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A new probabilistic coverage model for ambulances deployment with hypercube queuing approach

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Abstract

Aiming at improving the efficiency and reliability of ambulance service, several location models for ambulance stations have been proposed in the facility location literature. Two well-known approaches to this problem are coverage and median models. Coverage model looks for the location to maximize the (deterministic or probabilistic) covered demand of ambulance calls. Hence, this model can be thought of reliability-oriented model. In median model, the objective is to minimize the total traveling distance of the ambulances from the station to the scene of call and thus is the cost-oriented model. In this paper, a new probabilistic coverage model is introduced. It uses the idea of MEXCLP and mixes it with the hypercube queuing model. The model is applied in a real case for one of Tehran city's zones in Iran. The results were satisfactory and show the applicability of the model. Sensitivity analysis was conducted to determine the overall behavior of system responsiveness against parameters of the model. Discussions on sensitivity analysis are presented.

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References

  1. Goldberg JB (2004) Operations research models for the deployment of emergency services vehicles. EMS Manag J 1(1):20–39

    Google Scholar 

  2. Takeda RA, Widmera João A, Morabito R (2007) Analysis of ambulance decentralization in an urban emergency medical service using the hypercube queuing model. J Comput Oper Res 34:727–741. doi:10.1016/j.cor.2005.03.022

    Article  MATH  Google Scholar 

  3. Brandeau ML, Larson RC (1986) Extending and applying the hypercube queuing model to deploy ambulances in Boston. In: Ignall E, Swersey AJ (eds) J of Management Science and the Delivery of Urban Service, 22nd edn, TIMS Studies in the Management Sciences Series., pp 121–154

    Google Scholar 

  4. Eaton D, Daskin M, Simmons D, Bulloch B, Jansma G (1985) Determining emergency medical service vehicle deployment in Austin, Texas. Interfaces 15–1:96–108

    Article  Google Scholar 

  5. Fujiwara M, Makjamroen T, Gupta K (1987) Ambulance deployment analysis: a case study of Bangkok. Eur J Oper Res 31:9–18

    Article  Google Scholar 

  6. Batta R, Dolan JM, Krishnamurthy N (1989) the maximal expected covering location problem: revisited. Transp Sci 23:277–287

    Article  MATH  MathSciNet  Google Scholar 

  7. Daskin MS (1983) A maximum expected covering location model, formulation, properties, and heuristic solution. J Transp Sci 17:48–70

    Article  Google Scholar 

  8. Chiyoshi F, Galvão RD, Morabito R (2003) A note on solutions to the maximal expected covering location problem. Comput Oper Res 30:87–96

    Article  MATH  MathSciNet  Google Scholar 

  9. Saydam C, Aytug H (2003) Accurate estimation of expected coverage: revisited. Socio-Economic Planning Sciences 37:69–80

    Article  Google Scholar 

  10. Jarvis JP (1975) Optimization in stochastic systems with distinguishable servers. Tech Rep 23:19–75

    Google Scholar 

  11. Gendreau M, Laporte G, Semet F (1997) Solving an ambulance location model by Tabu search. Locat Sci 5:75–88

    Article  MATH  Google Scholar 

  12. Swersey AJ (1994) The deployment of police, fire, and emergency medical units. In: Pollock SM et al (eds) Handbooks in OR and MS, 6th edn., pp 151–200

    Google Scholar 

  13. ReVelle C, Hogan K (1989) The maximum availability location problem. Transp Sci 23:192–200

    Article  MATH  MathSciNet  Google Scholar 

  14. Church R, Weaver J (1985) A median location model with non-closest facility service. Transp Sci 19:58–74

    Article  MathSciNet  Google Scholar 

  15. ReVelle C, Hogan K (1989) The maximum reliability location problem and-reliable p-center problem: derivatives of the probabilistic location set covering problems. Ann Oper Res 18:155–174

    Article  MATH  MathSciNet  Google Scholar 

  16. Gendreau M, Laporte G, Semet F (1997) Solving an ambulance location model by tabu search. J Locat Sci 5–2:75–88

    Article  Google Scholar 

  17. Pirkul H, Scilling D (1988) The siting of emergency service facilities with workload capacities and backup service. Manag Sci 37–7:896–908

