Multi-objective optimization of ambulance location in Antofagasta, Chile
Abstract
In this paper, we solved an ambulance location problem with a multi-objective framework considering the case of the study of Emergency Medical Service (EMS) of Antofagasta (Chile). Nowadays, in Antofagasta, the ambulances are located in bases that are not necessarily the optimal location achieving an estimated 67% of coverage under the 8 min not meeting the requirements dictated by the Chilean Ministry of Health. We used a multi-objective model considering mean response time, maximum response time, and the demand not covered. The model is solved using an iterative ε-constraint method to generate a Pareto set of efficient solutions. We considered historical data from the years 2015 and 2016 to generate the demand and emergency nodes with a clustering algorithm. The results show improvements on all criteria of the multi-objective model, where we highlight a potential increment on coverage within 8 min from 67 to 99%. In order to test the new policy in a real setting, a pilot plan is proposed, which reaches 89% of coverage within 8 min.
Keyword : ambulance location, multi-objective optimization, multi-criteria decision-making, emergency medical service, Chile
How to Cite
Olivos, C., & Caceres, H. (2022). Multi-objective optimization of ambulance location in Antofagasta, Chile. Transport, 37(3), 177–189. https://doi.org/10.3846/transport.2022.17073
This work is licensed under a Creative Commons Attribution 4.0 International License.
References
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Alp, O., Erkut, E.; Drezner, Z. 2003. An efficient genetic algorithm for the p-median problem, Annals of Operations Research 122(1–4): 21–42. https://doi.org/10.1023/A:1026130003508
Bélanger, V.; Ruiz, A.; Soriano, P. 2019. Recent optimization models and trends in location, relocation, and dispatching of emergency medical vehicles, European Journal of Operational Research 272(1): 1–23. https://doi.org/10.1016/j.ejor.2018.02.055
Blackwell, T. H.; Kaufman, J. S. 2002. Response time effectiveness: comparison of response time and survival in an urban emergency medical services system, Academic Emergency Medicine 9(4): 288–295. https://doi.org/10.1197/aemj.9.4.288
Brotcorne, L.; Laporte, G.; Semet, F. 2003. Ambulance location and relocation models, European Journal of Operational Research 147(3): 451–463. https://doi.org/10.1016/S0377-2217(02)00364-8
Caccetta, L.; Dzator, M. 2015. Heuristic methods for locating emergency facilities, MODSIM 05: International Congress on Modelling and Simulation: Advances and Applications for Management and Decision Making, 12–15 December 2005, Melbourne, Australia, 1744–1750. Available from Internet: https://www.mssanz.org.au/modsim05/papers/caccetta_2.pdf
Calik, H.; Labbé, M.; Yaman, H. 2015. p-center problems, in G. Laporte, S. Nickel, F. Saldanha da Gama (Eds.). Location Science, 79–92. https://doi.org/10.1007/978-3-319-13111-5_4
Carson, Y. M.; Batta, R. 1990. Locating an ambulance on the Amherst Campus of the State University of New York at Buffalo, Interfaces 20(5): 43–49. https://doi.org/10.1287/inte.20.5.43
Chamandoust, H.; Derakhshan, G.; Hakimi, S. M.; Bahramara, S. 2020. Tri-objective scheduling of residential smart electrical distribution grids with optimal joint of responsive loads with renewable energy sources, Journal of Energy Storage 27: 101112. https://doi.org/10.1016/j.est.2019.101112
Church, R. L.; ReVelle, C. 1974. The maximal covering location problem, Papers of the Regional Science Association 32: 101–118. https://doi.org/10.1007/BF01942293
Church, R. L.; ReVelle, C. S. 1976. Theoretical and computational links between the p-median, location set-covering, and the maximal covering location problem, Geographical Analysis 8(4): 406–415. https://doi.org/10.1111/j.1538-4632.1976.tb00547.x
