Mathematical Methods of Operations Research

, Volume 74, Issue 3, pp 281–310 | Cite as

Covering models and optimization techniques for emergency response facility location and planning: a review

Original Article


With emergencies being, unfortunately, part of our lives, it is crucial to efficiently plan and allocate emergency response facilities that deliver effective and timely relief to people most in need. Emergency Medical Services (EMS) allocation problems deal with locating EMS facilities among potential sites to provide efficient and effective services over a wide area with spatially distributed demands. It is often problematic due to the intrinsic complexity of these problems. This paper reviews covering models and optimization techniques for emergency response facility location and planning in the literature from the past few decades, while emphasizing recent developments. We introduce several typical covering models and their extensions ordered from simple to complex, including Location Set Covering Problem (LSCP), Maximal Covering Location Problem (MCLP), Double Standard Model (DSM), Maximum Expected Covering Location Problem (MEXCLP), and Maximum Availability Location Problem (MALP) models. In addition, recent developments on hypercube queuing models, dynamic allocation models, gradual covering models, and cooperative covering models are also presented in this paper. The corresponding optimization techniques to solve these models, including heuristic algorithms, simulation, and exact methods, are summarized.


Emergency facility location Modeling and optimization Mathematical modeling Covering model Genetic algorithm Tabu search Simulation 


