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Health Care Management Science

, Volume 11, Issue 3, pp 262–274 | Cite as

Optimal ambulance location with random delays and travel times

  • Armann IngolfssonEmail author
  • Susan Budge
  • Erhan Erkut
Article

Abstract

We describe an ambulance location optimization model that minimizes the number of ambulances needed to provide a specified service level. The model measures service level as the fraction of calls reached within a given time standard and considers response time to be composed of a random delay (prior to travel to the scene) plus a random travel time. In addition to modeling the uncertainty in the delay and in the travel time, we incorporate uncertainty in the ambulance availability in determining the response time. Models that do not account for the uncertainty in all three of these components may overestimate the possible service level for a given number of ambulances and underestimate the number of ambulances needed to provide a specified service level. By explicitly modeling the randomness in the ambulance availability and in the delays and the travel times, we arrive at a more realistic ambulance location model. Our model is tractable enough to be solved with general-purpose optimization solvers for cities with populations around one Million. We illustrate the use of the model using actual data from Edmonton.

Keywords

Emergency medical services Ambulance location Facility location Dispatch delays 

Notes

Acknowledgment

This research was supported in part by the Natural Sciences and Engineering Research Council of Canada. We thank anonymous referees for several comments that led to improvements in the paper.

References

  1. 1.
    Atlason J, Epelman MA, Henderson SG (2007) Optimizing call center staffing using simulation and analytic center cutting-plane methods. Manage Sci, published online before print Dec 11, 2007. DOI  10.1287/mnsc.1070.0774
  2. 2.
    Berman O, Krass D (2001) Facility location problems with stochastic demands and congestion. In: Drezner Z, Hamacher HW (eds) Location analysis: applications and theory. Springer, New YorkGoogle Scholar
  3. 3.
    Brandeau M, Larson RC (1986) Extending and applying the hypercube model to deploy ambulances in Boston. In: Swersey A, Ignall E (eds) Delivery of urban services. North Holland, New YorkGoogle Scholar
  4. 4.
    Brotcorne L, Laporte G, Semet F (2003) Ambulance location and relocation models. Eur J Oper Res 147:451–463CrossRefGoogle Scholar
  5. 5.
    Budge S (2004) Emergency medical service systems: modelling uncertainty in response time. Ph.D. dissertation, Department of Finance and Management Science, University of Alberta, EdmontonGoogle Scholar
  6. 6.
    Budge S, Ingolfsson A, Erkut E (2007) Approximating vehicle dispatch probabilities for emergency service systems with location-specific service times and multiple units per location. Oper Res (in press)Google Scholar
  7. 7.
    Channouf N, L’Ecuyer P, Ingolfsson A, Avramidis AN (2007) The application of forecasting techniques to modeling emergency medical system calls in Calgary, Alberta. Health Care Manage Sci 10:25–45CrossRefGoogle Scholar
  8. 8.
    Church R, ReVelle C (1974) The maximal covering location problem. Pap Reg Sci Assoc 32:101–120CrossRefGoogle Scholar
  9. 9.
    Daskin MS (1983) A maximum expected covering location model: formulation, properties, and heuristic solution. Transp Sci 17:48–70Google Scholar
  10. 10.
    Daskin MS (1987) Location, dispatching, and routing model for emergency services with stochastic travel times. In: Ghosh A, Rushton G (eds) Spatial analysis and location-allocation models. Van Nostrand Reinhold, New York, pp 224–265Google Scholar
  11. 11.
    Eaton DJ, Daskin MS, Simmons D, Bulloch B, Jansma G (1985) Determining emergency medical service vehicle deployment in Austin, Texas. Interfaces 15:96–108Google Scholar
  12. 12.
    Erkut E, Fenske R, Kabanuk S, Gardiner Q, Davis J (2001) Improving the emergency service delivery in St. Albert. INFOR 39:416–433Google Scholar
  13. 13.