De Maio, V. J.; Stiell, I. G.; Wells, G. A.; Spaite, D. W. 2003. Optimal defibrillation response intervals for maximum out-of-hospital cardiac arrest survival rates, Annals of Emergency Medicine 42(2): 242–250. https://doi.org/10.1067/mem.2003.266
Dibene, J. C.; Maldonado, Y.; Vera, C.; De Oliveira, M.; Trujillo, L.; Schütze, O. 2017. Optimizing the location of ambulances in Tijuana, Mexico, Computers in Biology and Medicine 80: 107–115. https://doi.org/10.1016/j.compbiomed.2016.11.016
Dzator, M.; Dzator, J. 2013. An effective heuristic for the p-median problem with application to ambulance location, Opsearch 50(1): 60–74. https://doi.org/10.1007/s12597-012-0098-x
Eaton, D. J.; Sánchez, H. M.; Lantingua, R. R.; Morgan, J. 1986. Determining ambulance deployment in Santo Domingo, Dominican Republic, Journal of the Operational Research Society 37(2): 113–126. https://doi.org/10.2307/2582705
EMS World. 2004. EMS response time standards, EMS World, April 2004. Available from Internet: https://www.emsworld.com/article/10324786/ems-response-time-standards
Enayati, S.; Mayorga, M. E.; Rajagopalan, H. K.; Saydam, C. 2018. Real-time ambulance redeployment approach to improve service coverage with fair and restricted workload for EMS providers, Omega 79: 67–80. https://doi.org/10.1016/j.omega.2017.08.001
Erkut, E.; Ingolfsson, A.; Erdoğan, G. 2008. Ambulance location for maximum survival, Naval Research Logistics 55(1): 42–58. https://doi.org/10.1002/nav.20267
Fahimnia, B.; Jabbarzadeh, A.; Ghavamifar, A.; Bell, M. 2017. Supply chain design for efficient and effective blood supply in disasters, International Journal of Production Economics 183: 700–709. https://doi.org/10.1016/j.ijpe.2015.11.007
Fetzer, J.; Caceres, H.; He, Q.; Batta, R. 2018. A multi-objective optimization approach to the location of road weather information system in New York State, Journal of Intelligent Transportation Systems: Technology, Planning, and Operations 22(6): 503–516. https://doi.org/10.1080/15472450.2018.1439389
Goldberg, J. B. 2004. Operations research models for the deployment of emergency services vehicles, EMS Management Journal 1(1): 20–39.
Google LLC. 2014. Geocoding API. Google Maps Platform. Available from Internet: https://developers.google.com/maps/documentation/geocoding/start
Government of Ontario. 2022. Ambulance Act. Ontario Regulation 257/00. Ontario, Canada. Available from Internet: https://www.ontario.ca/laws/regulation/000257
Haghi, M.; Fatemi Ghomi, S. M. T.; Jolai, F. 2017. Developing a robust multi-objective model for pre/post disaster times under uncertainty in demand and resource, Journal of Cleaner Production 154: 188–202. https://doi.org/10.1016/j.jclepro.2017.03.102
Hakimi, S. L. 1964. Optimum locations of switching centers and the absolute centers and medians of a graph, Operations Research 12(3): 450–459. https://doi.org/10.1287/opre.12.3.450
Harewood, S. I. 2002. Emergency ambulance deployment in Barbados: a multi-objective approach, Journal of the Operational Research Society 53(2): 185–192. https://doi.org/10.1057/sj/jors/2601250
Heath, G.; Radcliffe, J. 2010. Exploring the utility of current performance measures for changing roles and practices of ambulance paramedics, Public Money & Management 30(3): 151–158. https://doi.org/10.1080/09540961003794287
Heath, G.; Radcliffe, J. 2007. Performance Measurement and the English Ambulance, Public Money & Management 27(3): 223–228. https://doi.org/10.1111/j.1467-9302.2007.00583.x
INE. 2017. Censo 2017. Instituto Nacional de Estadísticas (INE), Santiago, Chile. Available from Internet: http://www.censo2017.cl
Jaszkiewicz, A.; Branke, J. 2008. Interactive multiobjective evolutionary algorithms, Lecture Notes in Computer Science 5252: 179–193. https://doi.org/10.1007/978-3-540-88908-3_7
Karatas, M.; Yakıcı, E. 2018. An iterative solution approach to a multi-objective facility location problem, Applied Soft Computing 62: 272–287. https://doi.org/10.1016/j.asoc.2017.10.035