    Article  Google Scholar 

  18. Narasimhan S, Pirkul H, Scilling D (1992) Capacitated emergency facility siting with multiple levels of backup. Ann Oper Res 40–1:323–337

    Article  Google Scholar 

  19. Marianov V, ReVelle C (1996) The Queuing maximal availability location problem: a model for the sitting of emergency vehicles. Eur J Oper Res 93–1:110–120

    Article  Google Scholar 

  20. ReVelle C, Hogan K (1989) The maximum availability location problem. Transp Sci 23–3:192–200

    Article  MathSciNet  Google Scholar 

  21. Silva F, Serra D (2003) Locating emergency services with priority rules: the priority queuing covering location problem. Economics Working Papers, Department of Economics and Business, Universitat PompeuFabra

  22. Marianov V, ReVelle C (1994) The Queuing probabilistic location set covering problem and some extensions. Socio-Economic Planning Sciences:167–178

  23. Marianov V, Serra D (1998) Probabilistic maximal covering location–allocation models for congested systems. J Reg Sci 38–3:401–424

    Article  Google Scholar 

  24. Marianov V, Serra D (2002) Location–allocation of multiple-server service centers with constrained queues or waiting times. Ann Oper Res 111:35–50

    Article  MATH  MathSciNet  Google Scholar 

  25. Benveniste R (1985) Solving the combined zoning and location problem for several emergency units. J Oper Res Soc 36:433–450

    MATH  Google Scholar 

  26. Jarvis J (1985) Approximating the equilibrium behavior of multi-server loss systems. Manag Sci 31–2:235–239

    Article  Google Scholar 

  27. Goldberg J, Paz L (1991) Locating emergency vehicle bases when service time depends on call location. Transp Sci 25:264–280

    Article  MATH  Google Scholar 

  28. Morabito R, Mendonca F (2001) Analyzing emergency medical service ambulance deployment on a Brazilian highway using the hypercube model. J Oper Res Soc 52–3:261–270

    Google Scholar 

  29. Budge S, Ingolfsson A, Zerom D (2010) Empirical analysis of ambulance travel times: the case of Calgary Emergency Medical Services. Manag Sci 56(4):716–723

    Article  Google Scholar 

  30. Larson RC (1974) A hypercube queuing model for facility location and redistricting in urban emergency services. Comput Oper Res 1:67–95

    Article  Google Scholar 

  31. Larson RC (1975) Approximating the performance of urban emergency service systems. Oper Res 23:845–868

    Article  MATH  Google Scholar 

  32. Iannoni AP, Morabito R, Saydam C (2008) A hypercube queuing model embedded into a genetic algorithm for ambulance deployment on highways. Ann Oper Res 157:207–224

    Article  MATH  Google Scholar 

  33. Iannoni AP, Morabito R (2007) A multiple dispatch and partial backup hypercube queuing model to analyze emergency medical systems on highways. Transp Res E 43:755–771

    Article  Google Scholar 

  34. Geroliminis N, Karlaftis MG, Skabardonis A (2006) A generalized hypercube queuing model for locating emergency response vehicles in urban transportation networks, 85th Annual Meeting Transportation Research Board Washington, D.C

  35. Geroliminis N, Karlaftis M, Skabardonis A (2009) A spatial queuing model for the emergency vehicle districting and location problem. Transp Res B Methodol 43(7):798–811, ISSN 0191–2615

    Article  Google Scholar 

  36. Geroliminis N, Kepaptsoglou K, Karlaftis M (2011) A hybrid hypercube—genetic algorithm approach for deploying many emergency response mobile units in an urban network. Eur J Oper Res 210(2):287–300, ISSN 0377–2217

    Article  MATH  MathSciNet  Google Scholar 

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Davoudpour, H., Mortaz, E. & Hosseinijou, S.A. A new probabilistic coverage model for ambulances deployment with hypercube queuing approach. Int J Adv Manuf Technol 70, 1157–1168 (2014). https://doi.org/10.1007/s00170-013-5336-8

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  • DOI: https://doi.org/10.1007/s00170-013-5336-8

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