Abstract
Emergency medical services (EMS) systems provide out-of-hospital acute medical care and transportation to the appropriate health care provider to patients with illnesses and injuries. The objective of EMS systems is to satisfy demand requests by providing timely first care medical assistance to patients at the incident scene. This paper aims at designing a robust two-tiered EMS system while accounting for the inherent uncertainty of the demand. A two-stage stochastic programming location-allocation model is proposed to simultaneously determine the location of ambulance stations, the number and the type of ambulances to be deployed, and the demand areas served by each station. This problem is then solved efficiently using the sampling average approximation algorithm. Computational experiments highlight the performance of the proposed solution approach and its practical applicability.
Similar content being viewed by others
References
Aboueljinane L, Jemai Z, Evren S (2012) Reducing ambulance response time using simulation: the case of val-de-marne department emergency medical service. In: Proceedings of the winter simulation conference, Berlin, Germany
Ahmed S, Shapiro A (2008) Solving chance-constrained stochastic programs via sampling and integer programming. Tutorials in operations research. In: Chen Z-L, Raghavan S (eds) INFORMS, pp 261–269
Andersson T, Värbrand P (2007) Decision support tools for ambulance dispatch and relocation. J Oper Res Soc 58:195–201. doi:10.1057/palgrave.jors.2602174
Aringhieri R, Carello G, Morale D (2007) Ambulance location through optimization and simulation: the case of Milano urban area. In: Proceedings of the annual conference of the operations research society optimization and decision sciences, Milan, Italy
Ball O, Lin LF (1993) A reliability model applied to emergency service vehicle location. Oper Res 41:18–36. doi:10.1287/opre.41.1.18
Bélanger V, Ruiz A, Soriano P (2015) Recent advances in emergency medical services management. Available via CIRRELT. https://www.cirrelt.ca/DocumentsTravail/CIRRELT-2015-28. Accessed July 2015
Beraldi P, Bruni ME (2009) A probabilistic model applied to emergency service vehicle location. Eur J Oper Res 196:323–331. doi:10.1016/j.ejor.2008.02.027
Beraldi P, Bruni ME, Conforti D (2004) Designing robust emergency medical service via stochastic programming. Eur J Oper 158:183–193. doi:10.1016/S0377-2217(03)00351-5
Blanchard IE, Doig CJ, Hagel BE, Anton AR, Zygun DA, Kortbeek JB, Powell DG, Williamson TS, Fick GH, Innes GD (2012) Emergency medical services response time and mortality in an urban setting. Prehosp Emerg Care 16:142–511. doi:10.3109/10903127.2011.614046
Church R, ReVelle C (1974) The maximal covering location problem. Pap Reg Sci Assoc 32:101–118. doi:10.1111/j.1435-5597.1974.tb00902.x
Current J, Daskin M, Schilling D (2001) Discrete network location models. In: Drezner Z, Hamacher HW (eds) facility location: applications and theory. Springer, Berlin, pp 83–120
Daskin MS (1983) A maximum expected location model: formulation, properties and heuristic solution. Transp Sci 7:48–70. doi:10.1287/trsc.17.1.48
Erkut E, Ingolfsson A, Erdogan G (2008) Ambulance location for maximum survival. Nav Res Logist 55:42–58. doi:10.1002/nav.20267
Fitzsimmons JA (1971) An emergency medical system simulation model. In: Proceedings of the winter simulation conference, ACM, New York, USA, pp 18–25
Geroliminis N, Kepaptsoglou K, Karlaftis MG (2011) Ahybrid hypercube-genetic algorithm approach for deploying many emergency response mobile units in an urban network. Eur J Oper Res 210:287–300. doi:10.1016/j.ejor.2010.08.031