Kariv, O.; Hakimi, S. L. 1979. An algorithmic approach to network location problems. I: the p-centers, SIAM Journal on Applied Mathematics 37(3): 513–538. https://doi.org/10.1137/0137040
Knight, V. A.; Harper, P. R.; Smith, L. 2012. Ambulance allocation for maximal survival with heterogeneous outcome measures, Omega 40(6): 918–926. https://doi.org/10.1016/j.omega.2012.02.003
Lerner, E. B.; Moscati, R. M. 2001. The golden hour: scientific fact or medical “urban legend”?, Academic Emergency Medicine 8(7): 758–760. https://doi.org/10.1111/j.1553-2712.2001.tb00201.x
Li, X.; Zhao, Z.; Zhu, X.; Wyatt, T. 2011. Covering models and optimization techniques for emergency response facility location and planning: a review, Mathematical Methods of Operations Research 74(3): 281–310. https://doi.org/10.1007/s00186-011-0363-4
Luxen, D.; Vetter, C. 2011. Real-time routing with OpenStreetMap data, in GIS’11: Proceedings of the 19th ACM SIGSPATIAL International Conference on Advances in Geographic Information Systems, 1–4 November 2011, Chicago, IL, US, 513–516. https://doi.org/10.1145/2093973.2094062
Mavrotas, G. 2009. Effective implementation of the ε-constraint method in multi-objective mathematical programming problems, Applied Mathematics and Computation 213(2): 455–465. https://doi.org/10.1016/j.amc.2009.03.037
Milosavljević, M.; Bursać, M.; Tričković, G. 2018. Selection of the railroad container terminal in Serbia based on multi criteria decision-making methods, Decision Making: Applications in Management and Engineering 1(2): 1–15.
Nasrollahzadeh, A. A.; Khademi, A.; Mayorga, M. E. 2018. Real-time ambulance dispatching and relocation, Manufacturing and Service Operations Management 20(3): 467–480. https://doi.org/10.1287/msom.2017.0649
Newgard, C. D.; Schmicker, R. H.; Hedges, J. R.; Trickett, J. P.; Davis, D. P.; Bulger, E. M.; Aufderheide, T. P.; Minei, J. P.; Hata, J. S.; Gubler, K. D.; Brown, T. B.; Yelle, J.-D.; Bardarson, B.; Nichol, G. 2010. Emergency medical services intervals and survival in trauma: assessment of the “golden hour” in a North American prospective cohort, Annals of Emergency Medicine 55(3): 235–246. https://doi.org/10.1016/j.annemergmed.2009.07.024
O’Keeffe, C.; Nicholl, J.; Turner, J.; Goodacre, S. 2011. Role of ambulance response times in the survival of patients with out-of-hospital cardiac arrest, Emergency Medicine Journal 28(8): 703–706. https://doi.org/10.1136/emj.2009.086363
Pedregosa, F.; Varoquaux, G.; Gramfort, A.; Michel, V.; Thirion, B.; Grisel, O.; Blondel, M.; Prettenhofer, P.; Weiss, R.; Dubourg, V.; Vanderplas, J.; Passos, A.; Cournapeau, D.; Brucher, M.; Perrot, M.; Duchesnay, E. 2011. Scikit-learn: machine learning in Python, Journal of Machine Learning Research 12: 2825–2830. Available from Internet: https://www.jmlr.org/papers/volume12/pedregosa11a/pedregosa11a.pdf
Pons, P. T.; Haukoos, J. S.; Bludworth, W.; Cribley, T.; Pons, K. A.; Markovchick, V. J. 2005. Paramedic response time: does it affect patient survival?, Academic Emergency Medicine 12(7): 594–600. https://doi.org/10.1197/j.aem.2005.02.013
Pons, P. T.; Markovchick, V. J. 2002. Eight minutes or less: does the ambulance response time guideline impact trauma patient outcome?, Journal of Emergency Medicine 23(1): 43–48. https://doi.org/10.1016/S0736-4679(02)00460-2
Renkiewicz, G. K.; Hubble, M. W.; Wesley, D. R.; Dorian, P. A.; Losh, M. J.; Swain, R.; Taylor, S. E. 2014. Probability of a shockable presenting rhythm as a function of EMS response time, Prehospital Emergency Care 18(2): 224–230. https://doi.org/10.3109/10903127.2013.851308
ReVelle, C. S.; Swain, R. W. 1970. Central facilities location, Geographical Analysis 2(1): 30–42. https://doi.org/10.1111/j.1538-4632.1970.tb00142.x
Rikalović, A.; Soares, G. A.; Ignjatić, J. 2018. Spatial analysis of logistics center location: a comprehensive approach, Decision Making: Applications in Management and Engineering 1(1): 38–50.
