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Square Root Laws for Fire Engine Response Distances

Author

Listed:
  • Peter Kolesar

    (The New York City-RAND Institute)

  • Edward H. Blum

    (The New York City-RAND Institute)

Abstract

An inverse square-root function is developed for the relation between average response distance and the number of locations at which response units are stationed in a region. Analysis of theoretical models, simulation data, and empirical measurements are used to confirm the square-root model. The square-root response distance model is combined with response distance--response time relations to resolve decision problems important to the management of urban fire departments. The results can be used to find optimal resource allocations given resource constraints and response time standards, or to describe the response time consequences of proposed allocation plans.

Suggested Citation

  • Peter Kolesar & Edward H. Blum, 1973. "Square Root Laws for Fire Engine Response Distances," Management Science, INFORMS, vol. 19(12), pages 1368-1378, August.
    • Handle: RePEc:inm:ormnsc:v:19:y:1973:i:12:p:1368-1378
    DOI: 10.1287/mnsc.19.12.1368
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    Cited by:

    1. Benjamin M. Taylor, 2017. "Spatial modelling of emergency service response times," Journal of the Royal Statistical Society Series A, Royal Statistical Society, vol. 180(2), pages 433-453, February.
    2. Stijn Ferrari & Frank Verboven & Hans Degryse, 2010. "Investment and Usage of New Technologies: Evidence from a Shared ATM Network," American Economic Review, American Economic Association, vol. 100(3), pages 1046-1079, June.
    3. Linda V. Green & Peter J. Kolesar, 2004. "ANNIVERSARY ARTICLE: Improving Emergency Responsiveness with Management Science," Management Science, INFORMS, vol. 50(8), pages 1001-1014, August.
    4. Alfonso J. Pedraza-Martinez & Sameer Hasija & Luk N. Van Wassenhove, 2020. "Fleet Coordination in Decentralized Humanitarian Operations Funded by Earmarked Donations," Operations Research, INFORMS, vol. 68(4), pages 984-999, July.
    5. Rettke, Aaron J. & Robbins, Matthew J. & Lunday, Brian J., 2016. "Approximate dynamic programming for the dispatch of military medical evacuation assets," European Journal of Operational Research, Elsevier, vol. 254(3), pages 824-839.
    6. R B Van der Meer & J Quigley & J E Storbeck, 2005. "Using regression analysis to model the performance of UK Coastguard centres," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 56(6), pages 630-641, June.
    7. Peter J. Kolesar, 2012. "OM Forum --Some Lessons on Operations Management Model Implementation Drawn from the RAND Fire Project," Manufacturing & Service Operations Management, INFORMS, vol. 14(1), pages 1-6, January.
    8. P. Daniel Wright & Matthew J. Liberatore & Robert L. Nydick, 2006. "A Survey of Operations Research Models and Applications in Homeland Security," Interfaces, INFORMS, vol. 36(6), pages 514-529, December.
    9. Dmitrii Usanov & G.A. Guido Legemaate & Peter M. van de Ven & Rob D. van der Mei, 2019. "Fire truck relocation during major incidents," Naval Research Logistics (NRL), John Wiley & Sons, vol. 66(2), pages 105-122, March.
    10. Patrick Sun, 2014. "Quality Competition in Mobile Telecommunications: Evidence from Connecticut," Working Papers 14-05, NET Institute.
    11. Pavan, Giulia, 2017. "Green Car Adoption and the Supply of Alternative Fuels," TSE Working Papers 17-875, Toulouse School of Economics (TSE).
    12. Md Shahab Uddin & Pennung Warnitchai, 2020. "Decision support for infrastructure planning: a comprehensive location–allocation model for fire station in complex urban system," Natural Hazards: Journal of the International Society for the Prevention and Mitigation of Natural Hazards, Springer;International Society for the Prevention and Mitigation of Natural Hazards, vol. 102(3), pages 1475-1496, July.
    13. N C Simpson & P G Hancock, 2009. "Fifty years of operational research and emergency response," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 60(1), pages 126-139, May.
    14. Pieter L. van den Berg & Guido A. G. Legemaate & Rob D. van der Mei, 2017. "Increasing the Responsiveness of Firefighter Services by Relocating Base Stations in Amsterdam," Interfaces, INFORMS, vol. 47(4), pages 352-361, August.
    15. Nurski, Laura & Verboven, Frank, 2014. "Incumbency advantages, distribution networks and exclusivity — Evidence from the European car markets," International Journal of Industrial Organization, Elsevier, vol. 34(C), pages 75-79.
    16. Langevin, André & Mbaraga, Pontien & Campbell, James F., 1996. "Continuous approximation models in freight distribution: An overview," Transportation Research Part B: Methodological, Elsevier, vol. 30(3), pages 163-188, June.

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