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  1. Aickelin U (2002) An indirect genetic algorithm for set covering problems. J Oper Res Soc 53: 1118–1126MATHCrossRefGoogle Scholar
  2. Alsalloum OI, Rand GK (2003) A goal programming model applied to the ems system at riyadh city, saudi arabia, working PaperGoogle Scholar
  3. Alsalloum OI, Rand GK (2006) Extensions to emergency vehicle location models. Comput Oper Res 33: 2725–2743MATHCrossRefGoogle Scholar
  4. Aly AA, White JA (1978) Probabilistic formulation of the emergency service location problem. J Oper Res Soc 29: 1167–1179MATHGoogle Scholar
  5. Andersson T (2005) Decision support tools for dynamic fleet management. Ph.D. thesis, Department of Science and Technology, Linkoepings Universitet, Norrkoeping, SwedenGoogle Scholar
  6. Andersson T, Vaerband P (2007) Decision support tools for ambulance dispatch and relocation. J Oper Res Soc 58: 195–201MATHGoogle Scholar
  7. Araz C, Selim H, Ozkarahan I (2007) A fuzzy multi-objective covering-based vehicle location model for emergency services. Comput Oper Res 34: 705–726MATHCrossRefGoogle Scholar
  8. Arostegui MA, Kadipasaoglu SN, Khumawala BM (2006) An empirical comparison of tabu search, simulated annealing, and genetic algorithms for facilities location problems. Int J Prod Econ 103: 742–754CrossRefGoogle Scholar
  9. Aytug H, Saydam C (2002) Solving large-scale maximum expected covering location problems by genetic algorithms: a comparative study. Eur J Oper Res 141: 480–494MathSciNetMATHCrossRefGoogle Scholar
  10. Ball M, Lin F (1993) A reliability model applied to emergency service vehicle location. Oper Res 41: 18–36MATHCrossRefGoogle Scholar
  11. Basar A, Catay B, Unluyurt T (2008) A new model and tabu search approach for planning the emergency service stations. In: Operations research proceedingsGoogle Scholar
  12. Batta R, Dolan JM, Krishnamurthy NN (1989) The maximal expected covering location problem: revisited. Transport Sci 23: 277–287MathSciNetMATHCrossRefGoogle Scholar
  13. Beasley J, Chu P (1996) A genetic algorithm for the set covering problem. Eur J Oper Res 94: 392–404MATHCrossRefGoogle Scholar
  14. Berman O (1981) Dynamic repositioning of indistinguishable service units on transportation networks. Transport Sci 15: 115–136CrossRefGoogle Scholar
  15. Berman O (1981) Repositioning of distinguishable urban service units on networks. Comput Oper Res 8: 105–118CrossRefGoogle Scholar
  16. Berman O (1981) Repositioning of two distinguishable service vehicles on networks. IEEE Trans Syst Man Cybernet 11: 187–193CrossRefGoogle Scholar
  17. Berman O, Krass D (2002) Facility location problems with stochastic demands and congestion. In: Facility locations: application and theory. Springer, Berlin, pp 329–371Google Scholar
  18. Berman O, Drezner Z, Krass D (2010) Discrete cooperative covering problems. J Oper Res Soc. Advance online publicatin 15 December 2010Google Scholar
  19. Brandeau M, Larson R (1986) Extending and applying the hypercube queueing model to deploy ambulances in Boston. TIMS Stud Manage Sci 22: 121–153Google Scholar
  20. Brotcorne L, Laporte G, Semet F (2002) Fast heuristics for large scale covering-location problems. Comput Oper Res 29: 651–665MathSciNetMATHCrossRefGoogle Scholar
  21. Brotcorne L, Laporte G, Semet F (2003) Ambulance location and relocation models. Eur J Oper Res 147(4): 451–463MathSciNetMATHCrossRefGoogle Scholar
  22. Burwell T (1986) A spatially distributed queuing model for ambulance systems. Ph.D. thesis, Clemson University, ClemsonGoogle Scholar
  23. Burwell T, Jarvis J, McKnew M (1993) Modeling co-located servers and dispatch ties in the hypercube model. Comput Oper Res 20: 113–119MATHCrossRefGoogle Scholar
  24. Ceria S, Nobili P, Sassano A (1998) A lagrangian-based heuristic for large-scale set covering problems. Math Program 81: 215–228MathSciNetMATHGoogle Scholar
  25. Chan Y (2001) Location theory and decision analysis. South Western College Publishing, CincinnatiGoogle Scholar
  26. Chung C (1986) Recent applications of the maximal covering location planning (M.C.L.P.) model. J Oper Res Soc 37: 735–746MATHGoogle Scholar
  27. Church RL, ReVelle CS (1974) The maximum covering location problem. Papers Reg Sci Assoc 32: 101–118CrossRefGoogle Scholar
  28. Cooper L (1964) Heuristic methods for location-allocation problems. Soc Indus Appl Math 6: 37–53Google Scholar
  29. Cordeau J, Laporte G, Potvin J, Salvesbergh M (2007) Transportation on demand. In: Barnhart C, Laporte G (eds) Transportation, handbooks in operations research and management science. Elsevier, Amsterdam, pp 429–466Google Scholar
  30. Coskun N, Erol R (2010) An optimization model for locating and sizing emergency medical service stations. J Med Syst 34: 43–49CrossRefGoogle Scholar