SdRA. 2018. Resolución Exenta 198. Subsecretaría de Redes Asistenciales (SdRA) Santiago, Chile. Available from Internet: https://www.scribd.com/document/382207593/Indicadores-Minimos-Prehospitalarios-2018-1185306 (in Spanish).
Serra, D.; Marianov, V. 1998. The p-median problem in a changing network: the case of Barcelona, Location Science 6(1–4): 383–394. https://doi.org/10.1016/S0966-8349(98)00049-7
Singer, M.; Donoso, P. 2008. Assessing an ambulance service with queuing theory, Computers & Operations Research 35(8): 2549–2560. https://doi.org/10.1016/j.cor.2006.12.005
Subsecretaría de Redes Asistenciales. 2018. Aprueba Conjunto de Indicadores Mínimos Pre Hospitalarios (SAMU). Santiago, Chile. (in Spanish).
Talwar, M. 2002. Location of rescue helicopters in South Tyrol, in 37th Annual ORSNZ Conference, 29–30 November 2022, Auckland, New Zealand, 1–10. Available from Internet: https://orsnz.org.nz/conf37/Papers/Talwar.pdf
Toregas, C.; Swain, R.; ReVelle, C.; Bergman, L. 1971. The location of emergency service facilities, Operations Research 19(6): 1363–1373. https://doi.org/10.1287/opre.19.6.1363
Valencia-Nuñez, E. R.; López, H. V. M.; Cevallos-Torres, L. J. 2018. Probabilistic model for managing the arrival times of pre-hospital ambulances based on their geographical location (GIS), in 2018 International Conference on eDemocracy & eGovernment (ICEDEG), 4–6 April 2018, Ambato, Ecuador, 103–109. https://doi.org/10.1109/ICEDEG.2018.8372348
Van Buuren, M.; Jagtenberg, C.; Van Barneveld, T.; Van Der Mei, R.; Bhulai, S. 2018. Ambulance dispatch center pilots proactive relocation policies to enhance effectiveness, Interfaces 48(3): 235–246. https://doi.org/10.1287/inte.2017.0936
Alp, O., Erkut, E.; Drezner, Z. 2003. An efficient genetic algorithm for the p-median problem, Annals of Operations Research 122(1–4): 21–42. https://doi.org/10.1023/A:1026130003508
Bélanger, V.; Ruiz, A.; Soriano, P. 2019. Recent optimization models and trends in location, relocation, and dispatching of emergency medical vehicles, European Journal of Operational Research 272(1): 1–23. https://doi.org/10.1016/j.ejor.2018.02.055
Blackwell, T. H.; Kaufman, J. S. 2002. Response time effectiveness: comparison of response time and survival in an urban emergency medical services system, Academic Emergency Medicine 9(4): 288–295. https://doi.org/10.1197/aemj.9.4.288
Brotcorne, L.; Laporte, G.; Semet, F. 2003. Ambulance location and relocation models, European Journal of Operational Research 147(3): 451–463. https://doi.org/10.1016/S0377-2217(02)00364-8
Caccetta, L.; Dzator, M. 2015. Heuristic methods for locating emergency facilities, MODSIM 05: International Congress on Modelling and Simulation: Advances and Applications for Management and Decision Making, 12–15 December 2005, Melbourne, Australia, 1744–1750. Available from Internet: https://www.mssanz.org.au/modsim05/papers/caccetta_2.pdf
Calik, H.; Labbé, M.; Yaman, H. 2015. p-center problems, in G. Laporte, S. Nickel, F. Saldanha da Gama (Eds.). Location Science, 79–92. https://doi.org/10.1007/978-3-319-13111-5_4
