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A Markovian Decision Model for Deciding How Many Fire Companies to Dispatch

Author

Listed:
  • Arthur J. Swersey

    (Yale University)

Abstract

In deciding how many units to dispatch to an incoming alarm of unknown seventy the fire department is faced with a dilemma: If too few units are sent initially the extra units needed will be delayed; if too many units are sent, the extra units make a needless response and are temporarily unavailable for subsequent alarms. In this paper, we present a Markovian decision model for this problem. The model leads to a simple decision rule that considers three key factors: (1) the probability that the incoming alarm is serious (the greater the probability the more units dispatched); (2) the expected alarm rate in the area surrounding the alarm (the greater the alarm rate, the fewer units dispatched); and (3) the number of units available in the area surrounding the alarm (the more units available, the more units dispatched). We compare the decision rule to policies commonly in use and find that it results in significant improvements in response time to serious fires.

Suggested Citation

  • Arthur J. Swersey, 1982. "A Markovian Decision Model for Deciding How Many Fire Companies to Dispatch," Management Science, INFORMS, vol. 28(4), pages 352-365, April.
    • Handle: RePEc:inm:ormnsc:v:28:y:1982:i:4:p:352-365
    DOI: 10.1287/mnsc.28.4.352
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    Cited by:

    1. 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.
    2. 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.
    3. Adam Behrendt & Vineet M. Payyappalli & Jun Zhuang, 2019. "Modeling the Cost Effectiveness of Fire Protection Resource Allocation in the United States: Models and a 1980–2014 Case Study," Risk Analysis, John Wiley & Sons, vol. 39(6), pages 1358-1381, June.
    4. 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.
    5. 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.
    6. Laura A. McLay & Maria E. Mayorga, 2013. "A Dispatching Model for Server-to-Customer Systems That Balances Efficiency and Equity," Manufacturing & Service Operations Management, INFORMS, vol. 15(2), pages 205-220, May.
    7. Wang, Qingyi & Reed, Ashley & Nie, Xiaofeng, 2022. "Joint initial dispatching of official responders and registered volunteers during catastrophic mass-casualty incidents," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 159(C).
    8. Drent, Collin & Keizer, Minou Olde & Houtum, Geert-Jan van, 2020. "Dynamic dispatching and repositioning policies for fast-response service networks," European Journal of Operational Research, Elsevier, vol. 285(2), pages 583-598.
    9. 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.
    10. 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.
    11. Sardar Ansari & Laura Albert McLay & Maria E. Mayorga, 2017. "A Maximum Expected Covering Problem for District Design," Transportation Science, INFORMS, vol. 51(1), pages 376-390, February.
    12. Robbins, Matthew J. & Jenkins, Phillip R. & Bastian, Nathaniel D. & Lunday, Brian J., 2020. "Approximate dynamic programming for the aeromedical evacuation dispatching problem: Value function approximation utilizing multiple level aggregation," Omega, Elsevier, vol. 91(C).

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