  31. Daskin M, Stern E (1981) A hierarchical objective set covermg model for emergency medical service deployment. Tansport Sci 15: 137–152MathSciNetCrossRefGoogle Scholar
  32. Daskin MS (1983) A maximum expected covering location model: Formulation, properties and heuristic solution. Trans Sci 17: 48–68CrossRefGoogle Scholar
  33. Daskin M, Hogan K, ReVelle C (1988) Integration of multiple, excess, backup and expected covering models. Environ Plan B 15: 13–35CrossRefGoogle Scholar
  34. Daskin M (1995) Network and discrete location. Wiley, New YorkMATHCrossRefGoogle Scholar
  35. Dessouky M (2006) Rapid distribution of medical supplies. In: Patient flow: reducing delay in healthcare delivery. Springer, USA, pp 309–339Google Scholar
  36. Diaz B, Rodriguez F (1997) A simple search heuristic for the mclp: Application to the location of ambulance based in a rural region. Int J Manage Sci 25: 181–187Google Scholar
  37. Doerner K, Gutjahr W, Hartl R, Karall M, Reimann M (2005) Heuristic solution of an extended double-coverage ambulance location problem for austria. Cent Eur J Oper Res 13: 325–340MATHGoogle Scholar
  38. Doerner KF, Hartl RF (2008) Health care logistics, emergency preparedness, and disaster relief: New challenges for routing problems with a focus on the austrian situation. In: The vehicle rounting problem: lastest Advances and New Challenges. Springer, USA, pp 527–550Google Scholar
  39. Drezner T, Drezner Z, Goldstein Z (2010) A stochastic gradual cover location problem. Naval Res Logist 57: 367–372MathSciNetMATHGoogle Scholar
  40. Eaton D, Church R, Bennett V, Hamon B, Lopez L (1981) On deployment of health resources in rural valle del cauca, colombia. TIMS Stud Manage Sci 17: 331–359Google Scholar
  41. Eaton D, Daskin M, Simmons D, Bulloch B, Jansma G (1985) Determining emergency medical service vehicle deployment in austin, texas. Interfaces 15: 96–108CrossRefGoogle Scholar
  42. Eaton D, Sanchez H, Lantigua R, Morgan J (1986) Determining ambulance deployment in santo domingo, dominican republic. J Oper Res Soc 37: 113–126Google Scholar
  43. Eiselt HA, Marianov V (2009) Gradual location set covering with service quality. Socio Econ Plan Sci 43: 121–130CrossRefGoogle Scholar
  44. Erkut E, Ingolfsson A, Erdogan G (2007) Ambulance location for maximum survival. Naval Res Logist 55: 42–58MathSciNetCrossRefGoogle Scholar
  45. Fujiwara O, Makjamroen T, Gupta K (1987) Ambulance deployment analysis: a case study of Bangkok. Eur J Oper Res 31(1): 9–18CrossRefGoogle Scholar
  46. Fujiwara O, Kachenchai K, Makjamroen T, Gupta K (1988) An efficient scheme for deployment of ambulances in metropolitan Bangkok. In: Rand GK (ed) Operational research ’87, pp 730–741Google Scholar
  47. Galvao RD, ReVelle C (1996) A lagrangean heuristic for the maximal covering location problem. Eur J Oper Res 88: 114–123MATHCrossRefGoogle Scholar
  48. Galvao RD, Chiyoshi FY, Morabito R (2005) Towards unified formulations and extensions of two classical probabilistic location models. Comput Oper Res 32: 15–33MathSciNetMATHCrossRefGoogle Scholar
  49. Gendreau M, Laporte G, Semet F (1997) Solving an ambulance location model by tabu search. Location Sci 5(2): 77–88CrossRefGoogle Scholar
  50. Gendreau M, Laporte G, Semet F (2001) A dynamic model and parallel tabu search heuristic for real-time ambulance relocation. Parallel Comput 27: 1641–1653MATHCrossRefGoogle Scholar
  51. Gendreau M, Laporte G, Semet F (2006) The maximal expected coverage relocation problem for emergency vehicles. J Oper Res Soc 57: 22–28MATHCrossRefGoogle Scholar
  52. Geroliminis N, Karlaftis M, Skabardonis A (2006) A generalized hypercube queueing model for locating emergency response vehicles in urban transportation networks. TRB 2006 Annual Meeting CD-ROMGoogle Scholar
  53. Geroliminis N, Karlaftis M, Stathopoulos A, Kepaptsoglou K (2004) A districting and location model using spatial queues. TRB 2004 Annual Meeting CD-ROMGoogle Scholar
  54. Goldberg J (2004) Operations research models for the deployment of emergency services vehicles. EMS Manage J 1: 20–39Google Scholar
  55. Goldberg J, Dietrich R, Chen J, Mitwasi M, Valenzuela T, Criss E (1990) A simulation model for valuating a set of emergency vehicle base location: development, validation, and usage. Socio Econ Plan Sci 24: 125–141CrossRefGoogle Scholar
  56. Goldberg J, Dietrich R, Chen J, Mitwasi M, Valenzuela T, Criss E (1990) Validating and applying a model for locating emergency medical vehicles in tucson, az. Eur J Oper Res 49: 308–324CrossRefGoogle Scholar
  57. Goldberg J, Szidarovszky F (1991) Methods for solving nonlinear equations used in evaluating vehicle busy probabilities. Oper Res 39: 903–916MATHCrossRefGoogle Scholar
  58. Green L, Kolesar P (2004) Improving emergency responsiveness with management science. Manage Sci 50: 1001–1014CrossRefGoogle Scholar