Carson, Y. M.; Batta, R. 1990. Locating an ambulance on the Amherst Campus of the State University of New York at Buffalo, Interfaces 20(5): 43–49. https://doi.org/10.1287/inte.20.5.43
Chamandoust, H.; Derakhshan, G.; Hakimi, S. M.; Bahramara, S. 2020. Tri-objective scheduling of residential smart electrical distribution grids with optimal joint of responsive loads with renewable energy sources, Journal of Energy Storage 27: 101112. https://doi.org/10.1016/j.est.2019.101112
Church, R. L.; ReVelle, C. 1974. The maximal covering location problem, Papers of the Regional Science Association 32: 101–118. https://doi.org/10.1007/BF01942293
Church, R. L.; ReVelle, C. S. 1976. Theoretical and computational links between the p-median, location set-covering, and the maximal covering location problem, Geographical Analysis 8(4): 406–415. https://doi.org/10.1111/j.1538-4632.1976.tb00547.x
De Maio, V. J.; Stiell, I. G.; Wells, G. A.; Spaite, D. W. 2003. Optimal defibrillation response intervals for maximum out-of-hospital cardiac arrest survival rates, Annals of Emergency Medicine 42(2): 242–250. https://doi.org/10.1067/mem.2003.266
Dibene, J. C.; Maldonado, Y.; Vera, C.; De Oliveira, M.; Trujillo, L.; Schütze, O. 2017. Optimizing the location of ambulances in Tijuana, Mexico, Computers in Biology and Medicine 80: 107–115. https://doi.org/10.1016/j.compbiomed.2016.11.016
Dzator, M.; Dzator, J. 2013. An effective heuristic for the p-median problem with application to ambulance location, Opsearch 50(1): 60–74. https://doi.org/10.1007/s12597-012-0098-x
Eaton, D. J.; Sánchez, H. M.; Lantingua, R. R.; Morgan, J. 1986. Determining ambulance deployment in Santo Domingo, Dominican Republic, Journal of the Operational Research Society 37(2): 113–126. https://doi.org/10.2307/2582705
EMS World. 2004. EMS response time standards, EMS World, April 2004. Available from Internet: https://www.emsworld.com/article/10324786/ems-response-time-standards
Enayati, S.; Mayorga, M. E.; Rajagopalan, H. K.; Saydam, C. 2018. Real-time ambulance redeployment approach to improve service coverage with fair and restricted workload for EMS providers, Omega 79: 67–80. https://doi.org/10.1016/j.omega.2017.08.001
Erkut, E.; Ingolfsson, A.; Erdoğan, G. 2008. Ambulance location for maximum survival, Naval Research Logistics 55(1): 42–58. https://doi.org/10.1002/nav.20267
Fahimnia, B.; Jabbarzadeh, A.; Ghavamifar, A.; Bell, M. 2017. Supply chain design for efficient and effective blood supply in disasters, International Journal of Production Economics 183: 700–709. https://doi.org/10.1016/j.ijpe.2015.11.007
Fetzer, J.; Caceres, H.; He, Q.; Batta, R. 2018. A multi-objective optimization approach to the location of road weather information system in New York State, Journal of Intelligent Transportation Systems: Technology, Planning, and Operations 22(6): 503–516. https://doi.org/10.1080/15472450.2018.1439389
Goldberg, J. B. 2004. Operations research models for the deployment of emergency services vehicles, EMS Management Journal 1(1): 20–39.
