On Designing a Fire Emergency Vehicle Fleet

References

• Aringhieri R, Bruni ME, Khodaparasti S, Van Essen JT (2017) Emergency medical services and beyond: Addressing new challenges through a wide literature review. Comput. Oper. Res. 78:349–368.Crossref, Google Scholar
• Aumann RJ, Hart S (1986) Bi-convexity and bi-martingales. Israel J. Math. 54(2):159–180.Crossref, Google Scholar
• Baron O, Berman O, Kim S, Krass D (2009) Ensuring feasibility in location problems with stochastic demands and congestion. IIE Trans. 41(5):467–481.Crossref, Google Scholar
• Bélanger V, Ruiz A, Soriano P (2019) Recent optimization models and trends in location, relocation, and dispatching of emergency medical vehicles. Eur. J. Oper. Res. 272(1):1–23.Crossref, Google Scholar
• Bell CE, Allen D (1969) Optimal planning of an emergency ambulance service. Socioeconom. Planning Sci. 3(2):95–101.Crossref, Google Scholar
• Berman O, Hajizadeh I, Krass D (2013) The maximum covering problem with travel time uncertainty. IIE Trans. 45(1):81–96.Crossref, Google Scholar
• Berman O, Hajizadeh I, Krass D, Rahimi-Vahed A (2018) Reconfiguring a set of coverage-providing facilities under travel time uncertainty. Socioeconom. Planning Sci. 62(C):1–12.Google Scholar
• Boutilier JJ, Chan TC (2020) Ambulance emergency response optimization in developing countries. Oper. Res. 68(5):1315–1334.Link, Google Scholar
• Box GE, Jenkins GM, Reinsel GC (2016) Time Series Analysis: Forecasting and Control, 4th ed. (Wiley, Hoboken, NJ).Google Scholar
• Brushlinsky N, Ahrens M, Sokolov S, Wagner P (2016) World fire statistics. Report, Center of Fire Statistics, Geneva, Switzerland.Google Scholar
• Budge S, Ingolfsson A, Zerom D (2010) Empirical analysis of ambulance travel times: The case of Calgary emergency medical services. Management Sci. 56(4):716–723.Link, Google Scholar
• Buzacott JA, Shanthikumar JG (1993) Stochastic Models of Manufacturing Systems, vol. 4 (Prentice Hall, Englewood Cliffs, NJ).Google Scholar
• Carter GM, Chaiken JM, Ignall E (1972) Response areas for two emergency units. Oper. Res. 20(3):571–594.Link, Google Scholar
• Chong KC, Henderson SG, Lewis ME (2016) The vehicle mix decision in emergency medical service systems. Manufacturing Service Oper. Management 18(3):347–360.Link, Google Scholar
• City of Toronto (2025) Open data portal. Accessed March 30, 2025, https://open.toronto.ca/.Google Scholar
• Cohn AD (2005) Mutual aid: Intergovernmental agreements for emergency preparedness and response. The Urban Lawyer 37(1):1–51.Google Scholar
• Davoudpour H, Mortaz E, Hosseinijou S (2014) A new probabilistic coverage model for ambulances deployment with hypercube queuing approach. Internat. J. Adv. Manufacturing Tech. 70(5–8):1157–1168.Crossref, Google Scholar
• Department of Health and Social Care (2019) The handbook to the NHS constitution: For England GOV.UK (January 24), https://www.gov.uk/government/publications/supplements-to-the-nhs-constitution-for-england/the-handbook-to-the-nhs-constitution-for-england#overview.Google Scholar
• Eaton DJ, Daskin MS, Simmons D, Bulloch B, Jansma G (1985) Determining emergency medical service vehicle deployment in Austin, Texas. Interfaces 15(1):96–108.Link, Google Scholar
• Fitch J (2005) Response times: Myths, measurement & management. J. Emergency Medical Services 30(9):47.Google Scholar
• Fitzsimmons JA (1973) A methodology for emergency ambulance deployment. Management Sci. 19(6):627–636.Link, Google Scholar
• Garrido RA, Lamas P, Pino FJ (2015) A stochastic programming approach for floods emergency logistics. Transportation Res. Part E Logist. Transportation Rev. 75:18–31.Crossref, Google Scholar
• Ghobadi M, Arkat J, Tavakkoli-Moghaddam R (2019) Hypercube queuing models in emergency service systems: A state-of-the-art review. Sci. Iranica 26(2):909–931.Google Scholar
• Gorski J, Pfeuffer F, Klamroth K (2007) Biconvex sets and optimization with biconvex functions: A survey and extensions. Math. Methods Oper. Res. 66(3):373–407.Crossref, Google Scholar