Gonzales RP, Cummings GR, Phelan HA, Muleker MS, Rodning CB (2009) Does increased emergency medical services prehospital time affect patient mortality in rural motor vehicle crashes? A statewide analysis. Am J Surg 197:30–34. doi:10.1016/j.amjsurg.2007.11.018
Iannoni AP, Morabito R, Saydam C (2011) Optimizing large-scale emergency medical system operations on highways using the hypercube queuing model. Socioecon Plan Sci 45:105–117. doi:10.1016/j.seps.2010.11.001
Ingolfsson A, Erkut E, Budge S (2003) Simulation of single start station for Edmonton EMS. J Oper Res Soc 54:736–746. doi:10.1057/palgrave.jors.2601574
Ingolfsson A, Budge S, Erkut E (2008) Optimal ambulance location with random delays and travel times. Health Care Manag Sci 11:262–274. doi:10.1007/s10729-007-9048-1
Iskander WH (1989) Simulation modeling for emergency medical service systems. In: Proceedings of the winter simulation conference, Washington, USA, pp 1107–1111
Jagtenberg CJ, Bhulai S, van der Mei RD (2015) An efficient heuristic for real-time ambulance redeployment. Oper Res Health Care 4:27–35. doi:10.1016/j.orhc.2015.01.001
Kergosien Y, Bélanger V, Soriano P, Gendreau M, Ruiz A (2015) A generic and flexible simulation-based analysis tool for EMS management. Int J Prod Res 53:7299–7316. doi:10.1080/00207543.2015.1037405
Kleywegt AJ, Shapiro A, Homem-de-Mello T (2001) The sample average approximation method for stochastic discrete optimization. SIAM J Optim 12:479–502. doi:10.1137/S1052623499363220
Lam SSW, Ng YS, Lakshmanan MR, Ng YY, Marcus EHO (2016) Ambulance deployment under demand uncertainty. J Adv Manag Sci 4:187–194. doi:10.12720/joams.4.3.187-194
Larson RC (1974) A hypercube queueing model for facility location and redistricting in urban emergency service. Comput Oper Res 1:67–95. doi:10.1016/0305-0548(74)90076-8
Larson RC (1975) Approximating performance of urban emergency service systems. Oper Res 23:845–868. doi:10.1287/opre.23.5.845
Lubicz M, Mielczarek B (1987) Simulation modelling of emergency medical services. Eur J Oper Res 29:178–185. doi:10.1016/0377-2217(87)90107-X
Luedtke J, Ahmed S (2008) A Sample approximation approach for optimization with probabilistic constraints. SIAM J Optim 19:674–699. doi:10.1137/070702928
Mak WK, Morton DP, Wood RK (1999) Monte Carlo bounding techniques for determining solution quality in stochastic programs. Oper Res Lett 24:47–56. doi:10.1016/S0167-6377(98)00054-6
Mandell M (1998) Covering models for two-tiered emergency medical services systems. Locat Sci 6:355–368. doi:10.1016/S0966-8349(98)00058-8
Marianov V, ReVelle CS (1992) The capacitated standard response fire protection siting problem: deterministic and probabilistic models. Ann Oper Res 40:303–322. doi:10.1007/BF02060484
Maxwell MS, Henderson SG, Topaloglu H (2009) Ambulance redeployment: an approximate dynamic programming approach. In: Proceedings of the winter simulation conference, Piscataway NJ, USA, pp 1850–1860
McLay LA (2009) A maximum expected covering location model with two types of servers. IIE Trans 41:730–741. doi:10.1080/07408170802702138
Naoum-Sawaya J, Elhedhli S (2013) A stochastic optimization model for real-time ambulance redeployment. Comput Oper Res 40:1972–1978. doi:10.1016/j.cor.2013.02.006
Nickel S, Reuter-Oppermann M, Saldanha-da-Gama F (2015) Ambulance location under stochastic demand: a sampling approach. Oper Res Health Care 8:24–32. doi:10.1016/j.orhc.2015.06.006
Norkin VI, Pflug GC, Ruszczynski A (1998) A branch and bound method for stochastic global optimization. Math Program 83:425–450. doi:10.1007/BF02680569