  59. Harewood S (2002) Emergency ambulance deployment in barbados: a multi-objective approach. J Oper Res Soc 53: 185–192MATHCrossRefGoogle Scholar
  60. Henderson S, Mason A (2004) Ambulance service planning: simulation and data visualization. In: Operations research and health care: a handbook of methods and applications. Kluwer, Boston, pp 77–102Google Scholar
  61. Hogan K, ReVelle C (1986) Concepts and applications of backup coverage. Manage Sci 32: 1434–1444CrossRefGoogle Scholar
  62. Iannoni AP, Morabito R (2007) A multiple dispatch and partial backup hypercube queuing model to analyze emergency medical systems on highways. Trans Res Part E 43: 755–771CrossRefGoogle Scholar
  63. Iannoni AP, Morabito R, Saydam C (2008) A hypercube queueing model embedded into a genetic algorithm for ambulance depolyment on highways. Ann Oper Res 157: 207–224MATHCrossRefGoogle Scholar
  64. Iannoni AP, Morabito R, Saydam C (2009) An optimization approach for ambulance location and the districting of the response segments on highways. Eur J Oper Res 195: 528–542MATHCrossRefGoogle Scholar
  65. Jaramillo J, Bhadury J, Batta R (2002) On the use of genetic algorithms to solve location problems. Comput Oper Res 29: 761–779MathSciNetMATHCrossRefGoogle Scholar
  66. Jarvis JP (1985) Approximating the equilibrium behavior of multi-server loss systems. Manage Sci 32: 235–239CrossRefGoogle Scholar
  67. Jia H, Ordonez F, Dessouky MM (2007) A modeling framework for facility location of medical service for large-scale emergency. IIE Trans 39(1): 35–41CrossRefGoogle Scholar
  68. Jia H, Ordonez F, Dessouky MM (2007) Solution approaches for facility location of medical supplies for large-scale emergecies. Comput Indus Eng 52(1): 257–276CrossRefGoogle Scholar
  69. Karasakal O, Karasakal EK (2004) A maximal covering location model in the presence of partial coverage. Comput Oper Res 31: 1515–1526MathSciNetMATHCrossRefGoogle Scholar
  70. Laporte G, Louveaux FV, Semet F, Thirion A (2009) Application of the double standard model for ambulance location. In: Innovations in distribution logistics. Springer, Berlin, pp 235–249Google Scholar
  71. Larson R, Odoni A (1981) Urban operations research. Prentice-Hall, Englewood CliffsGoogle Scholar
  72. Larson RC (1974) A hypercube queuing model for facility location and redistricting in urban emergency services. Comput Oper Res 1: 67–95MathSciNetCrossRefGoogle Scholar
  73. Larson RC (1975) Approximating the performance of urban emergency service systems. Oper Res 23: 845–867MATHCrossRefGoogle Scholar
  74. Liu M, Lee J (1988) A simulation of a hospital emergency call system using slam ii. Simulation 51: 216–221CrossRefGoogle Scholar
  75. Mannino C, Sassano A (1995) Solving hard set covering problem. Oper Res Lett 18: 1–5MathSciNetMATHCrossRefGoogle Scholar
  76. Marianov V, ReVelle C (1994) The queuing probabilistic location set covering problem and some extensions. Socio Econ Plan Sci 28: 167–178CrossRefGoogle Scholar
  77. Marianov V, ReVelle C (1995) Sitting emergency services. In: Facility location: a survey of appication and methods. Springer, New York, pp 199–223Google Scholar
  78. Marianov V, ReVelle C (1996) The queueing maximal availability locationm problem: a model for the siting of emergency vehicles. Eur J Oper Res 93(1): 110–120MATHCrossRefGoogle Scholar
  79. Marianov V, Serra D (1998) Probabilistic maximal covering location allocation models for congested systems. J Reg Sci 38: 401–424CrossRefGoogle Scholar
  80. Marianov V, Serra D (2002) Location problems in the public sector. In: Facility locations: application and theory. Springer, Berlin, pp 119–150Google Scholar
  81. Maxwell MS, Henderson SG, Topalogu H (2009a) Ambulance redeployment: an approximate dynamic programming approach. In: Rossetti MD, Hill RR, Johansson B, Dunkin A, Ingalls R (eds) Proceedings of 2009 winter simulation conferenceGoogle Scholar
  82. Maxwell MS, Restrepo M, Henderson SG, Topaloglu H (2009b) Approximate dynamic programming for ambulance redeployment (to appear)Google Scholar
  83. McKnew MA (1983) An approximation to the hypercube model with patrol initiated activities: an application to police. Decis Sci 14: 408–418CrossRefGoogle Scholar
  84. McLay LA (2009) A maximum expected covering location model with two types of servers. IIE Trans 41: 730–741CrossRefGoogle Scholar
  85. Mendonca FC, Morabito R (2001) Analysing emergency medical service ambulance deployment on a brazilian highway using the hypercube model. J Oper Res Soc 52: 261–270MATHCrossRefGoogle Scholar
  86. Nair R, Miller-Hooks E (2006) A case study of ambulance location and relocation. Presentation in INFORMS Annual Meeting, Pittsburgh PennsylvaniaGoogle Scholar
  87. Ohlsson M, Peterson C, Soderberg B (2001) An efficient mean field approach to the set covering problem. Eur J Oper Res 133: 583–595MathSciNetMATHCrossRefGoogle Scholar