    Ernst AT, Jiang H, Krishnamoorthy M, Sier D (2004) Staff scheduling and rostering: a review of applications, methods and models. Eur J Oper Res 153:3–27CrossRefGoogle Scholar
  14. 14.
    Goldberg J, Dietrich R, Chen JM, Mitwasi MG, Valenzuela T, Criss E (1990) A simulation model for evaluating a set of emergency vehicle base locations: development, validation, and usage. Socio-Econ Plann Sci 24:125–141CrossRefGoogle Scholar
  15. 15.
    Goldberg J, Dietrich R, Chen JM, Mitwasi MG, 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
  16. 16.
    Goldberg J, Paz L (1991) Locating emergency vehicle bases when service time depends on call location. Transp Sci 25:264–280CrossRefGoogle Scholar
  17. 17.
    Green LV, Kolesar PJ, Soares J (2001) Improving the SIPP approach for staffing service systems that have cyclic demand. Oper Res 49:549–564CrossRefGoogle Scholar
  18. 18.
    Gross D, Harris CM (1998) Fundamentals of queueing theory, 3rd edn. Wiley, New YorkGoogle Scholar
  19. 19.
    Henderson SG, Mason AJ (2000) Development of a simulation and data visualisation tool to assist in strategic operations management in emergency services. School of Engineering Technical Report 595, University of Auckland, January 2000Google Scholar
  20. 20.
    Henderson SG, Mason AJ (2004) Ambulance service planning: simulation and data visualisation. In: Brandeau M, Sainfort F, Pierskalla W (eds) Operations research and health care: a handbook of methods and applications. Springer, New YorkGoogle Scholar
  21. 21.
    Ingolfsson A, Erkut E, Budge S (2003) Simulating a single start station for Edmonton EMS. J Oper Res Soc 54:736–746CrossRefGoogle Scholar
  22. 22.
    Ingolfsson A, Cabral E, Wu X (2007) Combining integer programming and the randomization method to schedule employees. Working paper. http://www.business.ualberta.ca/aingolfsson/publications.htm
  23. 23.
    Jarvis J (1981) Optimal assignments in a Markovian queueing system. Comput Oper Res 8:17–23CrossRefGoogle Scholar
  24. 24.
    Jarvis J (1985) Approximating the equilibrium behavior of multi-server loss systems. Manage Sci 31:235–239CrossRefGoogle Scholar
  25. 25.
    Kolesar PJ, Rider KL, Crabill TB, Walker WE (1975) A queuing-linear programming approach to scheduling police patrol cars. Oper Res 23:1045–1062Google Scholar
  26. 26.
    Larson RC (1974) A hypercube queueing model for facility location and redistricting in urban emergency services. Comput Oper Res 1:67–95CrossRefGoogle Scholar
  27. 27.
    Larson RC (1975) Approximating the performance of urban emergency service systems. Oper Res 23:845–868Google Scholar
  28. 28.
    Larson RC (1979) Structural system models for locational decisions: an example using the hypercube queueing model. In: Haley KB (ed) Operational Research ’78, Proceedings of the Eighth IFORS International Conference on Operations Research. North-Holland Publishing, Amsterdam, HollandGoogle Scholar
  29. 29.
    Marianov V, ReVelle C (1995) In: Drezner Z (ed) Siting emergency services. Facility location: a survey of applications and methods. Springer, New YorkGoogle Scholar
  30. 30.
    Marianov V, ReVelle C (1996) The queueing maximal availability location problem: a model for the siting of emergency vehicles. Eur J Oper Res 93:110–120CrossRefGoogle Scholar
  31. 31.
    Swersey AJ (1994) In: Pollock SM, Rothkopf MH, Barnett A (eds) The deployment of police, fire, and emergency medical units. Handbooks in operations research and management science, vol. 6: operations research and the public sector. North-Holland Publishing, Amsterdam, HollandGoogle Scholar
  32. 32.
    Toregas C, Swain R, ReVelle C, Bergman L (1971) The location of emergency service facilities. Oper Res 19:1363–1373Google Scholar
  33. 33.
    Willemain TR, Larson RC (eds) (1977) Emergency medical systems analysis. Lexington Books, Lexington, MAGoogle Scholar

Copyright information

© Springer Science+Business Media, LLC 2007

Authors and Affiliations

  1. 1.University of Alberta School of BusinessEdmontonCanada
  2. 2.Ozyegin UniversityIstanbulTurkey

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