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Methods for Solving Nonlinear Equations Used in Evaluating Emergency Vehicle Busy Probabilities

Author

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  • Jeffrey Goldberg

    (University of Arizona, Tucson, Arizona)

  • Ferenc Szidarovszky

    (University of Arizona, Tucson, Arizona)

Abstract

In this paper we present two iterative methods for solving a model to evaluate busy probabilities for Emergency Medical Service (EMS) vehicles. The model considers location dependent service times and is an alternative to the mean service calibration method; a procedure, used with the Hypercube Model, to accommodate travel times and location-dependent service times. We use monotonicity arguments to prove that one iterative method always converges to a solution. A large computational experiment suggests that both methods work satisfactorily in EMS systems with low ambulance busy probabilities and the method that always converges to a solution performs significantly better in EMS systems with high busy probabilities.

Suggested Citation

  • Jeffrey Goldberg & Ferenc Szidarovszky, 1991. "Methods for Solving Nonlinear Equations Used in Evaluating Emergency Vehicle Busy Probabilities," Operations Research, INFORMS, vol. 39(6), pages 903-916, December.
    • Handle: RePEc:inm:oropre:v:39:y:1991:i:6:p:903-916
    DOI: 10.1287/opre.39.6.903
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    Cited by:

    1. Sorensen, Paul & Church, Richard, 2010. "Integrating expected coverage and local reliability for emergency medical services location problems," Socio-Economic Planning Sciences, Elsevier, vol. 44(1), pages 8-18, March.
    2. Iannoni, Ana Paula & Morabito, Reinaldo & Saydam, Cem, 2011. "Optimizing large-scale emergency medical system operations on highways using the hypercube queuing model," Socio-Economic Planning Sciences, Elsevier, vol. 45(3), pages 105-117, September.
    3. Susana Baptista & Rui Oliveira, 2012. "A case study on the application of an approximated hypercube model to emergency medical systems management," Central European Journal of Operations Research, Springer;Slovak Society for Operations Research;Hungarian Operational Research Society;Czech Society for Operations Research;Österr. Gesellschaft für Operations Research (ÖGOR);Slovenian Society Informatika - Section for Operational Research;Croatian Operational Research Society, vol. 20(4), pages 559-581, December.
    4. Sun Hoon Kim & Young Hoon Lee, 2016. "Iterative optimization algorithm with parameter estimation for the ambulance location problem," Health Care Management Science, Springer, vol. 19(4), pages 362-382, December.
    5. Susan Budge & Armann Ingolfsson & Erhan Erkut, 2009. "Technical Note---Approximating Vehicle Dispatch Probabilities for Emergency Service Systems with Location-Specific Service Times and Multiple Units per Location," Operations Research, INFORMS, vol. 57(1), pages 251-255, February.
    6. Marcos Singer & Patricio Donoso & Natalia Jadue, 2004. "Evaluacion De Las Oportunidades De Mejoramiento De La Logistica Directa De Emergencia," Abante, Escuela de Administracion. Pontificia Universidad Católica de Chile., vol. 7(2), pages 179-209.
    7. Marcos Singer & Patricio Donoso & Alan Scheller-Wolf, 2008. "Una Introducción A La Teoría De Colas Aplicada A La Gestión De Servicios," Abante, Escuela de Administracion. Pontificia Universidad Católica de Chile., vol. 11(2), pages 93-120.
    8. Akbar Karimi & Michel Gendreau & Vedat Verter, 2018. "Performance Approximation of Emergency Service Systems with Priorities and Partial Backups," Transportation Science, INFORMS, vol. 52(5), pages 1235-1252, October.
    9. Xueping Li & Zhaoxia Zhao & Xiaoyan Zhu & Tami Wyatt, 2011. "Covering models and optimization techniques for emergency response facility location and planning: a review," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 74(3), pages 281-310, December.
    10. Iannoni, Ana Paula & Morabito, Reinaldo & Saydam, Cem, 2009. "An optimization approach for ambulance location and the districting of the response segments on highways," European Journal of Operational Research, Elsevier, vol. 195(2), pages 528-542, June.

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