Noyan N (2010) Alternate risk measures for emergency medical service system design. Ann Oper Res 181:559–589. doi:10.1007/s10479-010-0787-x
O’Keeffe C, Nicholl J, Turnerl J, Goodacre S (2010) Role of ambulance response times in the survival of patients with out-of-hospital cardiac arrest. Emerg Med J 28:703–706. doi:10.1136/emj.2009.086363
ReVelle C, Hogan K (1989) The maximum reliability location problemand α-reliable P-Center problems: derivatives of the probabilistic location set covering problem. Ann Oper Res 18:155–174. doi:10.1007/BF02097801
ReVelle C, Marianov V (1991) A probabilistic FLEET model with individual reliability requirements. Eur J Oper Res 53:93–105. doi:10.1016/0377-2217(91)90095-D
Ruszczynski A, Shapiro A (2004) Stochastic programming. Handbooks in Operations research and management science. Elsevier, Amsterdam
Savas ES (1969) Simulation and cost-effectiveness analysis of New York’s emergency ambulance service. Manag Sci 15:608–627. doi:10.1287/mnsc.15.12.B608
Schilling DA, Elzinga DJ, Cohon J, Church RL, ReVelle CS (1979) The TEAM/FLEET models for simultaneous facility and equipment sitting. Transp Sci 13:163–175. doi:10.1287/trsc.13.2.163
Schmid V (2012) Solving the dynamic ambulance relocation and dispatching problem using approximate dynamic programming. Eur J Oper Res 219:611–621. doi:10.1016/j.ejor.2011.10.043
Silva PMS, Pinto LR (2010) Emergency medical systems analysis by simulation and optimization. In: Proceedings of the winter simulation conference, Baltimore, Maryland, pp 1850–1860
Snyder LV (2006) Facility location under uncertainty: a review. IIE Trans 38:537–554. doi:10.1080/07408170500216480
Stout J, Pepe PE, Mosesso VN (2000) All-advanced life support vs tiered-response ambulance systems. Prehosp Emerg Care 4:1–6. doi:10.1016/S1090-3127(00)70065-7
Su S, Shih C-L (2003) Modeling an emergency medical services system using computer simulation. Int J Med Inform 72:57–72. doi:10.1016/j.ijmedinf.2003.08.003
Sund B, Svensson L, Rosenqvist M, Hollenberg J (2011) Favourable cost-benefit in an early defibrillation programme using dual dispatch of ambulance and fire services in out-of-hospital cardiac arrest. Eur J Health Econ 13:811–818. doi:10.1007/s10198-011-0338-7
Swoveland C, Uyeno D, Vertinsky I, Vickson R (1973) A simulation-based methodology for optimization of ambulance service policies. Socio-Econ Plan Sci 7:697–703. doi:10.1016/0038-0121(73)90033-5
van Buuren M, van der Mei R, Aardal K, Post H (2012) Evaluating dynamic dispatch strategies for emergency medical services: TIFAR simulation tool. In: Proceedings of the winter simulation conference, Berlin, Germany
Van Essen JT, Hurink JL, Nickel S, Reuter M (2014) Models for ambulance planning on the strategic and the tactical level. Beta publishing. http://doc.utwente.nl/87377. Accessed 2013
Wolsey LA (1998) Integer programming. Wiley-Interscience series in Discrete Mathematics and Optimization, New York
Zhang Z-H, Jiang H (2014) A robust counterpart approach to the bi-objective medical service design problem. Appl Math Model 38:1033–1040. doi:10.1016/j.apm.2013.07.028
Zhang Z-H, Li K (2015) A novel probabilistic formulation for locating and sizing emergency medical service stations. Ann Oper Res 229:813–835. doi:10.1007/s10479-014-1758-4
Acknowledgements
Funding was provided by Ministry of Higher Education and Scientific Research (TN).
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Boujemaa, R., Jebali, A., Hammami, S. et al. A stochastic approach for designing two-tiered emergency medical service systems. Flex Serv Manuf J 30, 123–152 (2018). https://doi.org/10.1007/s10696-017-9286-6
Published:
Issue Date:
DOI: https://doi.org/10.1007/s10696-017-9286-6