J. Swersey, Eds., TIMS Studies in the Management Sciences Series, North-Holland/ Elsevier.Google Scholar
  60. [60]
    Daskin, M.S. (1982). Application of an expected covering model to EMS system design. Decision Sciences, 13, 416–439.CrossRefGoogle Scholar
  61. [61]
    Daskin, M.S. (1983). A maximum expected covering location model: Formulation, properties and heuristic solution. Transportation Science, 17, 48–70.CrossRefGoogle Scholar
  62. [62]
    Repende, J.F. and J.J. Bernardo (1994). Developing and validating a decision support system for locating emergency medical vehicles in Louisville, Kentucky. European Journal of Operational Research, 75, 567–581.CrossRefGoogle Scholar
  63. [63]
    Batta, R., J.M. Dolan, and N.N. Krishnamurthy (1989). The maximal expected covering location problem: Revisited. Transportation Science, 23, 277–287.MathSciNetCrossRefGoogle Scholar
  64. [64]
    ReVelle, C. and K. Hogan (1989). The maximum reliability location problem and α-reliable P-center problem: Derivatives of the probabilistic location set covering problem. Annals of Operations Research, 18, 155–174.CrossRefMathSciNetGoogle Scholar
  65. [65]
    ReVelle, C. and K. Hogan (1989). The maximum availability location problem. Transportation Science, 23, 192–200.MathSciNetCrossRefGoogle Scholar
  66. [66]
    Ball, M.O. and F.L. Lin (1993). A reliability model applied to emergency service vehicle location. Operations Research, 41, 18–36.CrossRefGoogle Scholar
  67. [67]
    Goldberg, J., et al. (1990). Validating and applying a model for locating emergency medical vehicles in Tucson, AZ. European Journal of Operational Research, 49, 308–324.CrossRefGoogle Scholar
  68. [68]
    Mandell, M. (1998). Covering models for two-tiered emergency medical services systems. Location Science, 6, 355–368.CrossRefGoogle Scholar
  69. [69]
    Aly, A.A. and J.A. White (1978). Probabilistic formulation of the emergency service location problem. Journal of the Operational Research Society, 29, 1167–1179.PubMedGoogle Scholar
  70. [70]
    Laporte, G., F. Semet, V.V. Dadeshidze, and L.J. Olsson (1998). A tiling and routing heuristic for the screening of cytological samples. Journal of the Operational Research Society, 49, 1233–1238.CrossRefGoogle Scholar
  71. [71]
    Balas, E. and A. Ho (1980). Set covering algorithms using cutting planes, heuristics, and subgradient optimization: a computational study. Math Programming Study, 12, 37–60.MathSciNetGoogle Scholar
  72. [72]
    Daganzo, C.F. (1984). The length of tours in zones of different shapes. Transportation Research B, 18B, 135–145.MathSciNetCrossRefGoogle Scholar
  73. [73]
    Brotcorne, L., G. Laporte, and F. Semet (2002). Fast heuristics for large scale covering-location problems. Computers and Operations Research, 29, 651–665.CrossRefMathSciNetGoogle Scholar
  74. [74]
    Snyder, L. (2003). Supply Chain Robustness and Reliability: Models and Algorithms. Department of Industrial Engineering and Management Sciences, Northwestern University, Evanston, IL.Google Scholar
  75. [75]
    Menezes, M., O. Berman, and D. Krass (2003). The Median problem with unreliable facilities. EURO/Informs Meeting. Istanbul, Turkey.Google Scholar
  76. [76]
    Daskin, M. and L. Snyder (2003). The reliability P-median problem. EURO/Informs Meeting. Istanbul, Turkey.Google Scholar
  77. [77]
    Lee, E.K., R.J. Gallagher, D. Silvern, C.-S. Wuu, and M. Zaider (1999). Treatment planning for brachytherapy: An integer programming model, two computational approaches and experiments with permanent prostate implant planning. Physics in Medicine and Biology, 44, 145–165.CrossRefADSPubMedGoogle Scholar

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© Springer Science + Business Media, Inc. 2005

Authors and Affiliations

  1. 1.Department of Industrial Engineering and Management SciencesNorthwestern UniversityEvanston

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