• Greene WH (2018) Econometric Analysis, 8th ed. (Pearson Education, Harlow, UK).Google Scholar
• Gupta V, Harchol-Balter M, Dai J, Zwart B (2010) On the inapproximability of m/g/k: Why two moments of job size distribution are not enough. Queueing Systems 64(1):5–48.Crossref, Google Scholar
• Gurvich I, Whitt W (2009) Queue-and-idleness-ratio controls in many-server service systems. Math. Oper. Res. 34(2):363–396.Link, Google Scholar
• Haghani A, Yang S (2007) Real-time emergency response fleet deployment: Concepts, systems, simulation & case studies. Golden B, Raghavan S, Wasil E, eds. Dynamic Fleet Management (Springer, Boston), 133–162.Crossref, Google Scholar
• Home Office (2022) Detailed analysis of response times to fires attended by fire and rescue services, England: April 2021 to March 2022. GOV.UK (December 15), https://www.gov.uk/government/statistics/detailed-analysis-of-response-times-to-fires-attended-by-fire-and-rescue-services-england-april-2021-to-march-2022?utm_source=chatgpt.com.Google Scholar
• Hua C, Swersey AJ (2022) Cross-trained fire-medics respond to medical calls and fire incidents: A fast algorithm for a three-state spatial queuing problem. Manufacturing Service Oper. Management 24(6):3177–3192.Link, Google Scholar
• Hua C, Wang T, Zhang J, Zhou Z (2023) Near-optimal dispatch policies for emergency medical services. Preprint, submitted March 12, https://dx.doi.org/10.2139/ssrn.4386239.Google Scholar
• Ingolfsson A (2013) EMS planning and management. Zaric GS, ed. Operations Research and Health Care Policy, International Series in Operations Research & Management Science (Springer, Cham, Switzerland), 105–128.Crossref, Google Scholar
• Karimi A, Gendreau M, Verter V (2018) Performance approximation of emergency service systems with priorities and partial backups. Transportation Sci. 52(5):1235–1252.Link, Google Scholar
• Larson R (1974) A hypercube queuing model for facility location and redistricting in urban emergency services. Comput. Oper. Res. 1(1):67–95.Crossref, Google Scholar
• Larson RC (1975) Approximating the performance of urban emergency service systems. Oper. Res. 23(5):845–868.Link, Google Scholar
• Lovrić M, ed. (2011) International Encyclopedia of Statistical Science (Springer, Berlin).Crossref, Google Scholar
• Mandelbaum A, Stolyar AL (2004) Scheduling flexible servers with convex delay costs: Heavy-traffic optimality of the generalized cμ-rule. Oper. Res. 52(6):836–855.Link, Google Scholar
• Marianov V (2017) Location models for emergency service applications. INFORMS Tutorial in Operations Research (INFORMS, Catonsville, MD), 237–262.Link, Google Scholar
• Moreno A, Alem D, Ferreira D (2016) Heuristic approaches for the multiperiod location-transportation problem with reuse of vehicles in emergency logistics. Comput. Oper. Res. 69:79–96. Crossref, Google Scholar
• Nasrollahzadeh AA, Khademi A, Mayorga ME (2018) Real-time ambulance dispatching and relocation. Manufacturing Service Oper. Management 20(3):467–480.Link, Google Scholar
• National Fire Information Database (2020) Fire loss in Canada during 2019. Report, Statistics Canada, Ottawa.Google Scholar
• National Fire Protection Association (2010) NFPA 1710: Standard for the organization and deployment of fire suppression operations, emergency medical operations, and special operations to the public by career fire departments. Technical Report NFPA 1710, National Fire Protection Association, Quincy, MA.Google Scholar
• National Fire Protection Association (2020) U.S. fire department profile: 2018. Accessed March 5, 2023, https://www.nfpa.org/codes-and-standards/all-codes-and-standards/list-of-codes-and- standards/detail?code=1710A.Google Scholar
• Newell G (1966) The m/g/∞ queue. SIAM J. Appl. Math. 14(1):86–88.Crossref, Google Scholar