  88. Owen S, Daskin M (1998) Strategic facility location: a review. Eur J Oper Res 111: 423–447MATHCrossRefGoogle Scholar
  89. Rajagopalan HK, Saydam C (2005) An effective and accurate hybrid meta heuristic for a probabilistic coverage location problem for dynamic deployment. In: Proceedings of 35th international coference on computers and industrial engineeringGoogle Scholar
  90. Rajagopalan HK, Saydam C, Xiao J (2005) A multiperiod expected covering location model for dynamic redeployment of ambulances. In: Proceedings of the joint conference-10th EWGT meeting and 16th Mini-EURO conference, Poznan, PolandGoogle Scholar
  91. Rajagopalan HK, Saydam C, Xiao J (2008) A multiperiod set covering location model for dynamic redeployment of ambulances. Comput Oper Res 35: 814–826MATHCrossRefGoogle Scholar
  92. Rajagopalan HK, Vergara FE, Saydam C, Xiao J (2007) Developing effective meta-heuristics for a probabilistic location model via experimental design. Eur J Oper Res 177: 83–101MATHCrossRefGoogle Scholar
  93. Repede JF, Bernardo JJ (1994) Developing and validating a decision support system for locating emergenct medical vehicles in louisville kentucky. Eur J Oper Res 75(5): 567–581CrossRefGoogle Scholar
  94. Restrepo M (2008) Computational methods for static allocation and real-time redeployment of ambulances. Ph.D. thesis, Cornell University, Ithaca, New YorkGoogle Scholar
  95. ReVelle C (1989) Review, extension and prediction in emergency siting models. Eur J Oper Res 40: 58–69MathSciNetMATHCrossRefGoogle Scholar
  96. ReVelle C (1991) Siting ambulances and fire companies: new tools for planners. J Am Plan Assoc 57: 471–484CrossRefGoogle Scholar
  97. ReVelle C, Hogan K (1989) The maximum availability location problem. Trans Sci 23: 192–200MathSciNetMATHCrossRefGoogle Scholar
  98. ReVelle C, Hogan K (1989) The maximum reliability location problem and alpha reliable p-center problems: derivatives of the probabilistic location set covering problem. Ann Oper Res 18: 155–174MathSciNetMATHCrossRefGoogle Scholar
  99. Saydam AC, McKnew MA (1985) A separable programming approach to expected coverage: an application to ambulance location. Decis Sci 16: 381–398CrossRefGoogle Scholar
  100. Saydam C, Aytug H (2003) Accurate estimation of expected coverage: revisited. Socio Econ Plan Sci 37: 69–80CrossRefGoogle Scholar
  101. Schilling D (1980) Dynamic location modeling for public-sector facilities: a multicriteria approach. Decis Sci 11: 714–724CrossRefGoogle Scholar
  102. Schilling D, Elzinga D, Cohon J, Church RL, ReVelle C (1979) The teem/fleet models for simultaneous facility and equipment sitting. Trans Sci 13: 163–175CrossRefGoogle Scholar
  103. Schilling D, Jayaraman V, Barkhi R (1993) A review of covering problems in facility location. Locat Sci 1: 25–55MATHGoogle Scholar
  104. Scott A (1971) Dynamic location-allocation systems: some basic planning strategies. Environ Plan 3: 73–82CrossRefGoogle Scholar
  105. Shiah D-M, Chen S-W (2007) Ambulance allocation capacity model. In: e-Health networking, applications and services, 2007 9th international conference, Taipei,TaiwanGoogle Scholar
  106. Sorensen P, Church R (2010) Integrating expected coverage and local reliability for emergency medical services location problems. Socio Econ Plan Sci 44: 8–18CrossRefGoogle Scholar
  107. Swoveland C, Uyeno D, Vertinsky I, Vickson R (1973) A simulation-based methodology for optimization of ambulance service policies. Socio Econ Plan Sci 7: 697–703CrossRefGoogle Scholar
  108. Takeda RA, Widmer JA, Morabito R (2007) Analysis of ambulance decentralization in an urban emergency medical service using the hypercube queueing model. Comput Oper Res 34: 727–741MATHCrossRefGoogle Scholar
  109. Toregas C, Swain R, ReVelle C, Bergman L (1971) The location of emergency service facilities. Oper Res 19: 1363–1373MATHCrossRefGoogle Scholar
  110. Wesolowsky G, Truscott W (1976) The multiperiod location-allocation problem with relocation of facilities. Manage Sci 22: 57–65CrossRefGoogle Scholar
  111. Zaki A, Cheng H, Parker B (1997) A simulation model for the analysis and management of an emergency service system. Socio Econ Plan Sci 31: 173–189CrossRefGoogle Scholar
  112. Zhang O, Mason AJ, Philpott AB (2008) Simulation and optimisation for ambulance logistics and relocation. Presentation in INFORMS Annual Meeting, Washington, DCGoogle Scholar

Copyright information

© Springer-Verlag 2011

Authors and Affiliations

  • Xueping Li
    • 1
  • Zhaoxia Zhao
    • 1
  • Xiaoyan Zhu
    • 1
  • Tami Wyatt
    • 2
  1. 1.Department of Industrial and Information EngineeringUniversity of TennesseeKnoxvilleUSA
  2. 2.College of NursingUniversity of TennesseeKnoxvilleUSA

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