Google LLC. 2014. Geocoding API. Google Maps Platform. Available from Internet: https://developers.google.com/maps/documentation/geocoding/start
Government of Ontario. 2022. Ambulance Act. Ontario Regulation 257/00. Ontario, Canada. Available from Internet: https://www.ontario.ca/laws/regulation/000257
Haghi, M.; Fatemi Ghomi, S. M. T.; Jolai, F. 2017. Developing a robust multi-objective model for pre/post disaster times under uncertainty in demand and resource, Journal of Cleaner Production 154: 188–202. https://doi.org/10.1016/j.jclepro.2017.03.102
Hakimi, S. L. 1964. Optimum locations of switching centers and the absolute centers and medians of a graph, Operations Research 12(3): 450–459. https://doi.org/10.1287/opre.12.3.450
Harewood, S. I. 2002. Emergency ambulance deployment in Barbados: a multi-objective approach, Journal of the Operational Research Society 53(2): 185–192. https://doi.org/10.1057/sj/jors/2601250
Heath, G.; Radcliffe, J. 2010. Exploring the utility of current performance measures for changing roles and practices of ambulance paramedics, Public Money & Management 30(3): 151–158. https://doi.org/10.1080/09540961003794287
Heath, G.; Radcliffe, J. 2007. Performance Measurement and the English Ambulance, Public Money & Management 27(3): 223–228. https://doi.org/10.1111/j.1467-9302.2007.00583.x
INE. 2017. Censo 2017. Instituto Nacional de Estadísticas (INE), Santiago, Chile. Available from Internet: http://www.censo2017.cl
Jaszkiewicz, A.; Branke, J. 2008. Interactive multiobjective evolutionary algorithms, Lecture Notes in Computer Science 5252: 179–193. https://doi.org/10.1007/978-3-540-88908-3_7
Karatas, M.; Yakıcı, E. 2018. An iterative solution approach to a multi-objective facility location problem, Applied Soft Computing 62: 272–287. https://doi.org/10.1016/j.asoc.2017.10.035
Kariv, O.; Hakimi, S. L. 1979. An algorithmic approach to network location problems. I: the p-centers, SIAM Journal on Applied Mathematics 37(3): 513–538. https://doi.org/10.1137/0137040
Knight, V. A.; Harper, P. R.; Smith, L. 2012. Ambulance allocation for maximal survival with heterogeneous outcome measures, Omega 40(6): 918–926. https://doi.org/10.1016/j.omega.2012.02.003
Lerner, E. B.; Moscati, R. M. 2001. The golden hour: scientific fact or medical “urban legend”?, Academic Emergency Medicine 8(7): 758–760. https://doi.org/10.1111/j.1553-2712.2001.tb00201.x
Li, X.; Zhao, Z.; Zhu, X.; Wyatt, T. 2011. Covering models and optimization techniques for emergency response facility location and planning: a review, Mathematical Methods of Operations Research 74(3): 281–310. https://doi.org/10.1007/s00186-011-0363-4
Luxen, D.; Vetter, C. 2011. Real-time routing with OpenStreetMap data, in GIS’11: Proceedings of the 19th ACM SIGSPATIAL International Conference on Advances in Geographic Information Systems, 1–4 November 2011, Chicago, IL, US, 513–516. https://doi.org/10.1145/2093973.2094062
Mavrotas, G. 2009. Effective implementation of the ε-constraint method in multi-objective mathematical programming problems, Applied Mathematics and Computation 213(2): 455–465. https://doi.org/10.1016/j.amc.2009.03.037
Milosavljević, M.; Bursać, M.; Tričković, G. 2018. Selection of the railroad container terminal in Serbia based on multi criteria decision-making methods, Decision Making: Applications in Management and Engineering 1(2): 1–15.