• Nicholson WC (2002) Legal issues in emergency response to terrorism incidents involving hazardous materials: The hazardous waste operations and emergency response (Hazwoper) standard, standard operating procedures, mutual aid and the incident management system. Widener Law Sympos. J. 9:295.Google Scholar
• NY Times (2024) Firefighters and traffic data in NYC. Accessed January 26, 2024, https://www.nytimes.com/2024/01/26/nyregion/newyorktoday/firefighters-traffic-data-nyc.html.Google Scholar
• Özdamar L, Ekinci E, Küçükyazici B (2004) Emergency logistics planning in natural disasters. Ann. Oper. Res. 129(1–4):217–245.Crossref, Google Scholar
• Reich M (2012) The offered-load process: Modeling, inference and applications. PhD thesis, Faculty of Industrial Engineering and Management, Technion-Israel Institute of Technology, Haifa, Israel.Google Scholar
• Reuter-Oppermann M, van den Berg PL, Vile JL (2017) Logistics for emergency medical service systems. Health Systems 6(3):187–208.Crossref, Google Scholar
• Ríos-Mercado R (2020) Optimal Districting and Territory Design, International Series in Operations Research & Management Science (Springer International Publishing, Cham, Switzerland).Google Scholar
• Robinne FN, Burns J, Kant P, Flannigan M, Kleine M, de Groot B, Wotton D (2018) Global fire challenges in a warming world. IUFRO Occasional Paper No. 32. International Union of Forest Research Organizations, Vienna, Austria.Google Scholar
• Scott DW, Factor LE, Gorry GA (1978) Predicting the response time of an urban ambulance system. Health Services Res. 13(4):404.Google Scholar
• Southwick L Jr, Butler RJ (1985) Fire department demand and supply in large cities. Appl. Econom. 17(6):1043–1064.Crossref, Google Scholar
• Sudtachat K, Mayorga ME, McLay LA (2014) Recommendations for dispatching emergency vehicles under multitiered response via simulation. Internat. Trans. Oper. Res. 21(4):581–617.Crossref, Google Scholar
• Swersey AJ (1994) The deployment of police, fire, and emergency medical units. Pollock SM, Rothkopf MH, Barnett A, eds. Handbooks in Operations Research and Management Science, Public Sector Operations Research, vol. 6 (Elsevier, Amsterdam), 151–200.Google Scholar
• Toronto Fire Services (2021) Annual report. Toronto Fire Services, https://www.toronto.ca/wp-content/uploads/2020/12/8d66-TFSAnnualReport-Web-AODA-5-RS1.pdf.Google Scholar
• Toronto Fire Services (2024) Toronto fire services annual report 2024. Accessed March 8, 2025, https://www.toronto.ca/wp-content/uploads/2024/06/9764-24-00134-Toronto-Fire-Ann-Report-2024-June5-AODA-4-PAC1-2-Dot-op-Rot-FPspread-3.pdf.Google Scholar
• Ünlüyurt T, Tunçer Y (2016) Estimating the performance of emergency medical service location models via discrete event simulation. Comput. Industrial Engrg. 102:467–475.Crossref, Google Scholar
• U.S. Fire Administration and National Fire Data Center (2006) Structure fire response times. Topical Fire Research Series, vol. 5, no 7 (U.S. Fire Administration, Emmitsburg, MD), https://apps.usfa.fema.gov/downloads/pdf/statistics/v5i7.pdf.Google Scholar
• Whitt W (1983) Comparison conjectures about the m/g/s queue. Oper. Res. Lett. 2(5):203–209.Crossref, Google Scholar
• Whitt W (2013) OM Forum—Offered load analysis for staffing. Manufacturing Service Oper. Management 15(2):166–169.Link, Google Scholar
• Worthington D, Utley M, Suen D (2020) Infinite-server queueing models of demand in healthcare: A review of applications and ideas for further work. J. Oper. Res. Soc. 71(8):1145–1160.Crossref, Google Scholar
• Yoon S, Albert LA, White VM (2021) A stochastic programming approach for locating and dispatching two types of ambulances. Transportation Sci. 55(2):275–296.Link, Google Scholar
• Zhang BO, Peng JIN, Li S (2017) Covering location problem of emergency service facilities in an uncertain environment. Appl. Math. Model. 51(4):429–447. Crossref, Google Scholar
• Zhang B, Li H, Li S, Peng J (2018) Sustainable multi-depot emergency facilities location-routing problem with uncertain information. Appl. Math. Comput. 333(C):506–520.Crossref, Google Scholar