Nasrollahzadeh, A. A.; Khademi, A.; Mayorga, M. E. 2018. Real-time ambulance dispatching and relocation, Manufacturing and Service Operations Management 20(3): 467–480. https://doi.org/10.1287/msom.2017.0649
Newgard, C. D.; Schmicker, R. H.; Hedges, J. R.; Trickett, J. P.; Davis, D. P.; Bulger, E. M.; Aufderheide, T. P.; Minei, J. P.; Hata, J. S.; Gubler, K. D.; Brown, T. B.; Yelle, J.-D.; Bardarson, B.; Nichol, G. 2010. Emergency medical services intervals and survival in trauma: assessment of the “golden hour” in a North American prospective cohort, Annals of Emergency Medicine 55(3): 235–246. https://doi.org/10.1016/j.annemergmed.2009.07.024
O’Keeffe, C.; Nicholl, J.; Turner, J.; Goodacre, S. 2011. Role of ambulance response times in the survival of patients with out-of-hospital cardiac arrest, Emergency Medicine Journal 28(8): 703–706. https://doi.org/10.1136/emj.2009.086363
Pedregosa, F.; Varoquaux, G.; Gramfort, A.; Michel, V.; Thirion, B.; Grisel, O.; Blondel, M.; Prettenhofer, P.; Weiss, R.; Dubourg, V.; Vanderplas, J.; Passos, A.; Cournapeau, D.; Brucher, M.; Perrot, M.; Duchesnay, E. 2011. Scikit-learn: machine learning in Python, Journal of Machine Learning Research 12: 2825–2830. Available from Internet: https://www.jmlr.org/papers/volume12/pedregosa11a/pedregosa11a.pdf
Pons, P. T.; Haukoos, J. S.; Bludworth, W.; Cribley, T.; Pons, K. A.; Markovchick, V. J. 2005. Paramedic response time: does it affect patient survival?, Academic Emergency Medicine 12(7): 594–600. https://doi.org/10.1197/j.aem.2005.02.013
Pons, P. T.; Markovchick, V. J. 2002. Eight minutes or less: does the ambulance response time guideline impact trauma patient outcome?, Journal of Emergency Medicine 23(1): 43–48. https://doi.org/10.1016/S0736-4679(02)00460-2
Renkiewicz, G. K.; Hubble, M. W.; Wesley, D. R.; Dorian, P. A.; Losh, M. J.; Swain, R.; Taylor, S. E. 2014. Probability of a shockable presenting rhythm as a function of EMS response time, Prehospital Emergency Care 18(2): 224–230. https://doi.org/10.3109/10903127.2013.851308
ReVelle, C. S.; Swain, R. W. 1970. Central facilities location, Geographical Analysis 2(1): 30–42. https://doi.org/10.1111/j.1538-4632.1970.tb00142.x
Rikalović, A.; Soares, G. A.; Ignjatić, J. 2018. Spatial analysis of logistics center location: a comprehensive approach, Decision Making: Applications in Management and Engineering 1(1): 38–50.
SdRA. 2018. Resolución Exenta 198. Subsecretaría de Redes Asistenciales (SdRA) Santiago, Chile. Available from Internet: https://www.scribd.com/document/382207593/Indicadores-Minimos-Prehospitalarios-2018-1185306 (in Spanish).
Serra, D.; Marianov, V. 1998. The p-median problem in a changing network: the case of Barcelona, Location Science 6(1–4): 383–394. https://doi.org/10.1016/S0966-8349(98)00049-7
Singer, M.; Donoso, P. 2008. Assessing an ambulance service with queuing theory, Computers & Operations Research 35(8): 2549–2560. https://doi.org/10.1016/j.cor.2006.12.005
Subsecretaría de Redes Asistenciales. 2018. Aprueba Conjunto de Indicadores Mínimos Pre Hospitalarios (SAMU). Santiago, Chile. (in Spanish).
Talwar, M. 2002. Location of rescue helicopters in South Tyrol, in 37th Annual ORSNZ Conference, 29–30 November 2022, Auckland, New Zealand, 1–10. Available from Internet: https://orsnz.org.nz/conf37/Papers/Talwar.pdf
Toregas, C.; Swain, R.; ReVelle, C.; Bergman, L. 1971. The location of emergency service facilities, Operations Research 19(6): 1363–1373. https://doi.org/10.1287/opre.19.6.1363
Valencia-Nuñez, E. R.; López, H. V. M.; Cevallos-Torres, L. J. 2018. Probabilistic model for managing the arrival times of pre-hospital ambulances based on their geographical location (GIS), in 2018 International Conference on eDemocracy & eGovernment (ICEDEG), 4–6 April 2018, Ambato, Ecuador, 103–109. https://doi.org/10.1109/ICEDEG.2018.8372348
Van Buuren, M.; Jagtenberg, C.; Van Barneveld, T.; Van Der Mei, R.; Bhulai, S. 2018. Ambulance dispatch center pilots proactive relocation policies to enhance effectiveness, Interfaces 48(3): 235–246. https://doi.org/10.1287/inte.2017.0936